Merge pull request #141 from jl777/jl777

sync jl777

src/cc/makecclib

@@ -1,2 +1,2 @@
 #!/bin/sh
-gcc -std=c++11 -I../univalue/include -I../cryptoconditions/include -I../cryptoconditions/src -I../cryptoconditions/src/asn -I.. -I. -fPIC -shared -c -o ../libcc.so cclib.cpp
+gcc -std=c++11 -I../secp256k1/include -I../univalue/include -I../cryptoconditions/include -I../cryptoconditions/src -I../cryptoconditions/src/asn -I.. -I. -fPIC -shared -c -o ../libcc.so cclib.cpp

src/cc/rogue/Makefile.in

@@ -128,9 +128,11 @@ MISC     = Makefile.std LICENSE.TXT rogue54.sln rogue54.vcproj rogue.spec \
     
 .c.o:
 	$(CC) $(CFLAGS) $(CPPFLAGS) -c $*.c
-    
+
+#$(RM) rogue.so ; $(CC) -shared -o rogue.so cursesd.c $(OBJS1) $(OBJS2); $(CC) $(CFLAGS) $(LDFLAGS) $(OBJS) $(LIBS) -o $@
+
 $(PROGRAM): $(HDRS) $(OBJS)
-	$(RM) rogue.so ; $(CC) -shared -o rogue.so $(OBJS1) $(OBJS2) -lcurses; $(CC) $(CFLAGS) $(LDFLAGS) $(OBJS) $(LIBS) -o $@
+	$(CC) $(CFLAGS) $(LDFLAGS) $(OBJS) $(LIBS) -o $@
 
 clean:
 	$(RM) $(OBJS1); $(RM) main.$(O) ; $(RM) rogue.so

src/cc/sudoku.cpp

@@ -3049,3 +3049,8 @@ bool sudoku_validate(struct CCcontract_info *cp,int32_t height,Eval *eval,const
     return eval->Invalid("not enough vouts");
 }
 
+#include <secp256k1.h>
+#include <secp256k1_schnorrsig.h>
+#include <secp256k1_musig.h>
+
+

src/cryptoconditions/src/include/secp256k1/src/ecmult_const.h

@@ -1,3 +1,5 @@
+#ifndef ENABLE_MODULE_MUSIG
+
 /**********************************************************************
  * Copyright (c) 2015 Andrew Poelstra                                 *
  * Distributed under the MIT software license, see the accompanying   *
@@ -13,3 +15,25 @@
 static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q);
 
 #endif /* SECP256K1_ECMULT_CONST_H */
+
+#else
+
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_ECMULT_CONST_H
+#define SECP256K1_ECMULT_CONST_H
+
+#include "scalar.h"
+#include "group.h"
+
+/* Here `bits` should be set to the maximum bitlength of the _absolute value_ of `q`, plus
+ * one because we internally sometimes add 2 to the number during the WNAF conversion. */
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q, int bits);
+
+
+#endif
+

src/secp256k1/Makefile.am

@@ -42,6 +42,8 @@ noinst_HEADERS += src/field_5x52_asm_impl.h
 noinst_HEADERS += src/java/org_bitcoin_NativeSecp256k1.h
 noinst_HEADERS += src/java/org_bitcoin_Secp256k1Context.h
 noinst_HEADERS += src/util.h
+noinst_HEADERS += src/scratch.h
+noinst_HEADERS += src/scratch_impl.h
 noinst_HEADERS += src/testrand.h
 noinst_HEADERS += src/testrand_impl.h
 noinst_HEADERS += src/hash.h
@@ -71,7 +73,7 @@ endif
 endif
 
 libsecp256k1_la_SOURCES = src/secp256k1.c
-libsecp256k1_la_CPPFLAGS = -DSECP256K1_BUILD -I$(top_srcdir)/include -I$(top_srcdir)/src $(SECP_INCLUDES)
+libsecp256k1_la_CPPFLAGS = -DENABLE_MODULE_MUSIG -DSECP256K1_BUILD -I$(top_srcdir)/include -I$(top_srcdir)/src $(SECP_INCLUDES)
 libsecp256k1_la_LIBADD = $(JNI_LIB) $(SECP_LIBS) $(COMMON_LIB)
 
 libsecp256k1_jni_la_SOURCES  = src/java/org_bitcoin_NativeSecp256k1.c src/java/org_bitcoin_Secp256k1Context.c
@@ -172,6 +174,11 @@ if ENABLE_MODULE_ECDH
 include src/modules/ecdh/Makefile.am.include
 endif
 
+#if ENABLE_MODULE_MUSIG
+include src/modules/schnorrsig/Makefile.am.include
+include src/modules/musig/Makefile.am.include
+#endif
+
 if ENABLE_MODULE_RECOVERY
 include src/modules/recovery/Makefile.am.include
 endif

src/secp256k1/include/secp256k1.h

@@ -42,6 +42,19 @@ extern "C" {
  */
 typedef struct secp256k1_context_struct secp256k1_context;
 
+/** Opaque data structure that holds rewriteable "scratch space"
+ *
+ *  The purpose of this structure is to replace dynamic memory allocations,
+ *  because we target architectures where this may not be available. It is
+ *  essentially a resizable (within specified parameters) block of bytes,
+ *  which is initially created either by memory allocation or TODO as a pointer
+ *  into some fixed rewritable space.
+ *
+ *  Unlike the context object, this cannot safely be shared between threads
+ *  without additional synchronization logic.
+ */
+typedef struct secp256k1_scratch_space_struct secp256k1_scratch_space;
+
 /** Opaque data structure that holds a parsed and valid public key.
  *
  *  The exact representation of data inside is implementation defined and not

src/secp256k1/include/secp256k1_musig.h

@@ -0,0 +1,432 @@
+#ifndef SECP256K1_MUSIG_H
+#define SECP256K1_MUSIG_H
+
+#include <stdint.h>
+
+/** This module implements a Schnorr-based multi-signature scheme called MuSig
+ * (https://eprint.iacr.org/2018/068.pdf). There's an example C source file in the
+ * module's directory (src/modules/musig/example.c) that demonstrates how it can be
+ * used.
+ */
+
+/** Data structure containing data related to a signing session resulting in a single
+ * signature.
+ *
+ * This structure is not opaque, but it MUST NOT be copied or read or written to it
+ * directly. A signer who is online throughout the whole process and can keep this
+ * structure in memory can use the provided API functions for a safe standard
+ * workflow.
+ *
+ * A signer who goes offline and needs to import/export or save/load this structure
+ * **must** take measures prevent replay attacks wherein an old state is loaded and
+ * the signing protocol forked from that point. One straightforward way to accomplish
+ * this is to attach the output of a monotonic non-resettable counter (hardware
+ * support is needed for this). Increment the counter before each output and
+ * encrypt+sign the entire package. If a package is deserialized with an old counter
+ * state or bad signature it should be rejected.
+ *
+ * Observe that an independent counter is needed for each concurrent signing session
+ * such a device is involved in. To avoid fragility, it is therefore recommended that
+ * any offline signer be usable for only a single session at once.
+ *
+ * Given access to such a counter, its output should be used as (or mixed into) the
+ * session ID to ensure uniqueness.
+ *
+ * Fields:
+ *      combined_pk: MuSig-computed combined public key
+ *        n_signers: Number of signers
+ *          pk_hash: The 32-byte hash of the original public keys
+ *   combined_nonce: Summed combined public nonce (undefined if `nonce_is_set` is false)
+ *     nonce_is_set: Whether the above nonce has been set
+ * nonce_is_negated: If `nonce_is_set`, whether the above nonce was negated after
+ *                   summing the participants' nonces. Needed to ensure the nonce's y
+ *                   coordinate has a quadratic-residue y coordinate
+ *              msg: The 32-byte message (hash) to be signed
+ *       msg_is_set: Whether the above message has been set
+ *  has_secret_data: Whether this session object has a signers' secret data; if this
+ *                   is `false`, it may still be used for verification purposes.
+ *           seckey: If `has_secret_data`, the signer's secret key
+ *         secnonce: If `has_secret_data`, the signer's secret nonce
+ *            nonce: If `has_secret_data`, the signer's public nonce
+ * nonce_commitments_hash: If `has_secret_data` and `nonce_commitments_hash_is_set`,
+ *                   the hash of all signers' commitments
+ * nonce_commitments_hash_is_set: If `has_secret_data`, whether the
+ *                   nonce_commitments_hash has been set
+ */
+typedef struct {
+    secp256k1_pubkey combined_pk;
+    uint32_t n_signers;
+    unsigned char pk_hash[32];
+    secp256k1_pubkey combined_nonce;
+    int nonce_is_set;
+    int nonce_is_negated;
+    unsigned char msg[32];
+    int msg_is_set;
+    int has_secret_data;
+    unsigned char seckey[32];
+    unsigned char secnonce[32];
+    secp256k1_pubkey nonce;
+    unsigned char nonce_commitments_hash[32];
+    int nonce_commitments_hash_is_set;
+} secp256k1_musig_session;
+
+/** Data structure containing data on all signers in a single session.
+ *
+ * The workflow for this structure is as follows:
+ *
+ * 1. This structure is initialized with `musig_session_initialize` or
+ *    `musig_session_initialize_verifier`, which set the `index` field, and zero out
+ *    all other fields. The public session is initialized with the signers'
+ *    nonce_commitments.
+ *
+ * 2. In a non-public session the nonce_commitments are set with the function
+ *    `musig_get_public_nonce`, which also returns the signer's public nonce. This
+ *    ensures that the public nonce is not exposed until all commitments have been
+ *    received.
+ *
+ * 3. Each individual data struct should be updated with `musig_set_nonce` once a
+ *    nonce is available. This function takes a single signer data struct rather than
+ *    an array because it may fail in the case that the provided nonce does not match
+ *    the commitment. In this case, it is desirable to identify the exact party whose
+ *    nonce was inconsistent.
+ *
+ * Fields:
+ *   present: indicates whether the signer's nonce is set
+ *     index: index of the signer in the MuSig key aggregation
+ *     nonce: public nonce, must be a valid curvepoint if the signer is `present`
+ * nonce_commitment: commitment to the nonce, or all-bits zero if a commitment
+ *                   has not yet been set
+ */
+typedef struct {
+    int present;
+    uint32_t index;
+    secp256k1_pubkey nonce;
+    unsigned char nonce_commitment[32];
+} secp256k1_musig_session_signer_data;
+
+/** Opaque data structure that holds a MuSig partial signature.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is however
+ *  guaranteed to be 32 bytes in size, and can be safely copied/moved. If you need
+ *  to convert to a format suitable for storage, transmission, or comparison, use the
+ *  `musig_partial_signature_serialize` and `musig_partial_signature_parse`
+ *  functions.
+ */
+typedef struct {
+    unsigned char data[32];
+} secp256k1_musig_partial_signature;
+
+/** Computes a combined public key and the hash of the given public keys
+ *
+ *  Returns: 1 if the public keys were successfully combined, 0 otherwise
+ *  Args:        ctx: pointer to a context object initialized for verification
+ *                    (cannot be NULL)
+ *           scratch: scratch space used to compute the combined pubkey by
+ *                    multiexponentiation. If NULL, an inefficient algorithm is used.
+ *  Out: combined_pk: the MuSig-combined public key (cannot be NULL)
+ *         pk_hash32: if non-NULL, filled with the 32-byte hash of all input public
+ *                    keys in order to be used in `musig_session_initialize`.
+ *   In:     pubkeys: input array of public keys to combine. The order is important;
+ *                    a different order will result in a different combined public
+ *                    key (cannot be NULL)
+ *         n_pubkeys: length of pubkeys array
+ */
+SECP256K1_API int secp256k1_musig_pubkey_combine(
+    const secp256k1_context* ctx,
+    secp256k1_scratch_space *scratch,
+    secp256k1_pubkey *combined_pk,
+    unsigned char *pk_hash32,
+    const secp256k1_pubkey *pubkeys,
+    size_t n_pubkeys
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(5);
+
+/** Initializes a signing session for a signer
+ *
+ *  Returns: 1: session is successfully initialized
+ *           0: session could not be initialized: secret key or secret nonce overflow
+ *  Args:         ctx: pointer to a context object, initialized for signing (cannot
+ *                     be NULL)
+ *  Out:      session: the session structure to initialize (cannot be NULL)
+ *            signers: an array of signers' data to be initialized. Array length must
+ *                     equal to `n_signers` (cannot be NULL)
+ * nonce_commitment32: filled with a 32-byte commitment to the generated nonce
+ *                     (cannot be NULL)
+ *  In:  session_id32: a *unique* 32-byte ID to assign to this session (cannot be
+ *                     NULL). If a non-unique session_id32 was given then a partial
+ *                     signature will LEAK THE SECRET KEY.
+ *              msg32: the 32-byte message to be signed. Shouldn't be NULL unless you
+ *                     require sharing public nonces before the message is known
+ *                     because it reduces nonce misuse resistance. If NULL, must be
+ *                     set with `musig_session_set_msg` before signing and verifying.
+ *        combined_pk: the combined public key of all signers (cannot be NULL)
+ *          pk_hash32: the 32-byte hash of the signers' individual keys (cannot be
+ *                     NULL)
+ *          n_signers: length of signers array. Number of signers participating in
+ *                     the MuSig. Must be greater than 0 and at most 2^32 - 1.
+ *           my_index: index of this signer in the signers array
+ *             seckey: the signer's 32-byte secret key (cannot be NULL)
+ */
+SECP256K1_API int secp256k1_musig_session_initialize(
+    const secp256k1_context* ctx,
+    secp256k1_musig_session *session,
+    secp256k1_musig_session_signer_data *signers,
+    unsigned char *nonce_commitment32,
+    const unsigned char *session_id32,
+    const unsigned char *msg32,
+    const secp256k1_pubkey *combined_pk,
+    const unsigned char *pk_hash32,
+    size_t n_signers,
+    size_t my_index,
+    const unsigned char *seckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5) SECP256K1_ARG_NONNULL(7) SECP256K1_ARG_NONNULL(8) SECP256K1_ARG_NONNULL(11);
+
+/** Gets the signer's public nonce given a list of all signers' data with commitments
+ *
+ *  Returns: 1: public nonce is written in nonce
+ *           0: signer data is missing commitments or session isn't initialized
+ *              for signing
+ *  Args:        ctx: pointer to a context object (cannot be NULL)
+ *           session: the signing session to get the nonce from (cannot be NULL)
+ *           signers: an array of signers' data initialized with
+ *                    `musig_session_initialize`. Array length must equal to
+ *                    `n_commitments` (cannot be NULL)
+ *  Out:       nonce: the nonce (cannot be NULL)
+ *  In:  commitments: array of 32-byte nonce commitments (cannot be NULL)
+ *     n_commitments: the length of commitments and signers array. Must be the total
+ *                    number of signers participating in the MuSig.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_session_get_public_nonce(
+    const secp256k1_context* ctx,
+    secp256k1_musig_session *session,
+    secp256k1_musig_session_signer_data *signers,
+    secp256k1_pubkey *nonce,
+    const unsigned char *const *commitments,
+    size_t n_commitments
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5);
+
+/** Initializes a verifier session that can be used for verifying nonce commitments
+ *  and partial signatures. It does not have secret key material and therefore can not
+ *  be used to create signatures.
+ *
+ *  Returns: 1 when session is successfully initialized, 0 otherwise
+ *  Args:        ctx: pointer to a context object (cannot be NULL)
+ *  Out:     session: the session structure to initialize (cannot be NULL)
+ *           signers: an array of signers' data to be initialized. Array length must
+ *                    equal to `n_signers`(cannot be NULL)
+ *  In:        msg32: the 32-byte message to be signed If NULL, must be set with
+ *                    `musig_session_set_msg` before using the session for verifying
+ *                    partial signatures.
+ *       combined_pk: the combined public key of all signers (cannot be NULL)
+ *         pk_hash32: the 32-byte hash of the signers' individual keys (cannot be NULL)
+ *       commitments: array of 32-byte nonce commitments. Array length must equal to
+ *                    `n_signers` (cannot be NULL)
+ *         n_signers: length of signers and commitments array. Number of signers
+ *                    participating in the MuSig. Must be greater than 0 and at most
+ *                    2^32 - 1.
+ */
+SECP256K1_API int secp256k1_musig_session_initialize_verifier(
+    const secp256k1_context* ctx,
+    secp256k1_musig_session *session,
+    secp256k1_musig_session_signer_data *signers,
+    const unsigned char *msg32,
+    const secp256k1_pubkey *combined_pk,
+    const unsigned char *pk_hash32,
+    const unsigned char *const *commitments,
+    size_t n_signers
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(5) SECP256K1_ARG_NONNULL(6) SECP256K1_ARG_NONNULL(7);
+
+/** Checks a signer's public nonce against a commitment to said nonce, and update
+ *  data structure if they match
+ *
+ *  Returns: 1: commitment was valid, data structure updated
+ *           0: commitment was invalid, nothing happened
+ *  Args:      ctx: pointer to a context object (cannot be NULL)
+ *          signer: pointer to the signer data to update (cannot be NULL). Must have
+ *                  been used with `musig_session_get_public_nonce` or initialized
+ *                  with `musig_session_initialize_verifier`.
+ *  In:     nonce: signer's alleged public nonce (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_set_nonce(
+    const secp256k1_context* ctx,
+    secp256k1_musig_session_signer_data *signer,
+    const secp256k1_pubkey *nonce
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Updates a session with the combined public nonce of all signers. The combined
+ * public nonce is the sum of every signer's public nonce.
+ *
+ *  Returns: 1: nonces are successfully combined
+ *           0: a signer's nonce is missing
+ *  Args:        ctx: pointer to a context object (cannot be NULL)
+ *           session: session to update with the combined public nonce (cannot be
+ *                    NULL)
+ *           signers: an array of signers' data, which must have had public nonces
+ *                    set with `musig_set_nonce`. Array length must equal to `n_signers`
+ *                    (cannot be NULL)
+ *         n_signers: the length of the signers array. Must be the total number of
+ *                    signers participating in the MuSig.
+ *  Out: nonce_is_negated: a pointer to an integer that indicates if the combined
+ *                    public nonce had to be negated.
+ *           adaptor: point to add to the combined public nonce. If NULL, nothing is
+ *                    added to the combined nonce.
+ */
+SECP256K1_API int secp256k1_musig_session_combine_nonces(
+    const secp256k1_context* ctx,
+    secp256k1_musig_session *session,
+    const secp256k1_musig_session_signer_data *signers,
+    size_t n_signers,
+    int *nonce_is_negated,
+    const secp256k1_pubkey *adaptor
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Sets the message of a session if previously unset
+ *
+ *  Returns 1 if the message was not set yet and is now successfully set
+ *          0 otherwise
+ *  Args:    ctx: pointer to a context object (cannot be NULL)
+ *       session: the session structure to update with the message (cannot be NULL)
+ *  In:    msg32: the 32-byte message to be signed (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_session_set_msg(
+    const secp256k1_context* ctx,
+    secp256k1_musig_session *session,
+    const unsigned char *msg32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize a MuSig partial signature or adaptor signature
+ *
+ *  Returns: 1 when the signature could be serialized, 0 otherwise
+ *  Args:    ctx: a secp256k1 context object
+ *  Out:   out32: pointer to a 32-byte array to store the serialized signature
+ *  In:      sig: pointer to the signature
+ */
+SECP256K1_API int secp256k1_musig_partial_signature_serialize(
+    const secp256k1_context* ctx,
+    unsigned char *out32,
+    const secp256k1_musig_partial_signature* sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Parse and verify a MuSig partial signature.
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args:    ctx: a secp256k1 context object
+ *  Out:     sig: pointer to a signature object
+ *  In:     in32: pointer to the 32-byte signature to be parsed
+ *
+ *  After the call, sig will always be initialized. If parsing failed or the
+ *  encoded numbers are out of range, signature verification with it is
+ *  guaranteed to fail for every message and public key.
+ */
+SECP256K1_API int secp256k1_musig_partial_signature_parse(
+    const secp256k1_context* ctx,
+    secp256k1_musig_partial_signature* sig,
+    const unsigned char *in32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Produces a partial signature
+ *
+ *  Returns: 1: partial signature constructed
+ *           0: session in incorrect or inconsistent state
+ *  Args:         ctx: pointer to a context object (cannot be NULL)
+ *            session: active signing session for which the combined nonce has been
+ *                     computed (cannot be NULL)
+ *  Out:  partial_sig: partial signature (cannot be NULL)
+ */
+SECP256K1_API int secp256k1_musig_partial_sign(
+    const secp256k1_context* ctx,
+    const secp256k1_musig_session *session,
+    secp256k1_musig_partial_signature *partial_sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Checks that an individual partial signature verifies
+ *
+ *  This function is essential when using protocols with adaptor signatures.
+ *  However, it is not essential for regular MuSig's, in the sense that if any
+ *  partial signatures does not verify, the full signature will also not verify, so the
+ *  problem will be caught. But this function allows determining the specific party
+ *  who produced an invalid signature, so that signing can be restarted without them.
+ *
+ *  Returns: 1: partial signature verifies
+ *           0: invalid signature or bad data
+ *  Args:         ctx: pointer to a context object (cannot be NULL)
+ *            session: active session for which the combined nonce has been computed
+ *                     (cannot be NULL)
+ *             signer: data for the signer who produced this signature (cannot be NULL)
+ *  In:   partial_sig: signature to verify (cannot be NULL)
+ *             pubkey: public key of the signer who produced the signature (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_partial_sig_verify(
+    const secp256k1_context* ctx,
+    const secp256k1_musig_session *session,
+    const secp256k1_musig_session_signer_data *signer,
+    const secp256k1_musig_partial_signature *partial_sig,
+    const secp256k1_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5);
+
+/** Combines partial signatures
+ *
+ *  Returns: 1: all partial signatures have values in range. Does NOT mean the
+ *              resulting signature verifies.
+ *           0: some partial signature had s/r out of range
+ *  Args:         ctx: pointer to a context object (cannot be NULL)
+ *            session: initialized session for which the combined nonce has been
+ *                     computed (cannot be NULL)
+ *  Out:          sig: complete signature (cannot be NULL)
+ *  In:  partial_sigs: array of partial signatures to combine (cannot be NULL)
+ *             n_sigs: number of signatures in the partial_sigs array
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_partial_sig_combine(
+    const secp256k1_context* ctx,
+    const secp256k1_musig_session *session,
+    secp256k1_schnorrsig *sig,
+    const secp256k1_musig_partial_signature *partial_sigs,
+    size_t n_sigs
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Converts a partial signature to an adaptor signature by adding a given secret
+ *  adaptor.
+ *
+ *  Returns: 1: signature and secret adaptor contained valid values
+ *           0: otherwise
+ *  Args:         ctx: pointer to a context object (cannot be NULL)
+ *  Out:  adaptor_sig: adaptor signature to produce (cannot be NULL)
+ *  In:   partial_sig: partial signature to tweak with secret adaptor (cannot be NULL)
+ *      sec_adaptor32: 32-byte secret adaptor to add to the partial signature (cannot
+ *                     be NULL)
+ *   nonce_is_negated: the `nonce_is_negated` output of `musig_session_combine_nonces`
+ */
+SECP256K1_API int secp256k1_musig_partial_sig_adapt(
+    const secp256k1_context* ctx,
+    secp256k1_musig_partial_signature *adaptor_sig,
+    const secp256k1_musig_partial_signature *partial_sig,
+    const unsigned char *sec_adaptor32,
+    int nonce_is_negated
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Extracts a secret adaptor from a MuSig, given all parties' partial
+ *  signatures. This function will not fail unless given grossly invalid data; if it
+ *  is merely given signatures that do not verify, the returned value will be
+ *  nonsense. It is therefore important that all data be verified at earlier steps of
+ *  any protocol that uses this function.
+ *
+ *  Returns: 1: signatures contained valid data such that an adaptor could be extracted
+ *           0: otherwise
+ *  Args:         ctx: pointer to a context object (cannot be NULL)
+ *  Out:sec_adaptor32: 32-byte secret adaptor (cannot be NULL)
+ *  In:           sig: complete 2-of-2 signature (cannot be NULL)
+ *       partial_sigs: array of partial signatures (cannot be NULL)
+ *     n_partial_sigs: number of elements in partial_sigs array
+ *   nonce_is_negated: the `nonce_is_negated` output of `musig_session_combine_nonces`
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_extract_secret_adaptor(
+    const secp256k1_context* ctx,
+    unsigned char *sec_adaptor32,
+    const secp256k1_schnorrsig *sig,
+    const secp256k1_musig_partial_signature *partial_sigs,
+    size_t n_partial_sigs,
+    int nonce_is_negated
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+#endif
+

src/secp256k1/include/secp256k1_schnorrsig.h

@@ -0,0 +1,119 @@
+#ifndef SECP256K1_SCHNORRSIG_H
+#define SECP256K1_SCHNORRSIG_H
+
+/** This module implements a variant of Schnorr signatures compliant with
+ * BIP-schnorr
+ * (https://github.com/sipa/bips/blob/bip-schnorr/bip-schnorr.mediawiki).
+ */
+
+/** Opaque data structure that holds a parsed Schnorr signature.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage, transmission, or
+ *  comparison, use the `secp256k1_schnorrsig_serialize` and
+ *  `secp256k1_schnorrsig_parse` functions.
+ */
+typedef struct {
+    unsigned char data[64];
+} secp256k1_schnorrsig;
+
+/** Serialize a Schnorr signature.
+ *
+ *  Returns: 1
+ *  Args:    ctx: a secp256k1 context object
+ *  Out:   out64: pointer to a 64-byte array to store the serialized signature
+ *  In:      sig: pointer to the signature
+ *
+ *  See secp256k1_schnorrsig_parse for details about the encoding.
+ */
+SECP256K1_API int secp256k1_schnorrsig_serialize(
+    const secp256k1_context* ctx,
+    unsigned char *out64,
+    const secp256k1_schnorrsig* sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Parse a Schnorr signature.
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args:    ctx: a secp256k1 context object
+ *  Out:     sig: pointer to a signature object
+ *  In:     in64: pointer to the 64-byte signature to be parsed
+ *
+ * The signature is serialized in the form R||s, where R is a 32-byte public
+ * key (x-coordinate only; the y-coordinate is considered to be the unique
+ * y-coordinate satisfying the curve equation that is a quadratic residue)
+ * and s is a 32-byte big-endian scalar.
+ *
+ * After the call, sig will always be initialized. If parsing failed or the
+ * encoded numbers are out of range, signature validation with it is
+ * guaranteed to fail for every message and public key.
+ */
+SECP256K1_API int secp256k1_schnorrsig_parse(
+    const secp256k1_context* ctx,
+    secp256k1_schnorrsig* sig,
+    const unsigned char *in64
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Create a Schnorr signature.
+ *
+ * Returns 1 on success, 0 on failure.
+ *  Args:    ctx: pointer to a context object, initialized for signing (cannot be NULL)
+ *  Out:     sig: pointer to the returned signature (cannot be NULL)
+ *       nonce_is_negated: a pointer to an integer indicates if signing algorithm negated the
+ *                nonce (can be NULL)
+ *  In:    msg32: the 32-byte message hash being signed (cannot be NULL)
+ *        seckey: pointer to a 32-byte secret key (cannot be NULL)
+ *       noncefp: pointer to a nonce generation function. If NULL, secp256k1_nonce_function_bipschnorr is used
+ *         ndata: pointer to arbitrary data used by the nonce generation function (can be NULL)
+ */
+SECP256K1_API int secp256k1_schnorrsig_sign(
+    const secp256k1_context* ctx,
+    secp256k1_schnorrsig *sig,
+    int *nonce_is_negated,
+    const unsigned char *msg32,
+    const unsigned char *seckey,
+    secp256k1_nonce_function noncefp,
+    void *ndata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5);
+
+/** Verify a Schnorr signature.
+ *
+ *  Returns: 1: correct signature
+ *           0: incorrect or unparseable signature
+ *  Args:    ctx: a secp256k1 context object, initialized for verification.
+ *  In:      sig: the signature being verified (cannot be NULL)
+ *         msg32: the 32-byte message hash being verified (cannot be NULL)
+ *        pubkey: pointer to a public key to verify with (cannot be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorrsig_verify(
+    const secp256k1_context* ctx,
+    const secp256k1_schnorrsig *sig,
+    const unsigned char *msg32,
+    const secp256k1_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Verifies a set of Schnorr signatures.
+ *
+ * Returns 1 if all succeeded, 0 otherwise. In particular, returns 1 if n_sigs is 0.
+ *
+ *  Args:    ctx: a secp256k1 context object, initialized for verification.
+ *       scratch: scratch space used for the multiexponentiation
+ *  In:      sig: array of signatures, or NULL if there are no signatures
+ *         msg32: array of messages, or NULL if there are no signatures
+ *            pk: array of public keys, or NULL if there are no signatures
+ *        n_sigs: number of signatures in above arrays. Must be smaller than
+ *                2^31 and smaller than half the maximum size_t value. Must be 0
+ *                if above arrays are NULL.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorrsig_verify_batch(
+    const secp256k1_context* ctx,
+    secp256k1_scratch_space *scratch,
+    const secp256k1_schnorrsig *const *sig,
+    const unsigned char *const *msg32,
+    const secp256k1_pubkey *const *pk,
+    size_t n_sigs
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
+#endif
+

src/secp256k1/src/ecmult.h

@@ -1,3 +1,5 @@
+#ifndef ENABLE_MODULE_MUSIG
+
 /**********************************************************************
  * Copyright (c) 2013, 2014 Pieter Wuille                             *
  * Distributed under the MIT software license, see the accompanying   *
@@ -29,3 +31,56 @@ static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx
 static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng);
 
 #endif /* SECP256K1_ECMULT_H */
+
+#else
+/**********************************************************************
+ * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_ECMULT_H
+#define SECP256K1_ECMULT_H
+
+#include "num.h"
+#include "group.h"
+#include "scalar.h"
+#include "scratch.h"
+
+typedef struct {
+    /* For accelerating the computation of a*P + b*G: */
+    secp256k1_ge_storage (*pre_g)[];    /* odd multiples of the generator */
+#ifdef USE_ENDOMORPHISM
+    secp256k1_ge_storage (*pre_g_128)[]; /* odd multiples of 2^128*generator */
+#endif
+} secp256k1_ecmult_context;
+
+static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx);
+static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb);
+static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst,
+                                           const secp256k1_ecmult_context *src, const secp256k1_callback *cb);
+static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx);
+static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx);
+
+/** Double multiply: R = na*A + ng*G */
+static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng);
+
+typedef int (secp256k1_ecmult_multi_callback)(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *data);
+
+/**
+ * Multi-multiply: R = inp_g_sc * G + sum_i ni * Ai.
+ * Chooses the right algorithm for a given number of points and scratch space
+ * size. Resets and overwrites the given scratch space. If the points do not
+ * fit in the scratch space the algorithm is repeatedly run with batches of
+ * points. If no scratch space is given then a simple algorithm is used that
+ * simply multiplies the points with the corresponding scalars and adds them up.
+ * Returns: 1 on success (including when inp_g_sc is NULL and n is 0)
+ *          0 if there is not enough scratch space for a single point or
+ *          callback returns 0
+ */
+static int secp256k1_ecmult_multi_var(const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n);
+
+#endif /* SECP256K1_ECMULT_H */
+
+#endif
+

src/secp256k1/src/ecmult_const.h

@@ -1,3 +1,5 @@
+#ifndef ENABLE_MODULE_MUSIG
+
 /**********************************************************************
  * Copyright (c) 2015 Andrew Poelstra                                 *
  * Distributed under the MIT software license, see the accompanying   *
@@ -13,3 +15,24 @@
 static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q);
 
 #endif /* SECP256K1_ECMULT_CONST_H */
+
+#else
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_ECMULT_CONST_H
+#define SECP256K1_ECMULT_CONST_H
+
+#include "scalar.h"
+#include "group.h"
+
+/* Here `bits` should be set to the maximum bitlength of the _absolute value_ of `q`, plus
+ * one because we internally sometimes add 2 to the number during the WNAF conversion. */
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q, int bits);
+
+#endif /* SECP256K1_ECMULT_CONST_H */
+#endif
+

src/secp256k1/src/ecmult_const_impl.h

@@ -1,3 +1,5 @@
+#ifndef ENABLE_MODULE_MUSIG
+
 /**********************************************************************
  * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra                  *
  * Distributed under the MIT software license, see the accompanying   *
@@ -238,3 +240,265 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons
 }
 
 #endif /* SECP256K1_ECMULT_CONST_IMPL_H */
+
+#else
+/**********************************************************************
+ * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra                  *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_ECMULT_CONST_IMPL_H
+#define SECP256K1_ECMULT_CONST_IMPL_H
+
+#include "scalar.h"
+#include "group.h"
+#include "ecmult_const.h"
+#include "ecmult_impl.h"
+
+/* This is like `ECMULT_TABLE_GET_GE` but is constant time */
+#define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
+int m; \
+int abs_n = (n) * (((n) > 0) * 2 - 1); \
+int idx_n = abs_n / 2; \
+secp256k1_fe neg_y; \
+VERIFY_CHECK(((n) & 1) == 1); \
+VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
+VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
+VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \
+VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \
+for (m = 0; m < ECMULT_TABLE_SIZE(w); m++) { \
+/* This loop is used to avoid secret data in array indices. See
+* the comment in ecmult_gen_impl.h for rationale. */ \
+secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \
+secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \
+} \
+(r)->infinity = 0; \
+secp256k1_fe_negate(&neg_y, &(r)->y, 1); \
+secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \
+} while(0)
+
+
+/** Convert a number to WNAF notation.
+ *  The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val.
+ *  It has the following guarantees:
+ *  - each wnaf[i] an odd integer between -(1 << w) and (1 << w)
+ *  - each wnaf[i] is nonzero
+ *  - the number of words set is always WNAF_SIZE(w) + 1
+ *
+ *  Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar
+ *  Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.)
+ *  CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlagy Berlin Heidelberg 2003
+ *
+ *  Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335
+ */
+static int secp256k1_wnaf_const(int *wnaf, secp256k1_scalar s, int w, int size) {
+    int global_sign;
+    int skew = 0;
+    int word = 0;
+    
+    /* 1 2 3 */
+    int u_last;
+    int u;
+    
+    int flip;
+    int bit;
+    secp256k1_scalar neg_s;
+    int not_neg_one;
+    /* Note that we cannot handle even numbers by negating them to be odd, as is
+     * done in other implementations, since if our scalars were specified to have
+     * width < 256 for performance reasons, their negations would have width 256
+     * and we'd lose any performance benefit. Instead, we use a technique from
+     * Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even)
+     * or 2 (for odd) to the number we are encoding, returning a skew value indicating
+     * this, and having the caller compensate after doing the multiplication.
+     *
+     * In fact, we _do_ want to negate numbers to minimize their bit-lengths (and in
+     * particular, to ensure that the outputs from the endomorphism-split fit into
+     * 128 bits). If we negate, the parity of our number flips, inverting which of
+     * {1, 2} we want to add to the scalar when ensuring that it's odd. Further
+     * complicating things, -1 interacts badly with `secp256k1_scalar_cadd_bit` and
+     * we need to special-case it in this logic. */
+    flip = secp256k1_scalar_is_high(&s);
+    /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */
+    bit = flip ^ !secp256k1_scalar_is_even(&s);
+    /* We check for negative one, since adding 2 to it will cause an overflow */
+    secp256k1_scalar_negate(&neg_s, &s);
+    not_neg_one = !secp256k1_scalar_is_one(&neg_s);
+    secp256k1_scalar_cadd_bit(&s, bit, not_neg_one);
+    /* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects
+     * that we added two to it and flipped it. In fact for -1 these operations are
+     * identical. We only flipped, but since skewing is required (in the sense that
+     * the skew must be 1 or 2, never zero) and flipping is not, we need to change
+     * our flags to claim that we only skewed. */
+    global_sign = secp256k1_scalar_cond_negate(&s, flip);
+    global_sign *= not_neg_one * 2 - 1;
+    skew = 1 << bit;
+    
+    /* 4 */
+    u_last = secp256k1_scalar_shr_int(&s, w);
+    while (word * w < size) {
+        int sign;
+        int even;
+        
+        /* 4.1 4.4 */
+        u = secp256k1_scalar_shr_int(&s, w);
+        /* 4.2 */
+        even = ((u & 1) == 0);
+        sign = 2 * (u_last > 0) - 1;
+        u += sign * even;
+        u_last -= sign * even * (1 << w);
+        
+        /* 4.3, adapted for global sign change */
+        wnaf[word++] = u_last * global_sign;
+        
+        u_last = u;
+    }
+    wnaf[word] = u * global_sign;
+    
+    VERIFY_CHECK(secp256k1_scalar_is_zero(&s));
+    VERIFY_CHECK(word == WNAF_SIZE_BITS(size, w));
+    return skew;
+}
+
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar, int size) {
+    secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_ge tmpa;
+    secp256k1_fe Z;
+    
+    int skew_1;
+#ifdef USE_ENDOMORPHISM
+    secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
+    int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)];
+    int skew_lam;
+    secp256k1_scalar q_1, q_lam;
+#endif
+    int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)];
+    
+    int i;
+    secp256k1_scalar sc = *scalar;
+    
+    /* build wnaf representation for q. */
+    int rsize = size;
+#ifdef USE_ENDOMORPHISM
+    if (size > 128) {
+        rsize = 128;
+        /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */
+        secp256k1_scalar_split_lambda(&q_1, &q_lam, &sc);
+        skew_1   = secp256k1_wnaf_const(wnaf_1,   q_1,   WINDOW_A - 1, 128);
+        skew_lam = secp256k1_wnaf_const(wnaf_lam, q_lam, WINDOW_A - 1, 128);
+    } else
+#endif
+    {
+        skew_1   = secp256k1_wnaf_const(wnaf_1, sc, WINDOW_A - 1, size);
+#ifdef USE_ENDOMORPHISM
+        skew_lam = 0;
+#endif
+    }
+    
+    /* Calculate odd multiples of a.
+     * All multiples are brought to the same Z 'denominator', which is stored
+     * in Z. Due to secp256k1' isomorphism we can do all operations pretending
+     * that the Z coordinate was 1, use affine addition formulae, and correct
+     * the Z coordinate of the result once at the end.
+     */
+    secp256k1_gej_set_ge(r, a);
+    secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r);
+    for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+        secp256k1_fe_normalize_weak(&pre_a[i].y);
+    }
+#ifdef USE_ENDOMORPHISM
+    if (size > 128) {
+        for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
+            secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
+        }
+    }
+#endif
+    
+    /* first loop iteration (separated out so we can directly set r, rather
+     * than having it start at infinity, get doubled several times, then have
+     * its new value added to it) */
+    i = wnaf_1[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)];
+    VERIFY_CHECK(i != 0);
+    ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A);
+    secp256k1_gej_set_ge(r, &tmpa);
+#ifdef USE_ENDOMORPHISM
+    if (size > 128) {
+        i = wnaf_lam[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)];
+        VERIFY_CHECK(i != 0);
+        ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A);
+        secp256k1_gej_add_ge(r, r, &tmpa);
+    }
+#endif
+    /* remaining loop iterations */
+    for (i = WNAF_SIZE_BITS(rsize, WINDOW_A - 1) - 1; i >= 0; i--) {
+        int n;
+        int j;
+        for (j = 0; j < WINDOW_A - 1; ++j) {
+            secp256k1_gej_double_nonzero(r, r, NULL);
+        }
+        
+        n = wnaf_1[i];
+        ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
+        VERIFY_CHECK(n != 0);
+        secp256k1_gej_add_ge(r, r, &tmpa);
+#ifdef USE_ENDOMORPHISM
+        if (size > 128) {
+            n = wnaf_lam[i];
+            ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
+            VERIFY_CHECK(n != 0);
+            secp256k1_gej_add_ge(r, r, &tmpa);
+        }
+#endif
+    }
+    
+    secp256k1_fe_mul(&r->z, &r->z, &Z);
+    
+    {
+        /* Correct for wNAF skew */
+        secp256k1_ge correction = *a;
+        secp256k1_ge_storage correction_1_stor;
+#ifdef USE_ENDOMORPHISM
+        secp256k1_ge_storage correction_lam_stor;
+#endif
+        secp256k1_ge_storage a2_stor;
+        secp256k1_gej tmpj;
+        secp256k1_gej_set_ge(&tmpj, &correction);
+        secp256k1_gej_double_var(&tmpj, &tmpj, NULL);
+        secp256k1_ge_set_gej(&correction, &tmpj);
+        secp256k1_ge_to_storage(&correction_1_stor, a);
+#ifdef USE_ENDOMORPHISM
+        if (size > 128) {
+            secp256k1_ge_to_storage(&correction_lam_stor, a);
+        }
+#endif
+        secp256k1_ge_to_storage(&a2_stor, &correction);
+        
+        /* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */
+        secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2);
+#ifdef USE_ENDOMORPHISM
+        if (size > 128) {
+            secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2);
+        }
+#endif
+        
+        /* Apply the correction */
+        secp256k1_ge_from_storage(&correction, &correction_1_stor);
+        secp256k1_ge_neg(&correction, &correction);
+        secp256k1_gej_add_ge(r, r, &correction);
+        
+#ifdef USE_ENDOMORPHISM
+        if (size > 128) {
+            secp256k1_ge_from_storage(&correction, &correction_lam_stor);
+            secp256k1_ge_neg(&correction, &correction);
+            secp256k1_ge_mul_lambda(&correction, &correction);
+            secp256k1_gej_add_ge(r, r, &correction);
+        }
+#endif
+    }
+}
+
+#endif /* SECP256K1_ECMULT_CONST_IMPL_H */
+
+#endif
+

src/secp256k1/src/modules/ecdh/main_impl.h

@@ -30,7 +30,7 @@ int secp256k1_ecdh(const secp256k1_context* ctx, unsigned char *result, const se
         unsigned char y[1];
         secp256k1_sha256 sha;
 
-        secp256k1_ecmult_const(&res, &pt, &s);
+        secp256k1_ecmult_const(&res, &pt, &s,256);
         secp256k1_ge_set_gej(&pt, &res);
         /* Compute a hash of the point in compressed form
          * Note we cannot use secp256k1_eckey_pubkey_serialize here since it does not

src/secp256k1/src/modules/musig/Makefile.am.include

@@ -0,0 +1,17 @@
+include_HEADERS += include/secp256k1_musig.h
+noinst_HEADERS += src/modules/musig/main_impl.h
+noinst_HEADERS += src/modules/musig/tests_impl.h
+
+noinst_PROGRAMS += example_musig
+example_musig_SOURCES = src/modules/musig/example.c
+example_musig_CPPFLAGS = -DSECP256K1_BUILD -I$(top_srcdir)/include $(SECP_INCLUDES)
+if !ENABLE_COVERAGE
+example_musig_CPPFLAGS += -DVERIFY
+endif
+example_musig_LDADD = libsecp256k1.la $(SECP_LIBS)
+example_musig_LDFLAGS = -static
+
+if USE_TESTS
+TESTS += example_musig
+endif
+

src/secp256k1/src/modules/musig/example.c

@@ -0,0 +1,166 @@
+/**********************************************************************
+ * Copyright (c) 2018 Jonas Nick                                      *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+/**
+ * This file demonstrates how to use the MuSig module to create a multisignature.
+ * Additionally, see the documentation in include/secp256k1_musig.h.
+ */
+
+#include <stdio.h>
+#include <assert.h>
+#include <secp256k1.h>
+#include <secp256k1_schnorrsig.h>
+#include <secp256k1_musig.h>
+
+ /* Number of public keys involved in creating the aggregate signature */
+#define N_SIGNERS 3
+ /* Create a key pair and store it in seckey and pubkey */
+int create_key(const secp256k1_context* ctx, unsigned char* seckey, secp256k1_pubkey* pubkey) {
+    int ret;
+    FILE *frand = fopen("/dev/urandom", "r");
+    if (frand == NULL) {
+        return 0;
+    }
+    do {
+         if(!fread(seckey, 32, 1, frand)) {
+             fclose(frand);
+             return 0;
+         }
+    /* The probability that this not a valid secret key is approximately 2^-128 */
+    } while (!secp256k1_ec_seckey_verify(ctx, seckey));
+    fclose(frand);
+    ret = secp256k1_ec_pubkey_create(ctx, pubkey, seckey);
+    return ret;
+}
+
+/* Sign a message hash with the given key pairs and store the result in sig */
+int sign(const secp256k1_context* ctx, unsigned char seckeys[][32], const secp256k1_pubkey* pubkeys, const unsigned char* msg32, secp256k1_schnorrsig *sig) {
+    secp256k1_musig_session musig_session[N_SIGNERS];
+    unsigned char nonce_commitment[N_SIGNERS][32];
+    const unsigned char *nonce_commitment_ptr[N_SIGNERS];
+    secp256k1_musig_session_signer_data signer_data[N_SIGNERS][N_SIGNERS];
+    secp256k1_pubkey nonce[N_SIGNERS];
+    int i, j;
+    secp256k1_musig_partial_signature partial_sig[N_SIGNERS];
+
+    for (i = 0; i < N_SIGNERS; i++) {
+        FILE *frand;
+        unsigned char session_id32[32];
+        unsigned char pk_hash[32];
+        secp256k1_pubkey combined_pk;
+
+        /* Create combined pubkey and initialize signer data */
+        if (!secp256k1_musig_pubkey_combine(ctx, NULL, &combined_pk, pk_hash, pubkeys, N_SIGNERS)) {
+            return 0;
+        }
+        /* Create random session ID. It is absolutely necessary that the session ID
+         * is unique for every call of secp256k1_musig_session_initialize. Otherwise
+         * it's trivial for an attacker to extract the secret key! */
+        frand = fopen("/dev/urandom", "r");
+        if(frand == NULL) {
+            return 0;
+        }
+        if (!fread(session_id32, 32, 1, frand)) {
+            fclose(frand);
+            return 0;
+        }
+        fclose(frand);
+        /* Initialize session */
+        if (!secp256k1_musig_session_initialize(ctx, &musig_session[i], signer_data[i], nonce_commitment[i], session_id32, msg32, &combined_pk, pk_hash, N_SIGNERS, i, seckeys[i])) {
+            return 0;
+        }
+        nonce_commitment_ptr[i] = &nonce_commitment[i][0];
+    }
+    /* Communication round 1: Exchange nonce commitments */
+    for (i = 0; i < N_SIGNERS; i++) {
+        /* Set nonce commitments in the signer data and get the own public nonce */
+        if (!secp256k1_musig_session_get_public_nonce(ctx, &musig_session[i], signer_data[i], &nonce[i], nonce_commitment_ptr, N_SIGNERS)) {
+            return 0;
+        }
+    }
+    /* Communication round 2: Exchange nonces */
+    for (i = 0; i < N_SIGNERS; i++) {
+        for (j = 0; j < N_SIGNERS; j++) {
+            if (!secp256k1_musig_set_nonce(ctx, &signer_data[i][j], &nonce[j])) {
+                /* Signer j's nonce does not match the nonce commitment. In this case
+                 * abort the protocol. If you make another attempt at finishing the
+                 * protocol, create a new session (with a fresh session ID!). */
+                return 0;
+            }
+        }
+        if (!secp256k1_musig_session_combine_nonces(ctx, &musig_session[i], signer_data[i], N_SIGNERS, NULL, NULL)) {
+            return 0;
+        }
+    }
+    for (i = 0; i < N_SIGNERS; i++) {
+        if (!secp256k1_musig_partial_sign(ctx, &musig_session[i], &partial_sig[i])) {
+            return 0;
+        }
+    }
+    /* Communication round 3: Exchange partial signatures */
+    for (i = 0; i < N_SIGNERS; i++) {
+        for (j = 0; j < N_SIGNERS; j++) {
+            /* To check whether signing was successful, it suffices to either verify
+             * the the combined signature with the combined public key using
+             * secp256k1_schnorrsig_verify, or verify all partial signatures of all
+             * signers individually. Verifying the combined signature is cheaper but
+             * verifying the individual partial signatures has the advantage that it
+             * can be used to determine which of the partial signatures are invalid
+             * (if any), i.e., which of the partial signatures cause the combined
+             * signature to be invalid and thus the protocol run to fail. It's also
+             * fine to first verify the combined sig, and only verify the individual
+             * sigs if it does not work.
+             */
+            if (!secp256k1_musig_partial_sig_verify(ctx, &musig_session[i], &signer_data[i][j], &partial_sig[j], &pubkeys[j])) {
+                return 0;
+            }
+        }
+    }
+    return secp256k1_musig_partial_sig_combine(ctx, &musig_session[0], sig, partial_sig, N_SIGNERS);
+}
+
+ int main(void) {
+    secp256k1_context* ctx;
+    int i;
+    unsigned char seckeys[N_SIGNERS][32];
+    secp256k1_pubkey pubkeys[N_SIGNERS];
+    secp256k1_pubkey combined_pk;
+    unsigned char msg[32] = "this_could_be_the_hash_of_a_msg!";
+    secp256k1_schnorrsig sig;
+
+    /* Create a context for signing and verification */
+    ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+    printf("Creating key pairs......");
+    for (i = 0; i < N_SIGNERS; i++) {
+        if (!create_key(ctx, seckeys[i], &pubkeys[i])) {
+            printf("FAILED\n");
+            return 1;
+        }
+    }
+    printf("ok\n");
+    printf("Combining public keys...");
+    if (!secp256k1_musig_pubkey_combine(ctx, NULL, &combined_pk, NULL, pubkeys, N_SIGNERS)) {
+        printf("FAILED\n");
+        return 1;
+    }
+    printf("ok\n");
+    printf("Signing message.........");
+    if (!sign(ctx, seckeys, pubkeys, msg, &sig)) {
+        printf("FAILED\n");
+        return 1;
+    }
+    printf("ok\n");
+    printf("Verifying signature.....");
+    if (!secp256k1_schnorrsig_verify(ctx, &sig, msg, &combined_pk)) {
+        printf("FAILED\n");
+        return 1;
+    }
+    printf("ok\n");
+    secp256k1_context_destroy(ctx);
+    return 0;
+}
+
+

src/secp256k1/src/modules/musig/main_impl.h

@@ -0,0 +1,631 @@
+
+/**********************************************************************
+ * Copyright (c) 2018 Andrew Poelstra, Jonas Nick                     *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_MUSIG_MAIN_
+#define _SECP256K1_MODULE_MUSIG_MAIN_
+
+#include "include/secp256k1.h"
+#include "include/secp256k1_musig.h"
+#include "hash.h"
+
+/* Computes ell = SHA256(pk[0], ..., pk[np-1]) */
+static int secp256k1_musig_compute_ell(const secp256k1_context *ctx, unsigned char *ell, const secp256k1_pubkey *pk, size_t np) {
+    secp256k1_sha256 sha;
+    size_t i;
+
+    secp256k1_sha256_initialize(&sha);
+    for (i = 0; i < np; i++) {
+        unsigned char ser[33];
+        size_t serlen = sizeof(ser);
+        if (!secp256k1_ec_pubkey_serialize(ctx, ser, &serlen, &pk[i], SECP256K1_EC_COMPRESSED)) {
+            return 0;
+        }
+        secp256k1_sha256_write(&sha, ser, serlen);
+    }
+    secp256k1_sha256_finalize(&sha, ell);
+    return 1;
+}
+
+/* Initializes SHA256 with fixed midstate. This midstate was computed by applying
+ * SHA256 to SHA256("MuSig coefficient")||SHA256("MuSig coefficient"). */
+static void secp256k1_musig_sha256_init_tagged(secp256k1_sha256 *sha) {
+    secp256k1_sha256_initialize(sha);
+
+    sha->s[0] = 0x0fd0690cul;
+    sha->s[1] = 0xfefeae97ul;
+    sha->s[2] = 0x996eac7ful;
+    sha->s[3] = 0x5c30d864ul;
+    sha->s[4] = 0x8c4a0573ul;
+    sha->s[5] = 0xaca1a22ful;
+    sha->s[6] = 0x6f43b801ul;
+    sha->s[7] = 0x85ce27cdul;
+    sha->bytes = 64;
+}
+
+/* Compute r = SHA256(ell, idx). The four bytes of idx are serialized least significant byte first. */
+static void secp256k1_musig_coefficient(secp256k1_scalar *r, const unsigned char *ell, uint32_t idx) {
+    secp256k1_sha256 sha;
+    unsigned char buf[32];
+    size_t i;
+
+    secp256k1_musig_sha256_init_tagged(&sha);
+    secp256k1_sha256_write(&sha, ell, 32);
+    /* We're hashing the index of the signer instead of its public key as specified
+     * in the MuSig paper. This reduces the total amount of data that needs to be
+     * hashed.
+     * Additionally, it prevents creating identical musig_coefficients for identical
+     * public keys. A participant Bob could choose his public key to be the same as
+     * Alice's, then replay Alice's messages (nonce and partial signature) to create
+     * a valid partial signature. This is not a problem for MuSig per se, but could
+     * result in subtle issues with protocols building on threshold signatures.
+     * With the assumption that public keys are unique, hashing the index is
+     * equivalent to hashing the public key. Because the public key can be
+     * identified by the index given the ordered list of public keys (included in
+     * ell), the index is just a different encoding of the public key.*/
+    for (i = 0; i < sizeof(uint32_t); i++) {
+        unsigned char c = idx;
+        secp256k1_sha256_write(&sha, &c, 1);
+        idx >>= 8;
+    }
+    secp256k1_sha256_finalize(&sha, buf);
+    secp256k1_scalar_set_b32(r, buf, NULL);
+}
+
+typedef struct {
+    const secp256k1_context *ctx;
+    unsigned char ell[32];
+    const secp256k1_pubkey *pks;
+} secp256k1_musig_pubkey_combine_ecmult_data;
+
+/* Callback for batch EC multiplication to compute ell_0*P0 + ell_1*P1 + ...  */
+static int secp256k1_musig_pubkey_combine_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *data) {
+    secp256k1_musig_pubkey_combine_ecmult_data *ctx = (secp256k1_musig_pubkey_combine_ecmult_data *) data;
+    secp256k1_musig_coefficient(sc, ctx->ell, idx);
+    return secp256k1_pubkey_load(ctx->ctx, pt, &ctx->pks[idx]);
+}
+
+
+static void secp256k1_musig_signers_init(secp256k1_musig_session_signer_data *signers, uint32_t n_signers) {
+    uint32_t i;
+    for (i = 0; i < n_signers; i++) {
+        memset(&signers[i], 0, sizeof(signers[i]));
+        signers[i].index = i;
+        signers[i].present = 0;
+    }
+}
+
+int secp256k1_musig_pubkey_combine(const secp256k1_context* ctx, secp256k1_scratch_space *scratch, secp256k1_pubkey *combined_pk, unsigned char *pk_hash32, const secp256k1_pubkey *pubkeys, size_t n_pubkeys) {
+    secp256k1_musig_pubkey_combine_ecmult_data ecmult_data;
+    secp256k1_gej pkj;
+    secp256k1_ge pkp;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(combined_pk != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(pubkeys != NULL);
+    ARG_CHECK(n_pubkeys > 0);
+
+    ecmult_data.ctx = ctx;
+    ecmult_data.pks = pubkeys;
+    if (!secp256k1_musig_compute_ell(ctx, ecmult_data.ell, pubkeys, n_pubkeys)) {
+        return 0;
+    }
+    if (!secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &pkj, NULL, secp256k1_musig_pubkey_combine_callback, (void *) &ecmult_data, n_pubkeys)) {
+        return 0;
+    }
+    secp256k1_ge_set_gej(&pkp, &pkj);
+    secp256k1_pubkey_save(combined_pk, &pkp);
+
+    if (pk_hash32 != NULL) {
+        memcpy(pk_hash32, ecmult_data.ell, 32);
+    }
+    return 1;
+}
+
+int secp256k1_musig_session_initialize(const secp256k1_context* ctx, secp256k1_musig_session *session, secp256k1_musig_session_signer_data *signers, unsigned char *nonce_commitment32, const unsigned char *session_id32, const unsigned char *msg32, const secp256k1_pubkey *combined_pk, const unsigned char *pk_hash32, size_t n_signers, size_t my_index, const unsigned char *seckey) {
+    unsigned char combined_ser[33];
+    size_t combined_ser_size = sizeof(combined_ser);
+    int overflow;
+    secp256k1_scalar secret;
+    secp256k1_scalar mu;
+    secp256k1_sha256 sha;
+    secp256k1_gej rj;
+    secp256k1_ge rp;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(session != NULL);
+    ARG_CHECK(signers != NULL);
+    ARG_CHECK(nonce_commitment32 != NULL);
+    ARG_CHECK(session_id32 != NULL);
+    ARG_CHECK(combined_pk != NULL);
+    ARG_CHECK(pk_hash32 != NULL);
+    ARG_CHECK(seckey != NULL);
+
+    memset(session, 0, sizeof(*session));
+
+    if (msg32 != NULL) {
+        memcpy(session->msg, msg32, 32);
+        session->msg_is_set = 1;
+    } else {
+        session->msg_is_set = 0;
+    }
+    memcpy(&session->combined_pk, combined_pk, sizeof(*combined_pk));
+    memcpy(session->pk_hash, pk_hash32, 32);
+    session->nonce_is_set = 0;
+    session->has_secret_data = 1;
+    if (n_signers == 0 || my_index >= n_signers) {
+        return 0;
+    }
+    if (n_signers > UINT32_MAX) {
+        return 0;
+    }
+    session->n_signers = (uint32_t) n_signers;
+    secp256k1_musig_signers_init(signers, session->n_signers);
+    session->nonce_commitments_hash_is_set = 0;
+
+    /* Compute secret key */
+    secp256k1_scalar_set_b32(&secret, seckey, &overflow);
+    if (overflow) {
+        secp256k1_scalar_clear(&secret);
+        return 0;
+    }
+    secp256k1_musig_coefficient(&mu, pk_hash32, (uint32_t) my_index);
+    secp256k1_scalar_mul(&secret, &secret, &mu);
+    secp256k1_scalar_get_b32(session->seckey, &secret);
+
+    /* Compute secret nonce */
+    secp256k1_sha256_initialize(&sha);
+    secp256k1_sha256_write(&sha, session_id32, 32);
+    if (session->msg_is_set) {
+        secp256k1_sha256_write(&sha, msg32, 32);
+    }
+    secp256k1_ec_pubkey_serialize(ctx, combined_ser, &combined_ser_size, combined_pk, SECP256K1_EC_COMPRESSED);
+    secp256k1_sha256_write(&sha, combined_ser, combined_ser_size);
+    secp256k1_sha256_write(&sha, seckey, 32);
+    secp256k1_sha256_finalize(&sha, session->secnonce);
+    secp256k1_scalar_set_b32(&secret, session->secnonce, &overflow);
+    if (overflow) {
+        secp256k1_scalar_clear(&secret);
+        return 0;
+    }
+
+    /* Compute public nonce and commitment */
+    secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &rj, &secret);
+    secp256k1_ge_set_gej(&rp, &rj);
+    secp256k1_pubkey_save(&session->nonce, &rp);
+
+    if (nonce_commitment32 != NULL) {
+        unsigned char commit[33];
+        size_t commit_size = sizeof(commit);
+        secp256k1_sha256_initialize(&sha);
+        secp256k1_ec_pubkey_serialize(ctx, commit, &commit_size, &session->nonce, SECP256K1_EC_COMPRESSED);
+        secp256k1_sha256_write(&sha, commit, commit_size);
+        secp256k1_sha256_finalize(&sha, nonce_commitment32);
+    }
+
+    secp256k1_scalar_clear(&secret);
+    return 1;
+}
+
+int secp256k1_musig_session_get_public_nonce(const secp256k1_context* ctx, secp256k1_musig_session *session, secp256k1_musig_session_signer_data *signers, secp256k1_pubkey *nonce, const unsigned char *const *commitments, size_t n_commitments) {
+    secp256k1_sha256 sha;
+    unsigned char nonce_commitments_hash[32];
+    size_t i;
+    (void) ctx;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(session != NULL);
+    ARG_CHECK(signers != NULL);
+    ARG_CHECK(nonce != NULL);
+    ARG_CHECK(commitments != NULL);
+
+    if (!session->has_secret_data || n_commitments != session->n_signers) {
+        return 0;
+    }
+    for (i = 0; i < n_commitments; i++) {
+        ARG_CHECK(commitments[i] != NULL);
+    }
+
+    secp256k1_sha256_initialize(&sha);
+    for (i = 0; i < n_commitments; i++) {
+        memcpy(signers[i].nonce_commitment, commitments[i], 32);
+        secp256k1_sha256_write(&sha, commitments[i], 32);
+    }
+    secp256k1_sha256_finalize(&sha, nonce_commitments_hash);
+    if (session->nonce_commitments_hash_is_set
+            && memcmp(session->nonce_commitments_hash, nonce_commitments_hash, 32) != 0) {
+        /* Abort if get_public_nonce has been called before with a different array of
+         * commitments. */
+        return 0;
+    }
+    memcpy(session->nonce_commitments_hash, nonce_commitments_hash, 32);
+    session->nonce_commitments_hash_is_set = 1;
+    memcpy(nonce, &session->nonce, sizeof(*nonce));
+    return 1;
+}
+
+int secp256k1_musig_session_initialize_verifier(const secp256k1_context* ctx, secp256k1_musig_session *session, secp256k1_musig_session_signer_data *signers, const unsigned char *msg32, const secp256k1_pubkey *combined_pk, const unsigned char *pk_hash32, const unsigned char *const *commitments, size_t n_signers) {
+    size_t i;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(session != NULL);
+    ARG_CHECK(signers != NULL);
+    ARG_CHECK(combined_pk != NULL);
+    ARG_CHECK(pk_hash32 != NULL);
+    ARG_CHECK(commitments != NULL);
+    /* Check n_signers before checking commitments to allow testing the case where
+     * n_signers is big without allocating the space. */
+    if (n_signers > UINT32_MAX) {
+        return 0;
+    }
+    for (i = 0; i < n_signers; i++) {
+        ARG_CHECK(commitments[i] != NULL);
+    }
+    (void) ctx;
+
+    memset(session, 0, sizeof(*session));
+
+    memcpy(&session->combined_pk, combined_pk, sizeof(*combined_pk));
+    if (n_signers == 0) {
+        return 0;
+    }
+    session->n_signers = (uint32_t) n_signers;
+    secp256k1_musig_signers_init(signers, session->n_signers);
+
+    memcpy(session->pk_hash, pk_hash32, 32);
+    session->nonce_is_set = 0;
+    session->msg_is_set = 0;
+    if (msg32 != NULL) {
+        memcpy(session->msg, msg32, 32);
+        session->msg_is_set = 1;
+    }
+    session->has_secret_data = 0;
+    session->nonce_commitments_hash_is_set = 0;
+
+    for (i = 0; i < n_signers; i++) {
+        memcpy(signers[i].nonce_commitment, commitments[i], 32);
+    }
+    return 1;
+}
+
+int secp256k1_musig_set_nonce(const secp256k1_context* ctx, secp256k1_musig_session_signer_data *signer, const secp256k1_pubkey *nonce) {
+    unsigned char commit[33];
+    size_t commit_size = sizeof(commit);
+    secp256k1_sha256 sha;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(signer != NULL);
+    ARG_CHECK(nonce != NULL);
+
+    secp256k1_sha256_initialize(&sha);
+    secp256k1_ec_pubkey_serialize(ctx, commit, &commit_size, nonce, SECP256K1_EC_COMPRESSED);
+    secp256k1_sha256_write(&sha, commit, commit_size);
+    secp256k1_sha256_finalize(&sha, commit);
+
+    if (memcmp(commit, signer->nonce_commitment, 32) != 0) {
+        return 0;
+    }
+    memcpy(&signer->nonce, nonce, sizeof(*nonce));
+    signer->present = 1;
+    return 1;
+}
+
+int secp256k1_musig_session_combine_nonces(const secp256k1_context* ctx, secp256k1_musig_session *session, const secp256k1_musig_session_signer_data *signers, size_t n_signers, int *nonce_is_negated, const secp256k1_pubkey *adaptor) {
+    secp256k1_gej combined_noncej;
+    secp256k1_ge combined_noncep;
+    secp256k1_ge noncep;
+    secp256k1_sha256 sha;
+    unsigned char nonce_commitments_hash[32];
+    size_t i;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(session != NULL);
+    ARG_CHECK(signers != NULL);
+
+    if (n_signers != session->n_signers) {
+        return 0;
+    }
+    secp256k1_sha256_initialize(&sha);
+    secp256k1_gej_set_infinity(&combined_noncej);
+    for (i = 0; i < n_signers; i++) {
+        if (!signers[i].present) {
+            return 0;
+        }
+        secp256k1_sha256_write(&sha, signers[i].nonce_commitment, 32);
+        secp256k1_pubkey_load(ctx, &noncep, &signers[i].nonce);
+        secp256k1_gej_add_ge_var(&combined_noncej, &combined_noncej, &noncep, NULL);
+    }
+    secp256k1_sha256_finalize(&sha, nonce_commitments_hash);
+    /* Either the session is a verifier session or or the nonce_commitments_hash has
+     * been set in `musig_session_get_public_nonce`. */
+    VERIFY_CHECK(!session->has_secret_data || session->nonce_commitments_hash_is_set);
+    if (session->has_secret_data
+            && memcmp(session->nonce_commitments_hash, nonce_commitments_hash, 32) != 0) {
+        /* If the signers' commitments changed between get_public_nonce and now we
+         * have to abort because in that case they may have seen our nonce before
+         * creating their commitment. That can happen if the signer_data given to
+         * this function is different to the signer_data given to get_public_nonce.
+         * */
+        return 0;
+    }
+
+    /* Add public adaptor to nonce */
+    if (adaptor != NULL) {
+        secp256k1_pubkey_load(ctx, &noncep, adaptor);
+        secp256k1_gej_add_ge_var(&combined_noncej, &combined_noncej, &noncep, NULL);
+    }
+    secp256k1_ge_set_gej(&combined_noncep, &combined_noncej);
+    if (secp256k1_fe_is_quad_var(&combined_noncep.y)) {
+        session->nonce_is_negated = 0;
+    } else {
+        session->nonce_is_negated = 1;
+        secp256k1_ge_neg(&combined_noncep, &combined_noncep);
+    }
+    if (nonce_is_negated != NULL) {
+        *nonce_is_negated = session->nonce_is_negated;
+    }
+    secp256k1_pubkey_save(&session->combined_nonce, &combined_noncep);
+    session->nonce_is_set = 1;
+    return 1;
+}
+
+int secp256k1_musig_session_set_msg(const secp256k1_context* ctx, secp256k1_musig_session *session, const unsigned char *msg32) {
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(session != NULL);
+    ARG_CHECK(msg32 != NULL);
+
+    if (session->msg_is_set) {
+        return 0;
+    }
+    memcpy(session->msg, msg32, 32);
+    session->msg_is_set = 1;
+    return 1;
+}
+
+int secp256k1_musig_partial_signature_serialize(const secp256k1_context* ctx, unsigned char *out32, const secp256k1_musig_partial_signature* sig) {
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(out32 != NULL);
+    ARG_CHECK(sig != NULL);
+    memcpy(out32, sig->data, 32);
+    return 1;
+}
+
+int secp256k1_musig_partial_signature_parse(const secp256k1_context* ctx, secp256k1_musig_partial_signature* sig, const unsigned char *in32) {
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(in32 != NULL);
+    memcpy(sig->data, in32, 32);
+    return 1;
+}
+
+/* Compute msghash = SHA256(combined_nonce, combined_pk, msg) */
+static int secp256k1_musig_compute_messagehash(const secp256k1_context *ctx, unsigned char *msghash, const secp256k1_musig_session *session) {
+    unsigned char buf[33];
+    size_t bufsize = 33;
+    secp256k1_ge rp;
+    secp256k1_sha256 sha;
+
+    secp256k1_sha256_initialize(&sha);
+    if (!session->nonce_is_set) {
+        return 0;
+    }
+    secp256k1_pubkey_load(ctx, &rp, &session->combined_nonce);
+    secp256k1_fe_get_b32(buf, &rp.x);
+    secp256k1_sha256_write(&sha, buf, 32);
+    secp256k1_ec_pubkey_serialize(ctx, buf, &bufsize, &session->combined_pk, SECP256K1_EC_COMPRESSED);
+    VERIFY_CHECK(bufsize == 33);
+    secp256k1_sha256_write(&sha, buf, bufsize);
+    if (!session->msg_is_set) {
+        return 0;
+    }
+    secp256k1_sha256_write(&sha, session->msg, 32);
+    secp256k1_sha256_finalize(&sha, msghash);
+    return 1;
+}
+
+int secp256k1_musig_partial_sign(const secp256k1_context* ctx, const secp256k1_musig_session *session, secp256k1_musig_partial_signature *partial_sig) {
+    unsigned char msghash[32];
+    int overflow;
+    secp256k1_scalar sk;
+    secp256k1_scalar e, k;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(partial_sig != NULL);
+    ARG_CHECK(session != NULL);
+
+    if (!session->nonce_is_set || !session->has_secret_data) {
+        return 0;
+    }
+
+    /* build message hash */
+    if (!secp256k1_musig_compute_messagehash(ctx, msghash, session)) {
+        return 0;
+    }
+    secp256k1_scalar_set_b32(&e, msghash, NULL);
+
+    secp256k1_scalar_set_b32(&sk, session->seckey, &overflow);
+    if (overflow) {
+        secp256k1_scalar_clear(&sk);
+        return 0;
+    }
+
+    secp256k1_scalar_set_b32(&k, session->secnonce, &overflow);
+    if (overflow || secp256k1_scalar_is_zero(&k)) {
+        secp256k1_scalar_clear(&sk);
+        secp256k1_scalar_clear(&k);
+        return 0;
+    }
+    if (session->nonce_is_negated) {
+        secp256k1_scalar_negate(&k, &k);
+    }
+
+    /* Sign */
+    secp256k1_scalar_mul(&e, &e, &sk);
+    secp256k1_scalar_add(&e, &e, &k);
+    secp256k1_scalar_get_b32(&partial_sig->data[0], &e);
+    secp256k1_scalar_clear(&sk);
+    secp256k1_scalar_clear(&k);
+
+    return 1;
+}
+
+int secp256k1_musig_partial_sig_combine(const secp256k1_context* ctx, const secp256k1_musig_session *session, secp256k1_schnorrsig *sig, const secp256k1_musig_partial_signature *partial_sigs, size_t n_sigs) {
+    size_t i;
+    secp256k1_scalar s;
+    secp256k1_ge noncep;
+    (void) ctx;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(partial_sigs != NULL);
+    ARG_CHECK(session != NULL);
+
+    if (!session->nonce_is_set) {
+        return 0;
+    }
+    if (n_sigs != session->n_signers) {
+        return 0;
+    }
+    secp256k1_scalar_clear(&s);
+    for (i = 0; i < n_sigs; i++) {
+        int overflow;
+        secp256k1_scalar term;
+
+        secp256k1_scalar_set_b32(&term, partial_sigs[i].data, &overflow);
+        if (overflow) {
+            return 0;
+        }
+        secp256k1_scalar_add(&s, &s, &term);
+    }
+
+    secp256k1_pubkey_load(ctx, &noncep, &session->combined_nonce);
+    VERIFY_CHECK(secp256k1_fe_is_quad_var(&noncep.y));
+    secp256k1_fe_normalize(&noncep.x);
+    secp256k1_fe_get_b32(&sig->data[0], &noncep.x);
+    secp256k1_scalar_get_b32(&sig->data[32], &s);
+
+    return 1;
+}
+
+int secp256k1_musig_partial_sig_verify(const secp256k1_context* ctx, const secp256k1_musig_session *session, const secp256k1_musig_session_signer_data *signer, const secp256k1_musig_partial_signature *partial_sig, const secp256k1_pubkey *pubkey) {
+    unsigned char msghash[32];
+    secp256k1_scalar s;
+    secp256k1_scalar e;
+    secp256k1_scalar mu;
+    secp256k1_gej rj;
+    secp256k1_ge rp;
+    int overflow;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(session != NULL);
+    ARG_CHECK(signer != NULL);
+    ARG_CHECK(partial_sig != NULL);
+    ARG_CHECK(pubkey != NULL);
+
+    if (!session->nonce_is_set || !signer->present) {
+        return 0;
+    }
+    secp256k1_scalar_set_b32(&s, partial_sig->data, &overflow);
+    if (overflow) {
+        return 0;
+    }
+    if (!secp256k1_musig_compute_messagehash(ctx, msghash, session)) {
+        return 0;
+    }
+    secp256k1_scalar_set_b32(&e, msghash, NULL);
+
+    /* Multiplying the messagehash by the musig coefficient is equivalent
+     * to multiplying the signer's public key by the coefficient, except
+     * much easier to do. */
+    secp256k1_musig_coefficient(&mu, session->pk_hash, signer->index);
+    secp256k1_scalar_mul(&e, &e, &mu);
+
+    if (!secp256k1_pubkey_load(ctx, &rp, &signer->nonce)) {
+        return 0;
+    }
+
+    if (!secp256k1_schnorrsig_real_verify(ctx, &rj, &s, &e, pubkey)) {
+        return 0;
+    }
+    if (!session->nonce_is_negated) {
+        secp256k1_ge_neg(&rp, &rp);
+    }
+    secp256k1_gej_add_ge_var(&rj, &rj, &rp, NULL);
+
+    return secp256k1_gej_is_infinity(&rj);
+}
+
+int secp256k1_musig_partial_sig_adapt(const secp256k1_context* ctx, secp256k1_musig_partial_signature *adaptor_sig, const secp256k1_musig_partial_signature *partial_sig, const unsigned char *sec_adaptor32, int nonce_is_negated) {
+    secp256k1_scalar s;
+    secp256k1_scalar t;
+    int overflow;
+
+    (void) ctx;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(adaptor_sig != NULL);
+    ARG_CHECK(partial_sig != NULL);
+    ARG_CHECK(sec_adaptor32 != NULL);
+
+    secp256k1_scalar_set_b32(&s, partial_sig->data, &overflow);
+    if (overflow) {
+        return 0;
+    }
+    secp256k1_scalar_set_b32(&t, sec_adaptor32, &overflow);
+    if (overflow) {
+        secp256k1_scalar_clear(&t);
+        return 0;
+    }
+
+    if (nonce_is_negated) {
+        secp256k1_scalar_negate(&t, &t);
+    }
+
+    secp256k1_scalar_add(&s, &s, &t);
+    secp256k1_scalar_get_b32(adaptor_sig->data, &s);
+    secp256k1_scalar_clear(&t);
+    return 1;
+}
+
+int secp256k1_musig_extract_secret_adaptor(const secp256k1_context* ctx, unsigned char *sec_adaptor32, const secp256k1_schnorrsig *sig, const secp256k1_musig_partial_signature *partial_sigs, size_t n_partial_sigs, int nonce_is_negated) {
+    secp256k1_scalar t;
+    secp256k1_scalar s;
+    int overflow;
+    size_t i;
+
+    (void) ctx;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(sec_adaptor32 != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(partial_sigs != NULL);
+
+    secp256k1_scalar_set_b32(&t, &sig->data[32], &overflow);
+    if (overflow) {
+        return 0;
+    }
+    secp256k1_scalar_negate(&t, &t);
+
+    for (i = 0; i < n_partial_sigs; i++) {
+        secp256k1_scalar_set_b32(&s, partial_sigs[i].data, &overflow);
+        if (overflow) {
+            secp256k1_scalar_clear(&t);
+            return 0;
+        }
+        secp256k1_scalar_add(&t, &t, &s);
+    }
+
+    if (!nonce_is_negated) {
+        secp256k1_scalar_negate(&t, &t);
+    }
+    secp256k1_scalar_get_b32(sec_adaptor32, &t);
+    secp256k1_scalar_clear(&t);
+    return 1;
+}
+
+#endif
+

src/secp256k1/src/modules/musig/tests_impl.h

@@ -0,0 +1,758 @@
+/**********************************************************************
+ * Copyright (c) 2018 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_MUSIG_TESTS_
+#define _SECP256K1_MODULE_MUSIG_TESTS_
+
+#include "secp256k1_musig.h"
+
+void musig_api_tests(secp256k1_scratch_space *scratch) {
+    secp256k1_scratch_space *scratch_small;
+    secp256k1_musig_session session[2];
+    secp256k1_musig_session verifier_session;
+    secp256k1_musig_session_signer_data signer0[2];
+    secp256k1_musig_session_signer_data signer1[2];
+    secp256k1_musig_session_signer_data verifier_signer_data[2];
+    secp256k1_musig_partial_signature partial_sig[2];
+    secp256k1_musig_partial_signature partial_sig_adapted[2];
+    secp256k1_musig_partial_signature partial_sig_overflow;
+    secp256k1_schnorrsig final_sig;
+    secp256k1_schnorrsig final_sig_cmp;
+
+    unsigned char buf[32];
+    unsigned char sk[2][32];
+    unsigned char ones[32];
+    unsigned char session_id[2][32];
+    unsigned char nonce_commitment[2][32];
+    int nonce_is_negated;
+    const unsigned char *ncs[2];
+    unsigned char msg[32];
+    unsigned char msghash[32];
+    secp256k1_pubkey combined_pk;
+    unsigned char pk_hash[32];
+    secp256k1_pubkey pk[2];
+
+    unsigned char sec_adaptor[32];
+    unsigned char sec_adaptor1[32];
+    secp256k1_pubkey adaptor;
+
+    /** setup **/
+    secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+    secp256k1_context *sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
+    secp256k1_context *vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
+    int ecount;
+
+    secp256k1_context_set_error_callback(none, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(sign, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(vrfy, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
+
+    memset(ones, 0xff, 32);
+
+    secp256k1_rand256(session_id[0]);
+    secp256k1_rand256(session_id[1]);
+    secp256k1_rand256(sk[0]);
+    secp256k1_rand256(sk[1]);
+    secp256k1_rand256(msg);
+    secp256k1_rand256(sec_adaptor);
+
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pk[0], sk[0]) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pk[1], sk[1]) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &adaptor, sec_adaptor) == 1);
+
+    /** main test body **/
+
+    /* Key combination */
+    ecount = 0;
+    CHECK(secp256k1_musig_pubkey_combine(none, scratch, &combined_pk, pk_hash, pk, 2) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_musig_pubkey_combine(sign, scratch, &combined_pk, pk_hash, pk, 2) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_musig_pubkey_combine(vrfy, scratch, &combined_pk, pk_hash, pk, 2) == 1);
+    CHECK(ecount == 2);
+    /* pubkey_combine does not require a scratch space */
+    CHECK(secp256k1_musig_pubkey_combine(vrfy, NULL, &combined_pk, pk_hash, pk, 2) == 1);
+    CHECK(ecount == 2);
+    /* If a scratch space is given it shouldn't be too small */
+    scratch_small = secp256k1_scratch_space_create(ctx, 1);
+    CHECK(secp256k1_musig_pubkey_combine(vrfy, scratch_small, &combined_pk, pk_hash, pk, 2) == 0);
+    secp256k1_scratch_space_destroy(scratch_small);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_musig_pubkey_combine(vrfy, scratch, NULL, pk_hash, pk, 2) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_musig_pubkey_combine(vrfy, scratch, &combined_pk, NULL, pk, 2) == 1);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_musig_pubkey_combine(vrfy, scratch, &combined_pk, pk_hash, NULL, 2) == 0);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_musig_pubkey_combine(vrfy, scratch, &combined_pk, pk_hash, pk, 0) == 0);
+    CHECK(ecount == 5);
+    CHECK(secp256k1_musig_pubkey_combine(vrfy, scratch, &combined_pk, pk_hash, NULL, 0) == 0);
+    CHECK(ecount == 6);
+
+    CHECK(secp256k1_musig_pubkey_combine(vrfy, scratch, &combined_pk, pk_hash, pk, 2) == 1);
+    CHECK(secp256k1_musig_pubkey_combine(vrfy, scratch, &combined_pk, pk_hash, pk, 2) == 1);
+    CHECK(secp256k1_musig_pubkey_combine(vrfy, scratch, &combined_pk, pk_hash, pk, 2) == 1);
+
+    /** Session creation **/
+    ecount = 0;
+    CHECK(secp256k1_musig_session_initialize(none, &session[0], signer0, nonce_commitment[0], session_id[0], msg, &combined_pk, pk_hash, 2, 0, sk[0]) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_musig_session_initialize(vrfy, &session[0], signer0, nonce_commitment[0], session_id[0], msg, &combined_pk, pk_hash, 2, 0, sk[0]) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_musig_session_initialize(sign, &session[0], signer0, nonce_commitment[0], session_id[0], msg, &combined_pk, pk_hash, 2, 0, sk[0]) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_musig_session_initialize(sign, NULL, signer0, nonce_commitment[0], session_id[0], msg, &combined_pk, pk_hash, 2, 0, sk[0]) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_musig_session_initialize(sign, &session[0], NULL, nonce_commitment[0], session_id[0], msg, &combined_pk, pk_hash, 2, 0, sk[0]) == 0);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_musig_session_initialize(sign, &session[0], signer0, NULL, session_id[0], msg, &combined_pk, pk_hash, 2, 0, sk[0]) == 0);
+    CHECK(ecount == 5);
+    CHECK(secp256k1_musig_session_initialize(sign, &session[0], signer0, nonce_commitment[0], NULL, msg, &combined_pk, pk_hash, 2, 0, sk[0]) == 0);
+    CHECK(ecount == 6);
+    CHECK(secp256k1_musig_session_initialize(sign, &session[0], signer0, nonce_commitment[0], session_id[0], NULL, &combined_pk, pk_hash, 2, 0, sk[0]) == 1);
+    CHECK(ecount == 6);
+    CHECK(secp256k1_musig_session_initialize(sign, &session[0], signer0, nonce_commitment[0], session_id[0], msg, NULL, pk_hash, 2, 0, sk[0]) == 0);
+    CHECK(ecount == 7);
+    CHECK(secp256k1_musig_session_initialize(sign, &session[0], signer0, nonce_commitment[0], session_id[0], msg, &combined_pk, NULL, 2, 0, sk[0]) == 0);
+    CHECK(ecount == 8);
+    CHECK(secp256k1_musig_session_initialize(sign, &session[0], signer0, nonce_commitment[0], session_id[0], msg, &combined_pk, pk_hash, 0, 0, sk[0]) == 0);
+    CHECK(ecount == 8);
+    /* If more than UINT32_MAX fits in a size_t, test that session_initialize
+     * rejects n_signers that high. */
+    if (SIZE_MAX > UINT32_MAX) {
+        CHECK(secp256k1_musig_session_initialize(sign, &session[0], signer0, nonce_commitment[0], session_id[0], msg, &combined_pk, pk_hash, ((size_t) UINT32_MAX) + 2, 0, sk[0]) == 0);
+    }
+    CHECK(ecount == 8);
+    CHECK(secp256k1_musig_session_initialize(sign, &session[0], signer0, nonce_commitment[0], session_id[0], msg, &combined_pk, pk_hash, 2, 0, NULL) == 0);
+    CHECK(ecount == 9);
+    /* secret key overflows */
+    CHECK(secp256k1_musig_session_initialize(sign, &session[0], signer0, nonce_commitment[0], session_id[0], msg, &combined_pk, pk_hash, 2, 0, ones) == 0);
+    CHECK(ecount == 9);
+
+
+    {
+        secp256k1_musig_session session_without_msg;
+        CHECK(secp256k1_musig_session_initialize(sign, &session_without_msg, signer0, nonce_commitment[0], session_id[0], NULL, &combined_pk, pk_hash, 2, 0, sk[0]) == 1);
+        CHECK(secp256k1_musig_session_set_msg(none, &session_without_msg, msg) == 1);
+        CHECK(secp256k1_musig_session_set_msg(none, &session_without_msg, msg) == 0);
+    }
+    CHECK(secp256k1_musig_session_initialize(sign, &session[0], signer0, nonce_commitment[0], session_id[0], msg, &combined_pk, pk_hash, 2, 0, sk[0]) == 1);
+    CHECK(secp256k1_musig_session_initialize(sign, &session[1], signer1, nonce_commitment[1], session_id[1], msg, &combined_pk, pk_hash, 2, 1, sk[1]) == 1);
+    ncs[0] = nonce_commitment[0];
+    ncs[1] = nonce_commitment[1];
+
+    ecount = 0;
+    CHECK(secp256k1_musig_session_initialize_verifier(none, &verifier_session, verifier_signer_data, msg, &combined_pk, pk_hash, ncs, 2) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_musig_session_initialize_verifier(none, NULL, verifier_signer_data, msg, &combined_pk, pk_hash, ncs, 2) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_musig_session_initialize_verifier(none, &verifier_session, verifier_signer_data, NULL, &combined_pk, pk_hash, ncs, 2) == 1);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_musig_session_initialize_verifier(none, &verifier_session, verifier_signer_data, msg, NULL, pk_hash, ncs, 2) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_musig_session_initialize_verifier(none, &verifier_session, verifier_signer_data, msg, &combined_pk, NULL, ncs, 2) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_musig_session_initialize_verifier(none, &verifier_session, verifier_signer_data, msg, &combined_pk, pk_hash, NULL, 2) == 0);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_musig_session_initialize_verifier(none, &verifier_session, verifier_signer_data, msg, &combined_pk, pk_hash, ncs, 0) == 0);
+    CHECK(ecount == 4);
+    if (SIZE_MAX > UINT32_MAX) {
+        CHECK(secp256k1_musig_session_initialize_verifier(none, &verifier_session, verifier_signer_data, msg, &combined_pk, pk_hash, ncs, ((size_t) UINT32_MAX) + 2) == 0);
+    }
+    CHECK(ecount == 4);
+    CHECK(secp256k1_musig_session_initialize_verifier(none, &verifier_session, verifier_signer_data, msg, &combined_pk, pk_hash, ncs, 2) == 1);
+
+    CHECK(secp256k1_musig_compute_messagehash(none, msghash, &verifier_session) == 0);
+    CHECK(secp256k1_musig_compute_messagehash(none, msghash, &session[0]) == 0);
+
+    /** Signing step 0 -- exchange nonce commitments */
+    ecount = 0;
+    {
+        secp256k1_pubkey nonce;
+
+        /* Can obtain public nonce after commitments have been exchanged; still can't sign */
+        CHECK(secp256k1_musig_session_get_public_nonce(none, &session[0], signer0, &nonce, ncs, 2) == 1);
+        CHECK(secp256k1_musig_partial_sign(none, &session[0], &partial_sig[0]) == 0);
+        CHECK(ecount == 0);
+    }
+
+    /** Signing step 1 -- exchange nonces */
+    ecount = 0;
+    {
+        secp256k1_pubkey public_nonce[3];
+
+        CHECK(secp256k1_musig_session_get_public_nonce(none, &session[0], signer0, &public_nonce[0], ncs, 2) == 1);
+        CHECK(ecount == 0);
+        CHECK(secp256k1_musig_session_get_public_nonce(none, NULL, signer0, &public_nonce[0], ncs, 2) == 0);
+        CHECK(ecount == 1);
+        CHECK(secp256k1_musig_session_get_public_nonce(none, &session[0], NULL, &public_nonce[0], ncs, 2) == 0);
+        CHECK(ecount == 2);
+        CHECK(secp256k1_musig_session_get_public_nonce(none, &session[0], signer0, NULL, ncs, 2) == 0);
+        CHECK(ecount == 3);
+        CHECK(secp256k1_musig_session_get_public_nonce(none, &session[0], signer0, &public_nonce[0], NULL, 2) == 0);
+        CHECK(ecount == 4);
+        /* Number of commitments and number of signers are different */
+        CHECK(secp256k1_musig_session_get_public_nonce(none, &session[0], signer0, &public_nonce[0], ncs, 1) == 0);
+        CHECK(ecount == 4);
+
+        CHECK(secp256k1_musig_session_get_public_nonce(none, &session[0], signer0, &public_nonce[0], ncs, 2) == 1);
+        CHECK(secp256k1_musig_session_get_public_nonce(none, &session[1], signer1, &public_nonce[1], ncs, 2) == 1);
+
+        CHECK(secp256k1_musig_set_nonce(none, &signer0[0], &public_nonce[0]) == 1);
+        CHECK(secp256k1_musig_set_nonce(none, &signer0[1], &public_nonce[0]) == 0);
+        CHECK(secp256k1_musig_set_nonce(none, &signer0[1], &public_nonce[1]) == 1);
+        CHECK(secp256k1_musig_set_nonce(none, &signer0[1], &public_nonce[1]) == 1);
+        CHECK(ecount == 4);
+
+        CHECK(secp256k1_musig_set_nonce(none, NULL, &public_nonce[0]) == 0);
+        CHECK(ecount == 5);
+        CHECK(secp256k1_musig_set_nonce(none, &signer1[0], NULL) == 0);
+        CHECK(ecount == 6);
+
+        CHECK(secp256k1_musig_set_nonce(none, &signer1[0], &public_nonce[0]) == 1);
+        CHECK(secp256k1_musig_set_nonce(none, &signer1[1], &public_nonce[1]) == 1);
+        CHECK(secp256k1_musig_set_nonce(none, &verifier_signer_data[0], &public_nonce[0]) == 1);
+        CHECK(secp256k1_musig_set_nonce(none, &verifier_signer_data[1], &public_nonce[1]) == 1);
+
+        ecount = 0;
+        CHECK(secp256k1_musig_session_combine_nonces(none, &session[0], signer0, 2, &nonce_is_negated, &adaptor) == 1);
+        CHECK(secp256k1_musig_session_combine_nonces(none, NULL, signer0, 2, &nonce_is_negated, &adaptor) == 0);
+        CHECK(ecount == 1);
+        CHECK(secp256k1_musig_session_combine_nonces(none, &session[0], NULL, 2, &nonce_is_negated, &adaptor) == 0);
+        CHECK(ecount == 2);
+        /* Number of signers differs from number during intialization */
+        CHECK(secp256k1_musig_session_combine_nonces(none, &session[0], signer0, 1, &nonce_is_negated, &adaptor) == 0);
+        CHECK(ecount == 2);
+        CHECK(secp256k1_musig_session_combine_nonces(none, &session[0], signer0, 2, NULL, &adaptor) == 1);
+        CHECK(ecount == 2);
+        CHECK(secp256k1_musig_session_combine_nonces(none, &session[0], signer0, 2, &nonce_is_negated, NULL) == 1);
+
+        CHECK(secp256k1_musig_session_combine_nonces(none, &session[0], signer0, 2, &nonce_is_negated, &adaptor) == 1);
+        CHECK(secp256k1_musig_session_combine_nonces(none, &session[1], signer0, 2, &nonce_is_negated, &adaptor) == 1);
+        CHECK(secp256k1_musig_session_combine_nonces(none, &verifier_session, verifier_signer_data, 2, &nonce_is_negated, &adaptor) == 1);
+    }
+
+    /** Signing step 2 -- partial signatures */
+    ecount = 0;
+    CHECK(secp256k1_musig_partial_sign(none, &session[0], &partial_sig[0]) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_musig_partial_sign(none, NULL, &partial_sig[0]) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_musig_partial_sign(none, &session[0], NULL) == 0);
+    CHECK(ecount == 2);
+
+    CHECK(secp256k1_musig_partial_sign(none, &session[0], &partial_sig[0]) == 1);
+    CHECK(secp256k1_musig_partial_sign(none, &session[1], &partial_sig[1]) == 1);
+    /* observer can't sign */
+    CHECK(secp256k1_musig_partial_sign(none, &verifier_session, &partial_sig[2]) == 0);
+    CHECK(ecount == 2);
+
+    ecount = 0;
+    CHECK(secp256k1_musig_partial_signature_serialize(none, buf, &partial_sig[0]) == 1);
+    CHECK(secp256k1_musig_partial_signature_serialize(none, NULL, &partial_sig[0]) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_musig_partial_signature_serialize(none, buf, NULL) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_musig_partial_signature_parse(none, &partial_sig[0], buf) == 1);
+    CHECK(secp256k1_musig_partial_signature_parse(none, NULL, buf) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_musig_partial_signature_parse(none, &partial_sig[0], NULL) == 0);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_musig_partial_signature_parse(none, &partial_sig_overflow, ones) == 1);
+
+    /** Partial signature verification */
+    ecount = 0;
+    CHECK(secp256k1_musig_partial_sig_verify(none, &session[0], &signer0[0], &partial_sig[0], &pk[0]) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_musig_partial_sig_verify(sign, &session[0], &signer0[0], &partial_sig[0], &pk[0]) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_musig_partial_sig_verify(vrfy, &session[0], &signer0[0], &partial_sig[0], &pk[0]) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_musig_partial_sig_verify(vrfy, &session[0], &signer0[0], &partial_sig[1], &pk[0]) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_musig_partial_sig_verify(vrfy, NULL, &signer0[0], &partial_sig[0], &pk[0]) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_musig_partial_sig_verify(vrfy, &session[0], NULL, &partial_sig[0], &pk[0]) == 0);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_musig_partial_sig_verify(vrfy, &session[0], &signer0[0], NULL, &pk[0]) == 0);
+    CHECK(ecount == 5);
+    CHECK(secp256k1_musig_partial_sig_verify(vrfy, &session[0], &signer0[0], &partial_sig_overflow, &pk[0]) == 0);
+    CHECK(ecount == 5);
+    CHECK(secp256k1_musig_partial_sig_verify(vrfy, &session[0], &signer0[0], &partial_sig[0], NULL) == 0);
+    CHECK(ecount == 6);
+
+    CHECK(secp256k1_musig_partial_sig_verify(vrfy, &session[0], &signer0[0], &partial_sig[0], &pk[0]) == 1);
+    CHECK(secp256k1_musig_partial_sig_verify(vrfy, &session[1], &signer1[0], &partial_sig[0], &pk[0]) == 1);
+    CHECK(secp256k1_musig_partial_sig_verify(vrfy, &session[0], &signer0[1], &partial_sig[1], &pk[1]) == 1);
+    CHECK(secp256k1_musig_partial_sig_verify(vrfy, &session[1], &signer1[1], &partial_sig[1], &pk[1]) == 1);
+    CHECK(secp256k1_musig_partial_sig_verify(vrfy, &verifier_session, &verifier_signer_data[0], &partial_sig[0], &pk[0]) == 1);
+    CHECK(secp256k1_musig_partial_sig_verify(vrfy, &verifier_session, &verifier_signer_data[1], &partial_sig[1], &pk[1]) == 1);
+    CHECK(ecount == 6);
+
+    /** Adaptor signature verification */
+    memcpy(&partial_sig_adapted[1], &partial_sig[1], sizeof(partial_sig_adapted[1]));
+    ecount = 0;
+    CHECK(secp256k1_musig_partial_sig_adapt(none, &partial_sig_adapted[0], &partial_sig[0], sec_adaptor, nonce_is_negated) == 1);
+    CHECK(secp256k1_musig_partial_sig_adapt(none, NULL, &partial_sig[0], sec_adaptor, 0) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_musig_partial_sig_adapt(none, &partial_sig_adapted[0], NULL, sec_adaptor, 0) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_musig_partial_sig_adapt(none, &partial_sig_adapted[0], &partial_sig_overflow, sec_adaptor, nonce_is_negated) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_musig_partial_sig_adapt(none, &partial_sig_adapted[0], &partial_sig[0], NULL, 0) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_musig_partial_sig_adapt(none, &partial_sig_adapted[0], &partial_sig[0], ones, nonce_is_negated) == 0);
+    CHECK(ecount == 3);
+
+    /** Signing combining and verification */
+    ecount = 0;
+    CHECK(secp256k1_musig_partial_sig_combine(none, &session[0], &final_sig, partial_sig_adapted, 2) == 1);
+    CHECK(secp256k1_musig_partial_sig_combine(none, &session[0], &final_sig_cmp, partial_sig_adapted, 2) == 1);
+    CHECK(memcmp(&final_sig, &final_sig_cmp, sizeof(final_sig)) == 0);
+    CHECK(secp256k1_musig_partial_sig_combine(none, &session[0], &final_sig_cmp, partial_sig_adapted, 2) == 1);
+    CHECK(memcmp(&final_sig, &final_sig_cmp, sizeof(final_sig)) == 0);
+
+    CHECK(secp256k1_musig_partial_sig_combine(none, NULL, &final_sig, partial_sig_adapted, 2) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_musig_partial_sig_combine(none, &session[0], NULL, partial_sig_adapted, 2) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_musig_partial_sig_combine(none, &session[0], &final_sig, NULL, 2) == 0);
+    CHECK(ecount == 3);
+    {
+        secp256k1_musig_partial_signature partial_sig_tmp[2];
+        partial_sig_tmp[0] = partial_sig_adapted[0];
+        partial_sig_tmp[1] = partial_sig_overflow;
+        CHECK(secp256k1_musig_partial_sig_combine(none, &session[0], &final_sig, partial_sig_tmp, 2) == 0);
+    }
+    CHECK(ecount == 3);
+    /* Wrong number of partial sigs */
+    CHECK(secp256k1_musig_partial_sig_combine(none, &session[0], &final_sig, partial_sig_adapted, 1) == 0);
+    CHECK(ecount == 3);
+
+    CHECK(secp256k1_schnorrsig_verify(vrfy, &final_sig, msg, &combined_pk) == 1);
+
+    /** Secret adaptor can be extracted from signature */
+    ecount = 0;
+    CHECK(secp256k1_musig_extract_secret_adaptor(none, sec_adaptor1, &final_sig, partial_sig, 2, nonce_is_negated) == 1);
+    CHECK(memcmp(sec_adaptor, sec_adaptor1, 32) == 0);
+    CHECK(secp256k1_musig_extract_secret_adaptor(none, NULL, &final_sig, partial_sig, 2, 0) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_musig_extract_secret_adaptor(none, sec_adaptor1, NULL, partial_sig, 2, 0) == 0);
+    CHECK(ecount == 2);
+    {
+        secp256k1_schnorrsig final_sig_tmp = final_sig;
+        memcpy(&final_sig_tmp.data[32], ones, 32);
+        CHECK(secp256k1_musig_extract_secret_adaptor(none, sec_adaptor1, &final_sig_tmp, partial_sig, 2, nonce_is_negated) == 0);
+    }
+    CHECK(ecount == 2);
+    CHECK(secp256k1_musig_extract_secret_adaptor(none, sec_adaptor1, &final_sig, NULL, 2, 0) == 0);
+    CHECK(ecount == 3);
+    {
+        secp256k1_musig_partial_signature partial_sig_tmp[2];
+        partial_sig_tmp[0] = partial_sig[0];
+        partial_sig_tmp[1] = partial_sig_overflow;
+        CHECK(secp256k1_musig_extract_secret_adaptor(none, sec_adaptor1, &final_sig, partial_sig_tmp, 2, nonce_is_negated) == 0);
+    }
+    CHECK(ecount == 3);
+    CHECK(secp256k1_musig_extract_secret_adaptor(none, sec_adaptor1, &final_sig, partial_sig, 0, 0) == 1);
+    CHECK(secp256k1_musig_extract_secret_adaptor(none, sec_adaptor1, &final_sig, partial_sig, 2, 1) == 1);
+
+    /** cleanup **/
+    memset(&session, 0, sizeof(session));
+    secp256k1_context_destroy(none);
+    secp256k1_context_destroy(sign);
+    secp256k1_context_destroy(vrfy);
+}
+
+/* Initializes two sessions, one use the given parameters (session_id,
+ * nonce_commitments, etc.) except that `session_tmp` uses new signers with different
+ * public keys. The point of this test is to call `musig_session_get_public_nonce`
+ * with signers from `session_tmp` who have different public keys than the correct
+ * ones and return the resulting messagehash. This should not result in a different
+ * messagehash because the public keys of the signers are only used during session
+ * initialization. */
+int musig_state_machine_diff_signer_msghash_test(unsigned char *msghash, secp256k1_pubkey *pks, secp256k1_pubkey *combined_pk, unsigned char *pk_hash, const unsigned char * const *nonce_commitments, unsigned char *msg, secp256k1_pubkey *nonce_other, unsigned char *sk, unsigned char *session_id) {
+    secp256k1_musig_session session;
+    secp256k1_musig_session session_tmp;
+    unsigned char nonce_commitment[32];
+    secp256k1_musig_session_signer_data signers[2];
+    secp256k1_musig_session_signer_data signers_tmp[2];
+    unsigned char sk_dummy[32];
+    secp256k1_pubkey pks_tmp[2];
+    secp256k1_pubkey combined_pk_tmp;
+    unsigned char pk_hash_tmp[32];
+    secp256k1_pubkey nonce;
+
+    /* Set up signers with different public keys */
+    secp256k1_rand256(sk_dummy);
+    pks_tmp[0] = pks[0];
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pks_tmp[1], sk_dummy) == 1);
+    CHECK(secp256k1_musig_pubkey_combine(ctx, NULL, &combined_pk_tmp, pk_hash_tmp, pks_tmp, 2) == 1);
+    CHECK(secp256k1_musig_session_initialize(ctx, &session_tmp, signers_tmp, nonce_commitment, session_id, msg, &combined_pk_tmp, pk_hash_tmp, 2, 0, sk_dummy) == 1);
+
+    CHECK(secp256k1_musig_session_initialize(ctx, &session, signers, nonce_commitment, session_id, msg, combined_pk, pk_hash, 2, 0, sk) == 1);
+    CHECK(memcmp(nonce_commitment, nonce_commitments[1], 32) == 0);
+    /* Call get_public_nonce with different signers than the signers the session was
+     * initialized with. */
+    CHECK(secp256k1_musig_session_get_public_nonce(ctx, &session_tmp, signers, &nonce, nonce_commitments, 2) == 1);
+    CHECK(secp256k1_musig_session_get_public_nonce(ctx, &session, signers_tmp, &nonce, nonce_commitments, 2) == 1);
+    CHECK(secp256k1_musig_set_nonce(ctx, &signers[0], nonce_other) == 1);
+    CHECK(secp256k1_musig_set_nonce(ctx, &signers[1], &nonce) == 1);
+    CHECK(secp256k1_musig_session_combine_nonces(ctx, &session, signers, 2, NULL, NULL) == 1);
+
+    return secp256k1_musig_compute_messagehash(ctx, msghash, &session);
+}
+
+/* Creates a new session (with a different session id) and tries to use that session
+ * to combine nonces with given signers_other. This should fail, because the nonce
+ * commitments of signers_other do not match the nonce commitments the new session
+ * was initialized with. If do_test is 0, the correct signers are being used and
+ * therefore the function should return 1. */
+int musig_state_machine_diff_signers_combine_nonce_test(secp256k1_pubkey *combined_pk, unsigned char *pk_hash, unsigned char *nonce_commitment_other, secp256k1_pubkey *nonce_other, unsigned char *msg, unsigned char *sk, secp256k1_musig_session_signer_data *signers_other, int do_test) {
+    secp256k1_musig_session session;
+    secp256k1_musig_session_signer_data signers[2];
+    secp256k1_musig_session_signer_data *signers_to_use;
+    unsigned char nonce_commitment[32];
+    unsigned char session_id[32];
+    secp256k1_pubkey nonce;
+    const unsigned char *ncs[2];
+
+    /* Initialize new signers */
+    secp256k1_rand256(session_id);
+    CHECK(secp256k1_musig_session_initialize(ctx, &session, signers, nonce_commitment, session_id, msg, combined_pk, pk_hash, 2, 1, sk) == 1);
+    ncs[0] = nonce_commitment_other;
+    ncs[1] = nonce_commitment;
+    CHECK(secp256k1_musig_session_get_public_nonce(ctx, &session, signers, &nonce, ncs, 2) == 1);
+    CHECK(secp256k1_musig_set_nonce(ctx, &signers[0], nonce_other) == 1);
+    CHECK(secp256k1_musig_set_nonce(ctx, &signers[1], &nonce) == 1);
+    CHECK(secp256k1_musig_set_nonce(ctx, &signers[1], &nonce) == 1);
+    secp256k1_musig_session_combine_nonces(ctx, &session, signers_other, 2, NULL, NULL);
+    if (do_test) {
+        signers_to_use = signers_other;
+    } else {
+        signers_to_use = signers;
+    }
+    return secp256k1_musig_session_combine_nonces(ctx, &session, signers_to_use, 2, NULL, NULL);
+}
+
+/* Recreates a session with the given session_id, signers, pk, msg etc. parameters
+ * and tries to sign and verify the other signers partial signature. Both should fail
+ * if msg is NULL. */
+int musig_state_machine_missing_msg_test(secp256k1_pubkey *pks, secp256k1_pubkey *combined_pk, unsigned char *pk_hash, unsigned char *nonce_commitment_other, secp256k1_pubkey *nonce_other, secp256k1_musig_partial_signature *partial_sig_other, unsigned char *sk, unsigned char *session_id, unsigned char *msg) {
+    secp256k1_musig_session session;
+    secp256k1_musig_session_signer_data signers[2];
+    unsigned char nonce_commitment[32];
+    const unsigned char *ncs[2];
+    secp256k1_pubkey nonce;
+    secp256k1_musig_partial_signature partial_sig;
+    int partial_sign, partial_verify;
+
+    CHECK(secp256k1_musig_session_initialize(ctx, &session, signers, nonce_commitment, session_id, msg, combined_pk, pk_hash, 2, 0, sk) == 1);
+    ncs[0] = nonce_commitment_other;
+    ncs[1] = nonce_commitment;
+    CHECK(secp256k1_musig_session_get_public_nonce(ctx, &session, signers, &nonce, ncs, 2) == 1);
+    CHECK(secp256k1_musig_set_nonce(ctx, &signers[0], nonce_other) == 1);
+    CHECK(secp256k1_musig_set_nonce(ctx, &signers[1], &nonce) == 1);
+
+    CHECK(secp256k1_musig_session_combine_nonces(ctx, &session, signers, 2, NULL, NULL) == 1);
+    partial_sign = secp256k1_musig_partial_sign(ctx, &session, &partial_sig);
+    partial_verify = secp256k1_musig_partial_sig_verify(ctx, &session, &signers[0], partial_sig_other, &pks[0]);
+    if (msg != NULL) {
+        /* Return 1 if both succeeded */
+        return partial_sign && partial_verify;
+    }
+    /* Return 0 if both failed */
+    return partial_sign || partial_verify;
+}
+
+/* Recreates a session with the given session_id, signers, pk, msg etc. parameters
+ * and tries to verify and combine partial sigs. If do_combine is 0, the
+ * combine_nonces step is left out. In that case verify and combine should fail and
+ * this function should return 0. */
+int musig_state_machine_missing_combine_test(secp256k1_pubkey *pks, secp256k1_pubkey *combined_pk, unsigned char *pk_hash, unsigned char *nonce_commitment_other, secp256k1_pubkey *nonce_other, secp256k1_musig_partial_signature *partial_sig_other, unsigned char *msg, unsigned char *sk, unsigned char *session_id, secp256k1_musig_partial_signature *partial_sig, int do_combine) {
+    secp256k1_musig_session session;
+    secp256k1_musig_session_signer_data signers[2];
+    unsigned char nonce_commitment[32];
+    const unsigned char *ncs[2];
+    secp256k1_pubkey nonce;
+    secp256k1_musig_partial_signature partial_sigs[2];
+    secp256k1_schnorrsig sig;
+    int partial_verify, sig_combine;
+
+    CHECK(secp256k1_musig_session_initialize(ctx, &session, signers, nonce_commitment, session_id, msg, combined_pk, pk_hash, 2, 0, sk) == 1);
+    ncs[0] = nonce_commitment_other;
+    ncs[1] = nonce_commitment;
+    CHECK(secp256k1_musig_session_get_public_nonce(ctx, &session, signers, &nonce, ncs, 2) == 1);
+    CHECK(secp256k1_musig_set_nonce(ctx, &signers[0], nonce_other) == 1);
+    CHECK(secp256k1_musig_set_nonce(ctx, &signers[1], &nonce) == 1);
+
+    partial_sigs[0] = *partial_sig_other;
+    partial_sigs[1] = *partial_sig;
+    if (do_combine != 0) {
+        CHECK(secp256k1_musig_session_combine_nonces(ctx, &session, signers, 2, NULL, NULL) == 1);
+    }
+    partial_verify = secp256k1_musig_partial_sig_verify(ctx, &session, signers, partial_sig_other, &pks[0]);
+    sig_combine = secp256k1_musig_partial_sig_combine(ctx, &session, &sig, partial_sigs, 2);
+    if (do_combine != 0) {
+        /* Return 1 if both succeeded */
+        return partial_verify && sig_combine;
+    }
+    /* Return 0 if both failed */
+    return partial_verify || sig_combine;
+}
+
+void musig_state_machine_tests(secp256k1_scratch_space *scratch) {
+    size_t i;
+    secp256k1_musig_session session[2];
+    secp256k1_musig_session_signer_data signers0[2];
+    secp256k1_musig_session_signer_data signers1[2];
+    unsigned char nonce_commitment[2][32];
+    unsigned char session_id[2][32];
+    unsigned char msg[32];
+    unsigned char sk[2][32];
+    secp256k1_pubkey pk[2];
+    secp256k1_pubkey combined_pk;
+    unsigned char pk_hash[32];
+    secp256k1_pubkey nonce[2];
+    const unsigned char *ncs[2];
+    secp256k1_musig_partial_signature partial_sig[2];
+    unsigned char msghash1[32];
+    unsigned char msghash2[32];
+
+    /* Run state machine with the same objects twice to test that it's allowed to
+     * reinitialize session and session_signer_data. */
+    for (i = 0; i < 2; i++) {
+        /* Setup */
+        secp256k1_rand256(session_id[0]);
+        secp256k1_rand256(session_id[1]);
+        secp256k1_rand256(sk[0]);
+        secp256k1_rand256(sk[1]);
+        secp256k1_rand256(msg);
+        CHECK(secp256k1_ec_pubkey_create(ctx, &pk[0], sk[0]) == 1);
+        CHECK(secp256k1_ec_pubkey_create(ctx, &pk[1], sk[1]) == 1);
+        CHECK(secp256k1_musig_pubkey_combine(ctx, scratch, &combined_pk, pk_hash, pk, 2) == 1);
+        CHECK(secp256k1_musig_session_initialize(ctx, &session[0], signers0, nonce_commitment[0], session_id[0], msg, &combined_pk, pk_hash, 2, 0, sk[0]) == 1);
+        CHECK(secp256k1_musig_session_initialize(ctx, &session[1], signers1, nonce_commitment[1], session_id[1], msg, &combined_pk, pk_hash, 2, 1, sk[1]) == 1);
+
+        /* Set nonce commitments */
+        ncs[0] = nonce_commitment[0];
+        ncs[1] = nonce_commitment[1];
+        CHECK(secp256k1_musig_session_get_public_nonce(ctx, &session[0], signers0, &nonce[0], ncs, 2) == 1);
+        /* Changing a nonce commitment is not okay */
+        ncs[1] = (unsigned char*) "this isn't a nonce commitment...";
+        CHECK(secp256k1_musig_session_get_public_nonce(ctx, &session[0], signers0, &nonce[0], ncs, 2) == 0);
+        /* Repeating with the same nonce commitments is okay */
+        ncs[1] = nonce_commitment[1];
+        CHECK(secp256k1_musig_session_get_public_nonce(ctx, &session[0], signers0, &nonce[0], ncs, 2) == 1);
+
+        /* Get nonce for signer 1 */
+        CHECK(secp256k1_musig_session_get_public_nonce(ctx, &session[1], signers1, &nonce[1], ncs, 2) == 1);
+
+        /* Set nonces */
+        CHECK(secp256k1_musig_set_nonce(ctx, &signers0[0], &nonce[0]) == 1);
+        /* Can't set nonce that doesn't match nonce commitment */
+        CHECK(secp256k1_musig_set_nonce(ctx, &signers0[1], &nonce[0]) == 0);
+        /* Set correct nonce */
+        CHECK(secp256k1_musig_set_nonce(ctx, &signers0[1], &nonce[1]) == 1);
+
+        /* Combine nonces */
+        CHECK(secp256k1_musig_session_combine_nonces(ctx, &session[0], signers0, 2, NULL, NULL) == 1);
+        /* Not everyone is present from signer 1's view */
+        CHECK(secp256k1_musig_session_combine_nonces(ctx, &session[1], signers1, 2, NULL, NULL) == 0);
+        /* Make everyone present */
+        CHECK(secp256k1_musig_set_nonce(ctx, &signers1[0], &nonce[0]) == 1);
+        CHECK(secp256k1_musig_set_nonce(ctx, &signers1[1], &nonce[1]) == 1);
+
+        /* Can't combine nonces from signers of a different session */
+        CHECK(musig_state_machine_diff_signers_combine_nonce_test(&combined_pk, pk_hash, nonce_commitment[0], &nonce[0], msg, sk[1], signers1, 1) == 0);
+        CHECK(musig_state_machine_diff_signers_combine_nonce_test(&combined_pk, pk_hash, nonce_commitment[0], &nonce[0], msg, sk[1], signers1, 0) == 1);
+
+        /* Partially sign */
+        CHECK(secp256k1_musig_partial_sign(ctx, &session[0], &partial_sig[0]) == 1);
+        /* Can't verify or sign until nonce is combined */
+        CHECK(secp256k1_musig_partial_sig_verify(ctx, &session[1], &signers1[0], &partial_sig[0], &pk[0]) == 0);
+        CHECK(secp256k1_musig_partial_sign(ctx, &session[1], &partial_sig[1]) == 0);
+        CHECK(secp256k1_musig_session_combine_nonces(ctx, &session[1], signers1, 2, NULL, NULL) == 1);
+        CHECK(secp256k1_musig_partial_sig_verify(ctx, &session[1], &signers1[0], &partial_sig[0], &pk[0]) == 1);
+        /* messagehash should be the same as a session whose get_public_nonce was called
+         * with different signers (i.e. they diff in public keys). This is because the
+         * public keys of the signers is set in stone when initializing the session. */
+        CHECK(secp256k1_musig_compute_messagehash(ctx, msghash1, &session[1]) == 1);
+        CHECK(musig_state_machine_diff_signer_msghash_test(msghash2, pk, &combined_pk, pk_hash, ncs, msg, &nonce[0], sk[1], session_id[1]) == 1);
+        CHECK(memcmp(msghash1, msghash2, 32) == 0);
+        CHECK(secp256k1_musig_partial_sign(ctx, &session[1], &partial_sig[1]) == 1);
+        CHECK(secp256k1_musig_partial_sig_verify(ctx, &session[1], &signers1[1], &partial_sig[1], &pk[1]) == 1);
+        /* Wrong signature */
+        CHECK(secp256k1_musig_partial_sig_verify(ctx, &session[1], &signers1[1], &partial_sig[0], &pk[1]) == 0);
+        /* Can't sign or verify until msg is set */
+        CHECK(musig_state_machine_missing_msg_test(pk, &combined_pk, pk_hash, nonce_commitment[0], &nonce[0], &partial_sig[0], sk[1], session_id[1], NULL) == 0);
+        CHECK(musig_state_machine_missing_msg_test(pk, &combined_pk, pk_hash, nonce_commitment[0], &nonce[0], &partial_sig[0], sk[1], session_id[1], msg) == 1);
+
+        /* Can't verify and combine partial sigs until nonces are combined */
+        CHECK(musig_state_machine_missing_combine_test(pk, &combined_pk, pk_hash, nonce_commitment[0], &nonce[0], &partial_sig[0], msg, sk[1], session_id[1], &partial_sig[1], 0) == 0);
+        CHECK(musig_state_machine_missing_combine_test(pk, &combined_pk, pk_hash, nonce_commitment[0], &nonce[0], &partial_sig[0], msg, sk[1], session_id[1], &partial_sig[1], 1) == 1);
+    }
+}
+
+void scriptless_atomic_swap(secp256k1_scratch_space *scratch) {
+    /* Throughout this test "a" and "b" refer to two hypothetical blockchains,
+     * while the indices 0 and 1 refer to the two signers. Here signer 0 is
+     * sending a-coins to signer 1, while signer 1 is sending b-coins to signer
+     * 0. Signer 0 produces the adaptor signatures. */
+    secp256k1_schnorrsig final_sig_a;
+    secp256k1_schnorrsig final_sig_b;
+    secp256k1_musig_partial_signature partial_sig_a[2];
+    secp256k1_musig_partial_signature partial_sig_b_adapted[2];
+    secp256k1_musig_partial_signature partial_sig_b[2];
+    unsigned char sec_adaptor[32];
+    unsigned char sec_adaptor_extracted[32];
+    secp256k1_pubkey pub_adaptor;
+
+    unsigned char seckey_a[2][32];
+    unsigned char seckey_b[2][32];
+    secp256k1_pubkey pk_a[2];
+    secp256k1_pubkey pk_b[2];
+    unsigned char pk_hash_a[32];
+    unsigned char pk_hash_b[32];
+    secp256k1_pubkey combined_pk_a;
+    secp256k1_pubkey combined_pk_b;
+    secp256k1_musig_session musig_session_a[2];
+    secp256k1_musig_session musig_session_b[2];
+    unsigned char noncommit_a[2][32];
+    unsigned char noncommit_b[2][32];
+    const unsigned char *noncommit_a_ptr[2];
+    const unsigned char *noncommit_b_ptr[2];
+    secp256k1_pubkey pubnon_a[2];
+    secp256k1_pubkey pubnon_b[2];
+    int nonce_is_negated_a;
+    int nonce_is_negated_b;
+    secp256k1_musig_session_signer_data data_a[2];
+    secp256k1_musig_session_signer_data data_b[2];
+
+    const unsigned char seed[32] = "still tired of choosing seeds...";
+    const unsigned char msg32_a[32] = "this is the message blockchain a";
+    const unsigned char msg32_b[32] = "this is the message blockchain b";
+
+    /* Step 1: key setup */
+    secp256k1_rand256(seckey_a[0]);
+    secp256k1_rand256(seckey_a[1]);
+    secp256k1_rand256(seckey_b[0]);
+    secp256k1_rand256(seckey_b[1]);
+    secp256k1_rand256(sec_adaptor);
+
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pk_a[0], seckey_a[0]));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pk_a[1], seckey_a[1]));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pk_b[0], seckey_b[0]));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pk_b[1], seckey_b[1]));
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pub_adaptor, sec_adaptor));
+
+    CHECK(secp256k1_musig_pubkey_combine(ctx, scratch, &combined_pk_a, pk_hash_a, pk_a, 2));
+    CHECK(secp256k1_musig_pubkey_combine(ctx, scratch, &combined_pk_b, pk_hash_b, pk_b, 2));
+
+    CHECK(secp256k1_musig_session_initialize(ctx, &musig_session_a[0], data_a, noncommit_a[0], seed, msg32_a, &combined_pk_a, pk_hash_a, 2, 0, seckey_a[0]));
+    CHECK(secp256k1_musig_session_initialize(ctx, &musig_session_a[1], data_a, noncommit_a[1], seed, msg32_a, &combined_pk_a, pk_hash_a, 2, 1, seckey_a[1]));
+    noncommit_a_ptr[0] = noncommit_a[0];
+    noncommit_a_ptr[1] = noncommit_a[1];
+
+    CHECK(secp256k1_musig_session_initialize(ctx, &musig_session_b[0], data_b, noncommit_b[0], seed, msg32_b, &combined_pk_b, pk_hash_b, 2, 0, seckey_b[0]));
+    CHECK(secp256k1_musig_session_initialize(ctx, &musig_session_b[1], data_b, noncommit_b[1], seed, msg32_b, &combined_pk_b, pk_hash_b, 2, 1, seckey_b[1]));
+    noncommit_b_ptr[0] = noncommit_b[0];
+    noncommit_b_ptr[1] = noncommit_b[1];
+
+    /* Step 2: Exchange nonces */
+    CHECK(secp256k1_musig_session_get_public_nonce(ctx, &musig_session_a[0], data_a, &pubnon_a[0], noncommit_a_ptr, 2));
+    CHECK(secp256k1_musig_session_get_public_nonce(ctx, &musig_session_a[1], data_a, &pubnon_a[1], noncommit_a_ptr, 2));
+    CHECK(secp256k1_musig_session_get_public_nonce(ctx, &musig_session_b[0], data_b, &pubnon_b[0], noncommit_b_ptr, 2));
+    CHECK(secp256k1_musig_session_get_public_nonce(ctx, &musig_session_b[1], data_b, &pubnon_b[1], noncommit_b_ptr, 2));
+    CHECK(secp256k1_musig_set_nonce(ctx, &data_a[0], &pubnon_a[0]));
+    CHECK(secp256k1_musig_set_nonce(ctx, &data_a[1], &pubnon_a[1]));
+    CHECK(secp256k1_musig_set_nonce(ctx, &data_b[0], &pubnon_b[0]));
+    CHECK(secp256k1_musig_set_nonce(ctx, &data_b[1], &pubnon_b[1]));
+    CHECK(secp256k1_musig_session_combine_nonces(ctx, &musig_session_a[0], data_a, 2, &nonce_is_negated_a, &pub_adaptor));
+    CHECK(secp256k1_musig_session_combine_nonces(ctx, &musig_session_a[1], data_a, 2, NULL, &pub_adaptor));
+    CHECK(secp256k1_musig_session_combine_nonces(ctx, &musig_session_b[0], data_b, 2, &nonce_is_negated_b, &pub_adaptor));
+    CHECK(secp256k1_musig_session_combine_nonces(ctx, &musig_session_b[1], data_b, 2, NULL, &pub_adaptor));
+
+    /* Step 3: Signer 0 produces partial signatures for both chains. */
+    CHECK(secp256k1_musig_partial_sign(ctx, &musig_session_a[0], &partial_sig_a[0]));
+    CHECK(secp256k1_musig_partial_sign(ctx, &musig_session_b[0], &partial_sig_b[0]));
+
+    /* Step 4: Signer 1 receives partial signatures, verifies them and creates a
+     * partial signature to send B-coins to signer 0. */
+    CHECK(secp256k1_musig_partial_sig_verify(ctx, &musig_session_a[1], data_a, &partial_sig_a[0], &pk_a[0]) == 1);
+    CHECK(secp256k1_musig_partial_sig_verify(ctx, &musig_session_b[1], data_b, &partial_sig_b[0], &pk_b[0]) == 1);
+    CHECK(secp256k1_musig_partial_sign(ctx, &musig_session_b[1], &partial_sig_b[1]));
+
+    /* Step 5: Signer 0 adapts its own partial signature and combines it with the
+     * partial signature from signer 1. This results in a complete signature which
+     * is broadcasted by signer 0 to take B-coins. */
+    CHECK(secp256k1_musig_partial_sig_adapt(ctx, &partial_sig_b_adapted[0], &partial_sig_b[0], sec_adaptor, nonce_is_negated_b));
+    memcpy(&partial_sig_b_adapted[1], &partial_sig_b[1], sizeof(partial_sig_b_adapted[1]));
+    CHECK(secp256k1_musig_partial_sig_combine(ctx, &musig_session_b[0], &final_sig_b, partial_sig_b_adapted, 2) == 1);
+    CHECK(secp256k1_schnorrsig_verify(ctx, &final_sig_b, msg32_b, &combined_pk_b) == 1);
+
+    /* Step 6: Signer 1 extracts adaptor from the published signature, applies it to
+     * other partial signature, and takes A-coins. */
+    CHECK(secp256k1_musig_extract_secret_adaptor(ctx, sec_adaptor_extracted, &final_sig_b, partial_sig_b, 2, nonce_is_negated_b) == 1);
+    CHECK(memcmp(sec_adaptor_extracted, sec_adaptor, sizeof(sec_adaptor)) == 0); /* in real life we couldn't check this, of course */
+    CHECK(secp256k1_musig_partial_sig_adapt(ctx, &partial_sig_a[0], &partial_sig_a[0], sec_adaptor_extracted, nonce_is_negated_a));
+    CHECK(secp256k1_musig_partial_sign(ctx, &musig_session_a[1], &partial_sig_a[1]));
+    CHECK(secp256k1_musig_partial_sig_combine(ctx, &musig_session_a[1], &final_sig_a, partial_sig_a, 2) == 1);
+    CHECK(secp256k1_schnorrsig_verify(ctx, &final_sig_a, msg32_a, &combined_pk_a) == 1);
+}
+
+/* Checks that hash initialized by secp256k1_musig_sha256_init_tagged has the
+ * expected state. */
+void sha256_tag_test(void) {
+    char tag[17] = "MuSig coefficient";
+    secp256k1_sha256 sha;
+    secp256k1_sha256 sha_tagged;
+    unsigned char buf[32];
+    unsigned char buf2[32];
+    size_t i;
+
+    secp256k1_sha256_initialize(&sha);
+    secp256k1_sha256_write(&sha, (unsigned char *) tag, 17);
+    secp256k1_sha256_finalize(&sha, buf);
+    /* buf = SHA256("MuSig coefficient") */
+
+    secp256k1_sha256_initialize(&sha);
+    secp256k1_sha256_write(&sha, buf, 32);
+    secp256k1_sha256_write(&sha, buf, 32);
+    /* Is buffer fully consumed? */
+    CHECK((sha.bytes & 0x3F) == 0);
+
+    /* Compare with tagged SHA */
+    secp256k1_musig_sha256_init_tagged(&sha_tagged);
+    for (i = 0; i < 8; i++) {
+        CHECK(sha_tagged.s[i] == sha.s[i]);
+    }
+    secp256k1_sha256_write(&sha, buf, 32);
+    secp256k1_sha256_write(&sha_tagged, buf, 32);
+    secp256k1_sha256_finalize(&sha, buf);
+    secp256k1_sha256_finalize(&sha_tagged, buf2);
+    CHECK(memcmp(buf, buf2, 32) == 0);
+}
+
+void run_musig_tests(void) {
+    int i;
+    secp256k1_scratch_space *scratch = secp256k1_scratch_space_create(ctx, 1024 * 1024);
+
+    musig_api_tests(scratch);
+    musig_state_machine_tests(scratch);
+    for (i = 0; i < count; i++) {
+        /* Run multiple times to ensure that the nonce is negated in some tests */
+        scriptless_atomic_swap(scratch);
+    }
+    sha256_tag_test();
+
+    secp256k1_scratch_space_destroy(scratch);
+}
+
+#endif
+

src/secp256k1/src/modules/schnorrsig/Makefile.am.include

@@ -0,0 +1,9 @@
+include_HEADERS += include/secp256k1_schnorrsig.h
+noinst_HEADERS += src/modules/schnorrsig/main_impl.h
+noinst_HEADERS += src/modules/schnorrsig/tests_impl.h
+if USE_BENCHMARK
+noinst_PROGRAMS += bench_schnorrsig
+bench_schnorrsig_SOURCES = src/bench_schnorrsig.c
+bench_schnorrsig_LDADD = libsecp256k1.la $(SECP_LIBS) $(COMMON_LIB)
+endif
+

src/secp256k1/src/modules/schnorrsig/main_impl.h

@@ -0,0 +1,339 @@
+/**********************************************************************
+ * Copyright (c) 2018 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_SCHNORRSIG_MAIN_
+#define _SECP256K1_MODULE_SCHNORRSIG_MAIN_
+
+#include "include/secp256k1.h"
+#include "include/secp256k1_schnorrsig.h"
+#include "hash.h"
+
+int secp256k1_schnorrsig_serialize(const secp256k1_context* ctx, unsigned char *out64, const secp256k1_schnorrsig* sig) {
+    (void) ctx;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(out64 != NULL);
+    ARG_CHECK(sig != NULL);
+    memcpy(out64, sig->data, 64);
+    return 1;
+}
+
+int secp256k1_schnorrsig_parse(const secp256k1_context* ctx, secp256k1_schnorrsig* sig, const unsigned char *in64) {
+    (void) ctx;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(in64 != NULL);
+    memcpy(sig->data, in64, 64);
+    return 1;
+}
+
+int secp256k1_schnorrsig_sign(const secp256k1_context* ctx, secp256k1_schnorrsig *sig, int *nonce_is_negated, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, void *ndata) {
+    secp256k1_scalar x;
+    secp256k1_scalar e;
+    secp256k1_scalar k;
+    secp256k1_gej pkj;
+    secp256k1_gej rj;
+    secp256k1_ge pk;
+    secp256k1_ge r;
+    secp256k1_sha256 sha;
+    int overflow;
+    unsigned char buf[33];
+    size_t buflen = sizeof(buf);
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(seckey != NULL);
+
+    if (noncefp == NULL) {
+        noncefp = secp256k1_nonce_function_bipschnorr;
+    }
+    secp256k1_scalar_set_b32(&x, seckey, &overflow);
+    /* Fail if the secret key is invalid. */
+    if (overflow || secp256k1_scalar_is_zero(&x)) {
+        memset(sig, 0, sizeof(*sig));
+        return 0;
+    }
+
+    secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pkj, &x);
+    secp256k1_ge_set_gej(&pk, &pkj);
+
+    if (!noncefp(buf, msg32, seckey, NULL, (void*)ndata, 0)) {
+        return 0;
+    }
+    secp256k1_scalar_set_b32(&k, buf, NULL);
+    if (secp256k1_scalar_is_zero(&k)) {
+        return 0;
+    }
+
+    secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &rj, &k);
+    secp256k1_ge_set_gej(&r, &rj);
+
+    if (nonce_is_negated != NULL) {
+        *nonce_is_negated = 0;
+    }
+    if (!secp256k1_fe_is_quad_var(&r.y)) {
+        secp256k1_scalar_negate(&k, &k);
+        if (nonce_is_negated != NULL) {
+            *nonce_is_negated = 1;
+        }
+    }
+    secp256k1_fe_normalize(&r.x);
+    secp256k1_fe_get_b32(&sig->data[0], &r.x);
+
+    secp256k1_sha256_initialize(&sha);
+    secp256k1_sha256_write(&sha, &sig->data[0], 32);
+    secp256k1_eckey_pubkey_serialize(&pk, buf, &buflen, 1);
+    secp256k1_sha256_write(&sha, buf, buflen);
+    secp256k1_sha256_write(&sha, msg32, 32);
+    secp256k1_sha256_finalize(&sha, buf);
+
+    secp256k1_scalar_set_b32(&e, buf, NULL);
+    secp256k1_scalar_mul(&e, &e, &x);
+    secp256k1_scalar_add(&e, &e, &k);
+
+    secp256k1_scalar_get_b32(&sig->data[32], &e);
+    secp256k1_scalar_clear(&k);
+    secp256k1_scalar_clear(&x);
+
+    return 1;
+}
+
+/* Helper function for verification and batch verification.
+ * Computes R = sG - eP. */
+static int secp256k1_schnorrsig_real_verify(const secp256k1_context* ctx, secp256k1_gej *rj, const secp256k1_scalar *s, const secp256k1_scalar *e, const secp256k1_pubkey *pk) {
+    secp256k1_scalar nege;
+    secp256k1_ge pkp;
+    secp256k1_gej pkj;
+
+    secp256k1_scalar_negate(&nege, e);
+
+    if (!secp256k1_pubkey_load(ctx, &pkp, pk)) {
+        return 0;
+    }
+    secp256k1_gej_set_ge(&pkj, &pkp);
+
+    /* rj =  s*G + (-e)*pkj */
+    secp256k1_ecmult(&ctx->ecmult_ctx, rj, &pkj, &nege, s);
+    return 1;
+}
+
+int secp256k1_schnorrsig_verify(const secp256k1_context* ctx, const secp256k1_schnorrsig *sig, const unsigned char *msg32, const secp256k1_pubkey *pk) {
+    secp256k1_scalar s;
+    secp256k1_scalar e;
+    secp256k1_gej rj;
+    secp256k1_fe rx;
+    secp256k1_sha256 sha;
+    unsigned char buf[33];
+    size_t buflen = sizeof(buf);
+    int overflow;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(sig != NULL);
+    ARG_CHECK(msg32 != NULL);
+    ARG_CHECK(pk != NULL);
+
+    if (!secp256k1_fe_set_b32(&rx, &sig->data[0])) {
+        return 0;
+    }
+
+    secp256k1_scalar_set_b32(&s, &sig->data[32], &overflow);
+    if (overflow) {
+        return 0;
+    }
+
+    secp256k1_sha256_initialize(&sha);
+    secp256k1_sha256_write(&sha, &sig->data[0], 32);
+    secp256k1_ec_pubkey_serialize(ctx, buf, &buflen, pk, SECP256K1_EC_COMPRESSED);
+    secp256k1_sha256_write(&sha, buf, buflen);
+    secp256k1_sha256_write(&sha, msg32, 32);
+    secp256k1_sha256_finalize(&sha, buf);
+    secp256k1_scalar_set_b32(&e, buf, NULL);
+
+    if (!secp256k1_schnorrsig_real_verify(ctx, &rj, &s, &e, pk)
+        || !secp256k1_gej_has_quad_y_var(&rj) /* fails if rj is infinity */
+        || !secp256k1_gej_eq_x_var(&rx, &rj)) {
+        return 0;
+    }
+
+    return 1;
+}
+
+/* Data that is used by the batch verification ecmult callback */
+typedef struct {
+    const secp256k1_context *ctx;
+    /* Seed for the random number generator */
+    unsigned char chacha_seed[32];
+    /* Caches randomizers generated by the PRNG which returns two randomizers per call. Caching
+     * avoids having to call the PRNG twice as often. The very first randomizer will be set to 1 and
+     * the PRNG is called at every odd indexed schnorrsig to fill the cache. */
+    secp256k1_scalar randomizer_cache[2];
+    /* Signature, message, public key tuples to verify */
+    const secp256k1_schnorrsig *const *sig;
+    const unsigned char *const *msg32;
+    const secp256k1_pubkey *const *pk;
+    size_t n_sigs;
+} secp256k1_schnorrsig_verify_ecmult_context;
+
+/* Callback function which is called by ecmult_multi in order to convert the ecmult_context
+ * consisting of signature, message and public key tuples into scalars and points. */
+static int secp256k1_schnorrsig_verify_batch_ecmult_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *data) {
+    secp256k1_schnorrsig_verify_ecmult_context *ecmult_context = (secp256k1_schnorrsig_verify_ecmult_context *) data;
+
+    if (idx % 4 == 2) {
+        /* Every idx corresponds to a (scalar,point)-tuple. So this callback is called with 4
+         * consecutive tuples before we need to call the RNG for new randomizers:
+         * (-randomizer_cache[0], R1)
+         * (-randomizer_cache[0]*e1, P1)
+         * (-randomizer_cache[1], R2)
+         * (-randomizer_cache[1]*e2, P2) */
+        secp256k1_scalar_chacha20(&ecmult_context->randomizer_cache[0], &ecmult_context->randomizer_cache[1], ecmult_context->chacha_seed, idx / 4);
+    }
+
+    /* R */
+    if (idx % 2 == 0) {
+        secp256k1_fe rx;
+        *sc = ecmult_context->randomizer_cache[(idx / 2) % 2];
+        if (!secp256k1_fe_set_b32(&rx, &ecmult_context->sig[idx / 2]->data[0])) {
+            return 0;
+        }
+        if (!secp256k1_ge_set_xquad(pt, &rx)) {
+            return 0;
+        }
+    /* eP */
+    } else {
+        unsigned char buf[33];
+        size_t buflen = sizeof(buf);
+        secp256k1_sha256 sha;
+        secp256k1_sha256_initialize(&sha);
+        secp256k1_sha256_write(&sha, &ecmult_context->sig[idx / 2]->data[0], 32);
+        secp256k1_ec_pubkey_serialize(ecmult_context->ctx, buf, &buflen, ecmult_context->pk[idx / 2], SECP256K1_EC_COMPRESSED);
+        secp256k1_sha256_write(&sha, buf, buflen);
+        secp256k1_sha256_write(&sha, ecmult_context->msg32[idx / 2], 32);
+        secp256k1_sha256_finalize(&sha, buf);
+
+        secp256k1_scalar_set_b32(sc, buf, NULL);
+        secp256k1_scalar_mul(sc, sc, &ecmult_context->randomizer_cache[(idx / 2) % 2]);
+
+        if (!secp256k1_pubkey_load(ecmult_context->ctx, pt, ecmult_context->pk[idx / 2])) {
+            return 0;
+        }
+    }
+    return 1;
+}
+
+/** Helper function for batch verification. Hashes signature verification data into the
+ *  randomization seed and initializes ecmult_context.
+ *
+ *  Returns 1 if the randomizer was successfully initialized.
+ *
+ *  Args:    ctx: a secp256k1 context object
+ *  Out: ecmult_context: context for batch_ecmult_callback
+ *  In/Out   sha: an initialized sha256 object which hashes the schnorrsig input in order to get a
+ *                seed for the randomizer PRNG
+ *  In:      sig: array of signatures, or NULL if there are no signatures
+ *         msg32: array of messages, or NULL if there are no signatures
+ *            pk: array of public keys, or NULL if there are no signatures
+ *        n_sigs: number of signatures in above arrays (must be 0 if they are NULL)
+ */
+int secp256k1_schnorrsig_verify_batch_init_randomizer(const secp256k1_context *ctx, secp256k1_schnorrsig_verify_ecmult_context *ecmult_context, secp256k1_sha256 *sha, const secp256k1_schnorrsig *const *sig, const unsigned char *const *msg32, const secp256k1_pubkey *const *pk, size_t n_sigs) {
+    size_t i;
+
+    if (n_sigs > 0) {
+        ARG_CHECK(sig != NULL);
+        ARG_CHECK(msg32 != NULL);
+        ARG_CHECK(pk != NULL);
+    }
+
+    for (i = 0; i < n_sigs; i++) {
+        unsigned char buf[33];
+        size_t buflen = sizeof(buf);
+        secp256k1_sha256_write(sha, sig[i]->data, 64);
+        secp256k1_sha256_write(sha, msg32[i], 32);
+        secp256k1_ec_pubkey_serialize(ctx, buf, &buflen, pk[i], SECP256K1_EC_COMPRESSED);
+        secp256k1_sha256_write(sha, buf, 32);
+    }
+    ecmult_context->ctx = ctx;
+    ecmult_context->sig = sig;
+    ecmult_context->msg32 = msg32;
+    ecmult_context->pk = pk;
+    ecmult_context->n_sigs = n_sigs;
+
+    return 1;
+}
+
+/** Helper function for batch verification. Sums the s part of all signatures multiplied by their
+ *  randomizer.
+ *
+ *  Returns 1 if s is successfully summed.
+ *
+ *  In/Out: s: the s part of the input sigs is added to this s argument
+ *  In:  chacha_seed: PRNG seed for computing randomizers
+ *        sig: array of signatures, or NULL if there are no signatures
+ *     n_sigs: number of signatures in above array (must be 0 if they are NULL)
+ */
+int secp256k1_schnorrsig_verify_batch_sum_s(secp256k1_scalar *s, unsigned char *chacha_seed, const secp256k1_schnorrsig *const *sig, size_t n_sigs) {
+    secp256k1_scalar randomizer_cache[2];
+    size_t i;
+
+    secp256k1_scalar_set_int(&randomizer_cache[0], 1);
+    for (i = 0; i < n_sigs; i++) {
+        int overflow;
+        secp256k1_scalar term;
+        if (i % 2 == 1) {
+            secp256k1_scalar_chacha20(&randomizer_cache[0], &randomizer_cache[1], chacha_seed, i / 2);
+        }
+
+        secp256k1_scalar_set_b32(&term, &sig[i]->data[32], &overflow);
+        if (overflow) {
+            return 0;
+        }
+        secp256k1_scalar_mul(&term, &term, &randomizer_cache[i % 2]);
+        secp256k1_scalar_add(s, s, &term);
+    }
+    return 1;
+}
+
+/* schnorrsig batch verification.
+ * Seeds a random number generator with the inputs and derives a random number ai for every
+ * signature i. Fails if y-coordinate of any R is not a quadratic residue or if
+ * 0 != -(s1 + a2*s2 + ... + au*su)G + R1 + a2*R2 + ... + au*Ru + e1*P1 + (a2*e2)P2 + ... + (au*eu)Pu. */
+int secp256k1_schnorrsig_verify_batch(const secp256k1_context *ctx, secp256k1_scratch *scratch, const secp256k1_schnorrsig *const *sig, const unsigned char *const *msg32, const secp256k1_pubkey *const *pk, size_t n_sigs) {
+    secp256k1_schnorrsig_verify_ecmult_context ecmult_context;
+    secp256k1_sha256 sha;
+    secp256k1_scalar s;
+    secp256k1_gej rj;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx));
+    ARG_CHECK(scratch != NULL);
+    /* Check that n_sigs is less than half of the maximum size_t value. This is necessary because
+     * the number of points given to ecmult_multi is 2*n_sigs. */
+    ARG_CHECK(n_sigs <= SIZE_MAX / 2);
+    /* Check that n_sigs is less than 2^31 to ensure the same behavior of this function on 32-bit
+     * and 64-bit platforms. */
+    ARG_CHECK(n_sigs < (size_t)(1 << 31));
+
+    secp256k1_sha256_initialize(&sha);
+    if (!secp256k1_schnorrsig_verify_batch_init_randomizer(ctx, &ecmult_context, &sha, sig, msg32, pk, n_sigs)) {
+        return 0;
+    }
+    secp256k1_sha256_finalize(&sha, ecmult_context.chacha_seed);
+    secp256k1_scalar_set_int(&ecmult_context.randomizer_cache[0], 1);
+
+    secp256k1_scalar_clear(&s);
+    if (!secp256k1_schnorrsig_verify_batch_sum_s(&s, ecmult_context.chacha_seed, sig, n_sigs)) {
+        return 0;
+    }
+    secp256k1_scalar_negate(&s, &s);
+
+    return secp256k1_ecmult_multi_var(&ctx->ecmult_ctx, scratch, &rj, &s, secp256k1_schnorrsig_verify_batch_ecmult_callback, (void *) &ecmult_context, 2 * n_sigs)
+            && secp256k1_gej_is_infinity(&rj);
+}
+
+#endif
+

src/secp256k1/src/modules/schnorrsig/tests_impl.h

@@ -0,0 +1,727 @@
+/**********************************************************************
+ * Copyright (c) 2018 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_MODULE_SCHNORRSIG_TESTS_
+#define _SECP256K1_MODULE_SCHNORRSIG_TESTS_
+
+#include "secp256k1_schnorrsig.h"
+
+void test_schnorrsig_serialize(void) {
+    secp256k1_schnorrsig sig;
+    unsigned char in[64];
+    unsigned char out[64];
+
+    memset(in, 0x12, 64);
+    CHECK(secp256k1_schnorrsig_parse(ctx, &sig, in));
+    CHECK(secp256k1_schnorrsig_serialize(ctx, out, &sig));
+    CHECK(memcmp(in, out, 64) == 0);
+}
+
+void test_schnorrsig_api(secp256k1_scratch_space *scratch) {
+    unsigned char sk1[32];
+    unsigned char sk2[32];
+    unsigned char sk3[32];
+    unsigned char msg[32];
+    unsigned char sig64[64];
+    secp256k1_pubkey pk[3];
+    secp256k1_schnorrsig sig;
+    const secp256k1_schnorrsig *sigptr = &sig;
+    const unsigned char *msgptr = msg;
+    const secp256k1_pubkey *pkptr = &pk[0];
+    int nonce_is_negated;
+
+    /** setup **/
+    secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+    secp256k1_context *sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN);
+    secp256k1_context *vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY);
+    secp256k1_context *both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+    int ecount;
+
+    secp256k1_context_set_error_callback(none, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(sign, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(vrfy, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_error_callback(both, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount);
+    secp256k1_context_set_illegal_callback(both, counting_illegal_callback_fn, &ecount);
+
+    secp256k1_rand256(sk1);
+    secp256k1_rand256(sk2);
+    secp256k1_rand256(sk3);
+    secp256k1_rand256(msg);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pk[0], sk1) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pk[1], sk2) == 1);
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pk[2], sk3) == 1);
+
+    /** main test body **/
+    ecount = 0;
+    CHECK(secp256k1_schnorrsig_sign(none, &sig, &nonce_is_negated, msg, sk1, NULL, NULL) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_schnorrsig_sign(vrfy, &sig, &nonce_is_negated, msg, sk1, NULL, NULL) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_schnorrsig_sign(sign, &sig, &nonce_is_negated, msg, sk1, NULL, NULL) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_schnorrsig_sign(sign, NULL, &nonce_is_negated, msg, sk1, NULL, NULL) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_schnorrsig_sign(sign, &sig, NULL, msg, sk1, NULL, NULL) == 1);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_schnorrsig_sign(sign, &sig, &nonce_is_negated, NULL, sk1, NULL, NULL) == 0);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_schnorrsig_sign(sign, &sig, &nonce_is_negated, msg, NULL, NULL, NULL) == 0);
+    CHECK(ecount == 5);
+
+    ecount = 0;
+    CHECK(secp256k1_schnorrsig_serialize(none, sig64, &sig) == 1);
+    CHECK(ecount == 0);
+    CHECK(secp256k1_schnorrsig_serialize(none, NULL, &sig) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_schnorrsig_serialize(none, sig64, NULL) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_schnorrsig_parse(none, &sig, sig64) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_schnorrsig_parse(none, NULL, sig64) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_schnorrsig_parse(none, &sig, NULL) == 0);
+    CHECK(ecount == 4);
+
+    ecount = 0;
+    CHECK(secp256k1_schnorrsig_verify(none, &sig, msg, &pk[0]) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_schnorrsig_verify(sign, &sig, msg, &pk[0]) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_schnorrsig_verify(vrfy, &sig, msg, &pk[0]) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_schnorrsig_verify(vrfy, NULL, msg, &pk[0]) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_schnorrsig_verify(vrfy, &sig, NULL, &pk[0]) == 0);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_schnorrsig_verify(vrfy, &sig, msg, NULL) == 0);
+    CHECK(ecount == 5);
+
+    ecount = 0;
+    CHECK(secp256k1_schnorrsig_verify_batch(none, scratch, &sigptr, &msgptr, &pkptr, 1) == 0);
+    CHECK(ecount == 1);
+    CHECK(secp256k1_schnorrsig_verify_batch(sign, scratch, &sigptr, &msgptr, &pkptr, 1) == 0);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_schnorrsig_verify_batch(vrfy, scratch, &sigptr, &msgptr, &pkptr, 1) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_schnorrsig_verify_batch(vrfy, scratch, NULL, NULL, NULL, 0) == 1);
+    CHECK(ecount == 2);
+    CHECK(secp256k1_schnorrsig_verify_batch(vrfy, scratch, NULL, &msgptr, &pkptr, 1) == 0);
+    CHECK(ecount == 3);
+    CHECK(secp256k1_schnorrsig_verify_batch(vrfy, scratch, &sigptr, NULL, &pkptr, 1) == 0);
+    CHECK(ecount == 4);
+    CHECK(secp256k1_schnorrsig_verify_batch(vrfy, scratch, &sigptr, &msgptr, NULL, 1) == 0);
+    CHECK(ecount == 5);
+    CHECK(secp256k1_schnorrsig_verify_batch(vrfy, scratch, &sigptr, &msgptr, &pkptr, (size_t)1 << (sizeof(size_t)*8-1)) == 0);
+    CHECK(ecount == 6);
+    CHECK(secp256k1_schnorrsig_verify_batch(vrfy, scratch, &sigptr, &msgptr, &pkptr, 1 << 31) == 0);
+    CHECK(ecount == 7);
+
+    secp256k1_context_destroy(none);
+    secp256k1_context_destroy(sign);
+    secp256k1_context_destroy(vrfy);
+    secp256k1_context_destroy(both);
+}
+
+/* Helper function for schnorrsig_bip_vectors
+ * Signs the message and checks that it's the same as expected_sig. */
+void test_schnorrsig_bip_vectors_check_signing(const unsigned char *sk, const unsigned char *pk_serialized, const unsigned char *msg, const unsigned char *expected_sig, const int expected_nonce_is_negated) {
+    secp256k1_schnorrsig sig;
+    unsigned char serialized_sig[64];
+    secp256k1_pubkey pk;
+    int nonce_is_negated;
+
+    CHECK(secp256k1_schnorrsig_sign(ctx, &sig, &nonce_is_negated, msg, sk, NULL, NULL));
+    CHECK(nonce_is_negated == expected_nonce_is_negated);
+    CHECK(secp256k1_schnorrsig_serialize(ctx, serialized_sig, &sig));
+    CHECK(memcmp(serialized_sig, expected_sig, 64) == 0);
+
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pk, pk_serialized, 33));
+    CHECK(secp256k1_schnorrsig_verify(ctx, &sig, msg, &pk));
+}
+
+/* Helper function for schnorrsig_bip_vectors
+ * Checks that both verify and verify_batch return the same value as expected. */
+void test_schnorrsig_bip_vectors_check_verify(secp256k1_scratch_space *scratch, const unsigned char *pk_serialized, const unsigned char *msg32, const unsigned char *sig_serialized, int expected) {
+    const unsigned char *msg_arr[1];
+    const secp256k1_schnorrsig *sig_arr[1];
+    const secp256k1_pubkey *pk_arr[1];
+    secp256k1_pubkey pk;
+    secp256k1_schnorrsig sig;
+
+    CHECK(secp256k1_ec_pubkey_parse(ctx, &pk, pk_serialized, 33));
+    CHECK(secp256k1_schnorrsig_parse(ctx, &sig, sig_serialized));
+
+    sig_arr[0] = &sig;
+    msg_arr[0] = msg32;
+    pk_arr[0] = &pk;
+
+    CHECK(expected == secp256k1_schnorrsig_verify(ctx, &sig, msg32, &pk));
+    CHECK(expected == secp256k1_schnorrsig_verify_batch(ctx, scratch, sig_arr, msg_arr, pk_arr, 1));
+}
+
+/* Test vectors according to BIP-schnorr
+ * (https://github.com/sipa/bips/blob/7f6a73e53c8bbcf2d008ea0546f76433e22094a8/bip-schnorr/test-vectors.csv).
+ */
+void test_schnorrsig_bip_vectors(secp256k1_scratch_space *scratch) {
+    {
+        /* Test vector 1 */
+        const unsigned char sk1[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01
+        };
+        const unsigned char pk1[33] = {
+            0x02, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB,
+            0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B,
+            0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28,
+            0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17,
+            0x98
+        };
+        const unsigned char msg1[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
+        };
+        const unsigned char sig1[64] = {
+            0x78, 0x7A, 0x84, 0x8E, 0x71, 0x04, 0x3D, 0x28,
+            0x0C, 0x50, 0x47, 0x0E, 0x8E, 0x15, 0x32, 0xB2,
+            0xDD, 0x5D, 0x20, 0xEE, 0x91, 0x2A, 0x45, 0xDB,
+            0xDD, 0x2B, 0xD1, 0xDF, 0xBF, 0x18, 0x7E, 0xF6,
+            0x70, 0x31, 0xA9, 0x88, 0x31, 0x85, 0x9D, 0xC3,
+            0x4D, 0xFF, 0xEE, 0xDD, 0xA8, 0x68, 0x31, 0x84,
+            0x2C, 0xCD, 0x00, 0x79, 0xE1, 0xF9, 0x2A, 0xF1,
+            0x77, 0xF7, 0xF2, 0x2C, 0xC1, 0xDC, 0xED, 0x05
+        };
+        test_schnorrsig_bip_vectors_check_signing(sk1, pk1, msg1, sig1, 1);
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk1, msg1, sig1, 1);
+    }
+    {
+        /* Test vector 2 */
+        const unsigned char sk2[32] = {
+            0xB7, 0xE1, 0x51, 0x62, 0x8A, 0xED, 0x2A, 0x6A,
+            0xBF, 0x71, 0x58, 0x80, 0x9C, 0xF4, 0xF3, 0xC7,
+            0x62, 0xE7, 0x16, 0x0F, 0x38, 0xB4, 0xDA, 0x56,
+            0xA7, 0x84, 0xD9, 0x04, 0x51, 0x90, 0xCF, 0xEF
+        };
+        const unsigned char pk2[33] = {
+            0x02, 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C,
+            0x5F, 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41,
+            0xBE, 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE,
+            0xD8, 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6,
+            0x59
+        };
+        const unsigned char msg2[32] = {
+            0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3,
+            0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44,
+            0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0,
+            0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89
+        };
+        const unsigned char sig2[64] = {
+            0x2A, 0x29, 0x8D, 0xAC, 0xAE, 0x57, 0x39, 0x5A,
+            0x15, 0xD0, 0x79, 0x5D, 0xDB, 0xFD, 0x1D, 0xCB,
+            0x56, 0x4D, 0xA8, 0x2B, 0x0F, 0x26, 0x9B, 0xC7,
+            0x0A, 0x74, 0xF8, 0x22, 0x04, 0x29, 0xBA, 0x1D,
+            0x1E, 0x51, 0xA2, 0x2C, 0xCE, 0xC3, 0x55, 0x99,
+            0xB8, 0xF2, 0x66, 0x91, 0x22, 0x81, 0xF8, 0x36,
+            0x5F, 0xFC, 0x2D, 0x03, 0x5A, 0x23, 0x04, 0x34,
+            0xA1, 0xA6, 0x4D, 0xC5, 0x9F, 0x70, 0x13, 0xFD
+        };
+        test_schnorrsig_bip_vectors_check_signing(sk2, pk2, msg2, sig2, 0);
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk2, msg2, sig2, 1);
+    }
+    {
+        /* Test vector 3 */
+        const unsigned char sk3[32] = {
+            0xC9, 0x0F, 0xDA, 0xA2, 0x21, 0x68, 0xC2, 0x34,
+            0xC4, 0xC6, 0x62, 0x8B, 0x80, 0xDC, 0x1C, 0xD1,
+            0x29, 0x02, 0x4E, 0x08, 0x8A, 0x67, 0xCC, 0x74,
+            0x02, 0x0B, 0xBE, 0xA6, 0x3B, 0x14, 0xE5, 0xC7
+        };
+        const unsigned char pk3[33] = {
+            0x03, 0xFA, 0xC2, 0x11, 0x4C, 0x2F, 0xBB, 0x09,
+            0x15, 0x27, 0xEB, 0x7C, 0x64, 0xEC, 0xB1, 0x1F,
+            0x80, 0x21, 0xCB, 0x45, 0xE8, 0xE7, 0x80, 0x9D,
+            0x3C, 0x09, 0x38, 0xE4, 0xB8, 0xC0, 0xE5, 0xF8,
+            0x4B
+        };
+        const unsigned char msg3[32] = {
+            0x5E, 0x2D, 0x58, 0xD8, 0xB3, 0xBC, 0xDF, 0x1A,
+            0xBA, 0xDE, 0xC7, 0x82, 0x90, 0x54, 0xF9, 0x0D,
+            0xDA, 0x98, 0x05, 0xAA, 0xB5, 0x6C, 0x77, 0x33,
+            0x30, 0x24, 0xB9, 0xD0, 0xA5, 0x08, 0xB7, 0x5C
+        };
+        const unsigned char sig3[64] = {
+            0x00, 0xDA, 0x9B, 0x08, 0x17, 0x2A, 0x9B, 0x6F,
+            0x04, 0x66, 0xA2, 0xDE, 0xFD, 0x81, 0x7F, 0x2D,
+            0x7A, 0xB4, 0x37, 0xE0, 0xD2, 0x53, 0xCB, 0x53,
+            0x95, 0xA9, 0x63, 0x86, 0x6B, 0x35, 0x74, 0xBE,
+            0x00, 0x88, 0x03, 0x71, 0xD0, 0x17, 0x66, 0x93,
+            0x5B, 0x92, 0xD2, 0xAB, 0x4C, 0xD5, 0xC8, 0xA2,
+            0xA5, 0x83, 0x7E, 0xC5, 0x7F, 0xED, 0x76, 0x60,
+            0x77, 0x3A, 0x05, 0xF0, 0xDE, 0x14, 0x23, 0x80
+        };
+        test_schnorrsig_bip_vectors_check_signing(sk3, pk3, msg3, sig3, 0);
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk3, msg3, sig3, 1);
+    }
+    {
+        /* Test vector 4 */
+        const unsigned char pk4[33] = {
+            0x03, 0xDE, 0xFD, 0xEA, 0x4C, 0xDB, 0x67, 0x77,
+            0x50, 0xA4, 0x20, 0xFE, 0xE8, 0x07, 0xEA, 0xCF,
+            0x21, 0xEB, 0x98, 0x98, 0xAE, 0x79, 0xB9, 0x76,
+            0x87, 0x66, 0xE4, 0xFA, 0xA0, 0x4A, 0x2D, 0x4A,
+            0x34
+        };
+        const unsigned char msg4[32] = {
+            0x4D, 0xF3, 0xC3, 0xF6, 0x8F, 0xCC, 0x83, 0xB2,
+            0x7E, 0x9D, 0x42, 0xC9, 0x04, 0x31, 0xA7, 0x24,
+            0x99, 0xF1, 0x78, 0x75, 0xC8, 0x1A, 0x59, 0x9B,
+            0x56, 0x6C, 0x98, 0x89, 0xB9, 0x69, 0x67, 0x03
+        };
+        const unsigned char sig4[64] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x3B, 0x78, 0xCE, 0x56, 0x3F,
+            0x89, 0xA0, 0xED, 0x94, 0x14, 0xF5, 0xAA, 0x28,
+            0xAD, 0x0D, 0x96, 0xD6, 0x79, 0x5F, 0x9C, 0x63,
+            0x02, 0xA8, 0xDC, 0x32, 0xE6, 0x4E, 0x86, 0xA3,
+            0x33, 0xF2, 0x0E, 0xF5, 0x6E, 0xAC, 0x9B, 0xA3,
+            0x0B, 0x72, 0x46, 0xD6, 0xD2, 0x5E, 0x22, 0xAD,
+            0xB8, 0xC6, 0xBE, 0x1A, 0xEB, 0x08, 0xD4, 0x9D
+        };
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk4, msg4, sig4, 1);
+    }
+    {
+        /* Test vector 5 */
+        const unsigned char pk5[33] = {
+            0x03, 0x1B, 0x84, 0xC5, 0x56, 0x7B, 0x12, 0x64,
+            0x40, 0x99, 0x5D, 0x3E, 0xD5, 0xAA, 0xBA, 0x05,
+            0x65, 0xD7, 0x1E, 0x18, 0x34, 0x60, 0x48, 0x19,
+            0xFF, 0x9C, 0x17, 0xF5, 0xE9, 0xD5, 0xDD, 0x07,
+            0x8F
+        };
+        const unsigned char msg5[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
+        };
+        const unsigned char sig5[64] = {
+            0x52, 0x81, 0x85, 0x79, 0xAC, 0xA5, 0x97, 0x67,
+            0xE3, 0x29, 0x1D, 0x91, 0xB7, 0x6B, 0x63, 0x7B,
+            0xEF, 0x06, 0x20, 0x83, 0x28, 0x49, 0x92, 0xF2,
+            0xD9, 0x5F, 0x56, 0x4C, 0xA6, 0xCB, 0x4E, 0x35,
+            0x30, 0xB1, 0xDA, 0x84, 0x9C, 0x8E, 0x83, 0x04,
+            0xAD, 0xC0, 0xCF, 0xE8, 0x70, 0x66, 0x03, 0x34,
+            0xB3, 0xCF, 0xC1, 0x8E, 0x82, 0x5E, 0xF1, 0xDB,
+            0x34, 0xCF, 0xAE, 0x3D, 0xFC, 0x5D, 0x81, 0x87
+        };
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk5, msg5, sig5, 1);
+    }
+    {
+        /* Test vector 6 */
+        const unsigned char pk6[33] = {
+            0x03, 0xFA, 0xC2, 0x11, 0x4C, 0x2F, 0xBB, 0x09,
+            0x15, 0x27, 0xEB, 0x7C, 0x64, 0xEC, 0xB1, 0x1F,
+            0x80, 0x21, 0xCB, 0x45, 0xE8, 0xE7, 0x80, 0x9D,
+            0x3C, 0x09, 0x38, 0xE4, 0xB8, 0xC0, 0xE5, 0xF8,
+            0x4B
+        };
+        const unsigned char msg6[32] = {
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
+        };
+        const unsigned char sig6[64] = {
+            0x57, 0x0D, 0xD4, 0xCA, 0x83, 0xD4, 0xE6, 0x31,
+            0x7B, 0x8E, 0xE6, 0xBA, 0xE8, 0x34, 0x67, 0xA1,
+            0xBF, 0x41, 0x9D, 0x07, 0x67, 0x12, 0x2D, 0xE4,
+            0x09, 0x39, 0x44, 0x14, 0xB0, 0x50, 0x80, 0xDC,
+            0xE9, 0xEE, 0x5F, 0x23, 0x7C, 0xBD, 0x10, 0x8E,
+            0xAB, 0xAE, 0x1E, 0x37, 0x75, 0x9A, 0xE4, 0x7F,
+            0x8E, 0x42, 0x03, 0xDA, 0x35, 0x32, 0xEB, 0x28,
+            0xDB, 0x86, 0x0F, 0x33, 0xD6, 0x2D, 0x49, 0xBD
+        };
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk6, msg6, sig6, 1);
+    }
+    {
+        /* Test vector 7 */
+        const unsigned char pk7[33] = {
+            0x03, 0xEE, 0xFD, 0xEA, 0x4C, 0xDB, 0x67, 0x77,
+            0x50, 0xA4, 0x20, 0xFE, 0xE8, 0x07, 0xEA, 0xCF,
+            0x21, 0xEB, 0x98, 0x98, 0xAE, 0x79, 0xB9, 0x76,
+            0x87, 0x66, 0xE4, 0xFA, 0xA0, 0x4A, 0x2D, 0x4A,
+            0x34
+        };
+        secp256k1_pubkey pk7_parsed;
+        /* No need to check the signature of the test vector as parsing the pubkey already fails */
+        CHECK(!secp256k1_ec_pubkey_parse(ctx, &pk7_parsed, pk7, 33));
+    }
+    {
+        /* Test vector 8 */
+        const unsigned char pk8[33] = {
+            0x02, 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C,
+            0x5F, 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41,
+            0xBE, 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE,
+            0xD8, 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6,
+            0x59
+        };
+        const unsigned char msg8[32] = {
+            0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3,
+            0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44,
+            0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0,
+            0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89
+        };
+        const unsigned char sig8[64] = {
+            0x2A, 0x29, 0x8D, 0xAC, 0xAE, 0x57, 0x39, 0x5A,
+            0x15, 0xD0, 0x79, 0x5D, 0xDB, 0xFD, 0x1D, 0xCB,
+            0x56, 0x4D, 0xA8, 0x2B, 0x0F, 0x26, 0x9B, 0xC7,
+            0x0A, 0x74, 0xF8, 0x22, 0x04, 0x29, 0xBA, 0x1D,
+            0xFA, 0x16, 0xAE, 0xE0, 0x66, 0x09, 0x28, 0x0A,
+            0x19, 0xB6, 0x7A, 0x24, 0xE1, 0x97, 0x7E, 0x46,
+            0x97, 0x71, 0x2B, 0x5F, 0xD2, 0x94, 0x39, 0x14,
+            0xEC, 0xD5, 0xF7, 0x30, 0x90, 0x1B, 0x4A, 0xB7
+        };
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk8, msg8, sig8, 0);
+    }
+    {
+        /* Test vector 9 */
+        const unsigned char pk9[33] = {
+            0x03, 0xFA, 0xC2, 0x11, 0x4C, 0x2F, 0xBB, 0x09,
+            0x15, 0x27, 0xEB, 0x7C, 0x64, 0xEC, 0xB1, 0x1F,
+            0x80, 0x21, 0xCB, 0x45, 0xE8, 0xE7, 0x80, 0x9D,
+            0x3C, 0x09, 0x38, 0xE4, 0xB8, 0xC0, 0xE5, 0xF8,
+            0x4B
+        };
+        const unsigned char msg9[32] = {
+            0x5E, 0x2D, 0x58, 0xD8, 0xB3, 0xBC, 0xDF, 0x1A,
+            0xBA, 0xDE, 0xC7, 0x82, 0x90, 0x54, 0xF9, 0x0D,
+            0xDA, 0x98, 0x05, 0xAA, 0xB5, 0x6C, 0x77, 0x33,
+            0x30, 0x24, 0xB9, 0xD0, 0xA5, 0x08, 0xB7, 0x5C
+        };
+        const unsigned char sig9[64] = {
+            0x00, 0xDA, 0x9B, 0x08, 0x17, 0x2A, 0x9B, 0x6F,
+            0x04, 0x66, 0xA2, 0xDE, 0xFD, 0x81, 0x7F, 0x2D,
+            0x7A, 0xB4, 0x37, 0xE0, 0xD2, 0x53, 0xCB, 0x53,
+            0x95, 0xA9, 0x63, 0x86, 0x6B, 0x35, 0x74, 0xBE,
+            0xD0, 0x92, 0xF9, 0xD8, 0x60, 0xF1, 0x77, 0x6A,
+            0x1F, 0x74, 0x12, 0xAD, 0x8A, 0x1E, 0xB5, 0x0D,
+            0xAC, 0xCC, 0x22, 0x2B, 0xC8, 0xC0, 0xE2, 0x6B,
+            0x20, 0x56, 0xDF, 0x2F, 0x27, 0x3E, 0xFD, 0xEC
+        };
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk9, msg9, sig9, 0);
+    }
+    {
+        /* Test vector 10 */
+        const unsigned char pk10[33] = {
+            0x02, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB,
+            0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B,
+            0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28,
+            0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17,
+            0x98
+        };
+        const unsigned char msg10[32] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
+        };
+        const unsigned char sig10[64] = {
+            0x78, 0x7A, 0x84, 0x8E, 0x71, 0x04, 0x3D, 0x28,
+            0x0C, 0x50, 0x47, 0x0E, 0x8E, 0x15, 0x32, 0xB2,
+            0xDD, 0x5D, 0x20, 0xEE, 0x91, 0x2A, 0x45, 0xDB,
+            0xDD, 0x2B, 0xD1, 0xDF, 0xBF, 0x18, 0x7E, 0xF6,
+            0x8F, 0xCE, 0x56, 0x77, 0xCE, 0x7A, 0x62, 0x3C,
+            0xB2, 0x00, 0x11, 0x22, 0x57, 0x97, 0xCE, 0x7A,
+            0x8D, 0xE1, 0xDC, 0x6C, 0xCD, 0x4F, 0x75, 0x4A,
+            0x47, 0xDA, 0x6C, 0x60, 0x0E, 0x59, 0x54, 0x3C
+        };
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk10, msg10, sig10, 0);
+    }
+    {
+        /* Test vector 11 */
+        const unsigned char pk11[33] = {
+            0x03, 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C,
+            0x5F, 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41,
+            0xBE, 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE,
+            0xD8, 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6,
+            0x59
+        };
+        const unsigned char msg11[32] = {
+            0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3,
+            0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44,
+            0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0,
+            0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89
+        };
+        const unsigned char sig11[64] = {
+            0x2A, 0x29, 0x8D, 0xAC, 0xAE, 0x57, 0x39, 0x5A,
+            0x15, 0xD0, 0x79, 0x5D, 0xDB, 0xFD, 0x1D, 0xCB,
+            0x56, 0x4D, 0xA8, 0x2B, 0x0F, 0x26, 0x9B, 0xC7,
+            0x0A, 0x74, 0xF8, 0x22, 0x04, 0x29, 0xBA, 0x1D,
+            0x1E, 0x51, 0xA2, 0x2C, 0xCE, 0xC3, 0x55, 0x99,
+            0xB8, 0xF2, 0x66, 0x91, 0x22, 0x81, 0xF8, 0x36,
+            0x5F, 0xFC, 0x2D, 0x03, 0x5A, 0x23, 0x04, 0x34,
+            0xA1, 0xA6, 0x4D, 0xC5, 0x9F, 0x70, 0x13, 0xFD
+        };
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk11, msg11, sig11, 0);
+    }
+    {
+        /* Test vector 12 */
+        const unsigned char pk12[33] = {
+            0x02, 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C,
+            0x5F, 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41,
+            0xBE, 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE,
+            0xD8, 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6,
+            0x59
+        };
+        const unsigned char msg12[32] = {
+            0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3,
+            0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44,
+            0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0,
+            0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89
+        };
+        const unsigned char sig12[64] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x9E, 0x9D, 0x01, 0xAF, 0x98, 0x8B, 0x5C, 0xED,
+            0xCE, 0x47, 0x22, 0x1B, 0xFA, 0x9B, 0x22, 0x27,
+            0x21, 0xF3, 0xFA, 0x40, 0x89, 0x15, 0x44, 0x4A,
+            0x4B, 0x48, 0x90, 0x21, 0xDB, 0x55, 0x77, 0x5F
+        };
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk12, msg12, sig12, 0);
+    }
+    {
+        /* Test vector 13 */
+        const unsigned char pk13[33] = {
+            0x02, 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C,
+            0x5F, 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41,
+            0xBE, 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE,
+            0xD8, 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6,
+            0x59
+        };
+        const unsigned char msg13[32] = {
+            0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3,
+            0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44,
+            0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0,
+            0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89
+        };
+        const unsigned char sig13[64] = {
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+            0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
+            0xD3, 0x7D, 0xDF, 0x02, 0x54, 0x35, 0x18, 0x36,
+            0xD8, 0x4B, 0x1B, 0xD6, 0xA7, 0x95, 0xFD, 0x5D,
+            0x52, 0x30, 0x48, 0xF2, 0x98, 0xC4, 0x21, 0x4D,
+            0x18, 0x7F, 0xE4, 0x89, 0x29, 0x47, 0xF7, 0x28
+        };
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk13, msg13, sig13, 0);
+    }
+    {
+        /* Test vector 14 */
+        const unsigned char pk14[33] = {
+            0x02, 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C,
+            0x5F, 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41,
+            0xBE, 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE,
+            0xD8, 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6,
+            0x59
+        };
+        const unsigned char msg14[32] = {
+            0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3,
+            0x14, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44,
+            0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0,
+            0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89
+        };
+        const unsigned char sig14[64] = {
+            0x4A, 0x29, 0x8D, 0xAC, 0xAE, 0x57, 0x39, 0x5A,
+            0x15, 0xD0, 0x79, 0x5D, 0xDB, 0xFD, 0x1D, 0xCB,
+            0x56, 0x4D, 0xA8, 0x2B, 0x0F, 0x26, 0x9B, 0xC7,
+            0x0A, 0x74, 0xF8, 0x22, 0x04, 0x29, 0xBA, 0x1D,
+            0x1E, 0x51, 0xA2, 0x2C, 0xCE, 0xC3, 0x55, 0x99,
+            0xB8, 0xF2, 0x66, 0x91, 0x22, 0x81, 0xF8, 0x36,
+            0x5F, 0xFC, 0x2D, 0x03, 0x5A, 0x23, 0x04, 0x34,
+            0xA1, 0xA6, 0x4D, 0xC5, 0x9F, 0x70, 0x13, 0xFD
+        };
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk14, msg14, sig14, 0);
+    }
+    {
+        /* Test vector 15 */
+        const unsigned char pk15[33] = {
+            0x02, 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C,
+            0x5F, 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41,
+            0xBE, 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE,
+            0xD8, 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6,
+            0x59
+        };
+        const unsigned char msg15[32] = {
+            0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3,
+            0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44,
+            0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0,
+            0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89
+        };
+        const unsigned char sig15[64] = {
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, 0x2F,
+            0x1E, 0x51, 0xA2, 0x2C, 0xCE, 0xC3, 0x55, 0x99,
+            0xB8, 0xF2, 0x66, 0x91, 0x22, 0x81, 0xF8, 0x36,
+            0x5F, 0xFC, 0x2D, 0x03, 0x5A, 0x23, 0x04, 0x34,
+            0xA1, 0xA6, 0x4D, 0xC5, 0x9F, 0x70, 0x13, 0xFD
+        };
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk15, msg15, sig15, 0);
+    }
+    {
+        /* Test vector 16 */
+        const unsigned char pk16[33] = {
+            0x02, 0xDF, 0xF1, 0xD7, 0x7F, 0x2A, 0x67, 0x1C,
+            0x5F, 0x36, 0x18, 0x37, 0x26, 0xDB, 0x23, 0x41,
+            0xBE, 0x58, 0xFE, 0xAE, 0x1D, 0xA2, 0xDE, 0xCE,
+            0xD8, 0x43, 0x24, 0x0F, 0x7B, 0x50, 0x2B, 0xA6,
+            0x59
+        };
+        const unsigned char msg16[32] = {
+            0x24, 0x3F, 0x6A, 0x88, 0x85, 0xA3, 0x08, 0xD3,
+            0x13, 0x19, 0x8A, 0x2E, 0x03, 0x70, 0x73, 0x44,
+            0xA4, 0x09, 0x38, 0x22, 0x29, 0x9F, 0x31, 0xD0,
+            0x08, 0x2E, 0xFA, 0x98, 0xEC, 0x4E, 0x6C, 0x89
+        };
+        const unsigned char sig16[64] = {
+            0x2A, 0x29, 0x8D, 0xAC, 0xAE, 0x57, 0x39, 0x5A,
+            0x15, 0xD0, 0x79, 0x5D, 0xDB, 0xFD, 0x1D, 0xCB,
+            0x56, 0x4D, 0xA8, 0x2B, 0x0F, 0x26, 0x9B, 0xC7,
+            0x0A, 0x74, 0xF8, 0x22, 0x04, 0x29, 0xBA, 0x1D,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+            0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE,
+            0xBA, 0xAE, 0xDC, 0xE6, 0xAF, 0x48, 0xA0, 0x3B,
+            0xBF, 0xD2, 0x5E, 0x8C, 0xD0, 0x36, 0x41, 0x41
+        };
+        test_schnorrsig_bip_vectors_check_verify(scratch, pk16, msg16, sig16, 0);
+    }
+}
+
+/* Nonce function that returns constant 0 */
+static int nonce_function_failing(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+    (void) msg32;
+    (void) key32;
+    (void) algo16;
+    (void) data;
+    (void) counter;
+    (void) nonce32;
+    return 0;
+}
+
+/* Nonce function that sets nonce to 0 */
+static int nonce_function_0(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) {
+    (void) msg32;
+    (void) key32;
+    (void) algo16;
+    (void) data;
+    (void) counter;
+
+    memset(nonce32, 0, 32);
+    return 1;
+}
+
+void test_schnorrsig_sign(void) {
+    unsigned char sk[32];
+    const unsigned char msg[32] = "this is a msg for a schnorrsig..";
+    secp256k1_schnorrsig sig;
+
+    memset(sk, 23, sizeof(sk));
+    CHECK(secp256k1_schnorrsig_sign(ctx, &sig, NULL, msg, sk, NULL, NULL) == 1);
+
+    /* Overflowing secret key */
+    memset(sk, 0xFF, sizeof(sk));
+    CHECK(secp256k1_schnorrsig_sign(ctx, &sig, NULL, msg, sk, NULL, NULL) == 0);
+    memset(sk, 23, sizeof(sk));
+
+    CHECK(secp256k1_schnorrsig_sign(ctx, &sig, NULL, msg, sk, nonce_function_failing, NULL) == 0);
+    CHECK(secp256k1_schnorrsig_sign(ctx, &sig, NULL, msg, sk, nonce_function_0, NULL) == 0);
+}
+
+#define N_SIGS  200
+/* Creates N_SIGS valid signatures and verifies them with verify and verify_batch. Then flips some
+ * bits and checks that verification now fails. */
+void test_schnorrsig_sign_verify(secp256k1_scratch_space *scratch) {
+    const unsigned char sk[32] = "shhhhhhhh! this key is a secret.";
+    unsigned char msg[N_SIGS][32];
+    secp256k1_schnorrsig sig[N_SIGS];
+    size_t i;
+    const secp256k1_schnorrsig *sig_arr[N_SIGS];
+    const unsigned char *msg_arr[N_SIGS];
+    const secp256k1_pubkey *pk_arr[N_SIGS];
+    secp256k1_pubkey pk;
+
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pk, sk));
+
+    CHECK(secp256k1_schnorrsig_verify_batch(ctx, scratch, NULL, NULL, NULL, 0));
+
+    for (i = 0; i < N_SIGS; i++) {
+        secp256k1_rand256(msg[i]);
+        CHECK(secp256k1_schnorrsig_sign(ctx, &sig[i], NULL, msg[i], sk, NULL, NULL));
+        CHECK(secp256k1_schnorrsig_verify(ctx, &sig[i], msg[i], &pk));
+        sig_arr[i] = &sig[i];
+        msg_arr[i] = msg[i];
+        pk_arr[i] = &pk;
+    }
+
+    CHECK(secp256k1_schnorrsig_verify_batch(ctx, scratch, sig_arr, msg_arr, pk_arr, 1));
+    CHECK(secp256k1_schnorrsig_verify_batch(ctx, scratch, sig_arr, msg_arr, pk_arr, 2));
+    CHECK(secp256k1_schnorrsig_verify_batch(ctx, scratch, sig_arr, msg_arr, pk_arr, 4));
+    CHECK(secp256k1_schnorrsig_verify_batch(ctx, scratch, sig_arr, msg_arr, pk_arr, N_SIGS));
+
+    {
+        /* Flip a few bits in the signature and in the message and check that
+         * verify and verify_batch fail */
+        size_t sig_idx = secp256k1_rand_int(4);
+        size_t byte_idx = secp256k1_rand_int(32);
+        unsigned char xorbyte = secp256k1_rand_int(254)+1;
+        sig[sig_idx].data[byte_idx] ^= xorbyte;
+        CHECK(!secp256k1_schnorrsig_verify(ctx, &sig[sig_idx], msg[sig_idx], &pk));
+        CHECK(!secp256k1_schnorrsig_verify_batch(ctx, scratch, sig_arr, msg_arr, pk_arr, 4));
+        sig[sig_idx].data[byte_idx] ^= xorbyte;
+
+        byte_idx = secp256k1_rand_int(32);
+        sig[sig_idx].data[32+byte_idx] ^= xorbyte;
+        CHECK(!secp256k1_schnorrsig_verify(ctx, &sig[sig_idx], msg[sig_idx], &pk));
+        CHECK(!secp256k1_schnorrsig_verify_batch(ctx, scratch, sig_arr, msg_arr, pk_arr, 4));
+        sig[sig_idx].data[32+byte_idx] ^= xorbyte;
+
+        byte_idx = secp256k1_rand_int(32);
+        msg[sig_idx][byte_idx] ^= xorbyte;
+        CHECK(!secp256k1_schnorrsig_verify(ctx, &sig[sig_idx], msg[sig_idx], &pk));
+        CHECK(!secp256k1_schnorrsig_verify_batch(ctx, scratch, sig_arr, msg_arr, pk_arr, 4));
+        msg[sig_idx][byte_idx] ^= xorbyte;
+
+        /* Check that above bitflips have been reversed correctly */
+        CHECK(secp256k1_schnorrsig_verify(ctx, &sig[sig_idx], msg[sig_idx], &pk));
+        CHECK(secp256k1_schnorrsig_verify_batch(ctx, scratch, sig_arr, msg_arr, pk_arr, 4));
+    }
+}
+#undef N_SIGS
+
+void run_schnorrsig_tests(void) {
+    secp256k1_scratch_space *scratch = secp256k1_scratch_space_create(ctx, 1024 * 1024);
+
+    test_schnorrsig_serialize();
+    test_schnorrsig_api(scratch);
+    test_schnorrsig_bip_vectors(scratch);
+    test_schnorrsig_sign();
+    test_schnorrsig_sign_verify(scratch);
+
+    secp256k1_scratch_space_destroy(scratch);
+}
+
+#endif
+

src/secp256k1/src/scalar.h

@@ -1,3 +1,5 @@
+#ifndef ENABLE_MODULE_MUSIG
+
 /**********************************************************************
  * Copyright (c) 2014 Pieter Wuille                                   *
  * Distributed under the MIT software license, see the accompanying   *
@@ -104,3 +106,119 @@ static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar
 static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift);
 
 #endif /* SECP256K1_SCALAR_H */
+
+#else
+
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_SCALAR_H
+#define SECP256K1_SCALAR_H
+
+#include "num.h"
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#include "scalar_low.h"
+#elif defined(USE_SCALAR_4X64)
+#include "scalar_4x64.h"
+#elif defined(USE_SCALAR_8X32)
+#include "scalar_8x32.h"
+#else
+#error "Please select scalar implementation"
+#endif
+
+/** Clear a scalar to prevent the leak of sensitive data. */
+static void secp256k1_scalar_clear(secp256k1_scalar *r);
+
+/** Access bits from a scalar. All requested bits must belong to the same 32-bit limb. */
+static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count);
+
+/** Access bits from a scalar. Not constant time. */
+static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count);
+
+/** Set a scalar from a big endian byte array. */
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *bin, int *overflow);
+
+/** Set a scalar to an unsigned integer. */
+static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v);
+
+/** Set a scalar to an unsigned 64-bit integer */
+static void secp256k1_scalar_set_u64(secp256k1_scalar *r, uint64_t v);
+
+/** Convert a scalar to a byte array. */
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a);
+
+/** Add two scalars together (modulo the group order). Returns whether it overflowed. */
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b);
+
+/** Conditionally add a power of two to a scalar. The result is not allowed to overflow. */
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag);
+
+/** Multiply two scalars (modulo the group order). */
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b);
+
+/** Shift a scalar right by some amount strictly between 0 and 16, returning
+ *  the low bits that were shifted off */
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n);
+
+/** Compute the square of a scalar (modulo the group order). */
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Compute the inverse of a scalar (modulo the group order). */
+static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Compute the inverse of a scalar (modulo the group order), without constant-time guarantee. */
+static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Compute the complement of a scalar (modulo the group order). */
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a);
+
+/** Check whether a scalar equals zero. */
+static int secp256k1_scalar_is_zero(const secp256k1_scalar *a);
+
+/** Check whether a scalar equals one. */
+static int secp256k1_scalar_is_one(const secp256k1_scalar *a);
+
+/** Check whether a scalar, considered as an nonnegative integer, is even. */
+static int secp256k1_scalar_is_even(const secp256k1_scalar *a);
+
+/** Check whether a scalar is higher than the group order divided by 2. */
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a);
+
+/** Conditionally negate a number, in constant time.
+ * Returns -1 if the number was negated, 1 otherwise */
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *a, int flag);
+
+#ifndef USE_NUM_NONE
+/** Convert a scalar to a number. */
+static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a);
+
+/** Get the order of the group as a number. */
+static void secp256k1_scalar_order_get_num(secp256k1_num *r);
+#endif
+
+/** Compare two scalars. */
+static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b);
+
+#ifdef USE_ENDOMORPHISM
+/** Find r1 and r2 such that r1+r2*2^128 = a. */
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a);
+/** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (see secp256k1_gej_mul_lambda). */
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a);
+#endif
+
+/** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */
+static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift);
+
+/** Generate two scalars from a 32-byte seed and an integer using the chacha20 stream cipher */
+static void secp256k1_scalar_chacha20(secp256k1_scalar *r1, secp256k1_scalar *r2, const unsigned char *seed, uint64_t idx);
+
+#endif /* SECP256K1_SCALAR_H */
+#endif

src/secp256k1/src/scalar_4x64.h

@@ -1,3 +1,26 @@
+#ifndef ENABLE_MODULE_MUSIG
+
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_SCALAR_REPR_H
+#define SECP256K1_SCALAR_REPR_H
+
+#include <stdint.h>
+
+/** A scalar modulo the group order of the secp256k1 curve. */
+typedef struct {
+    uint64_t d[4];
+} secp256k1_scalar;
+
+#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{((uint64_t)(d1)) << 32 | (d0), ((uint64_t)(d3)) << 32 | (d2), ((uint64_t)(d5)) << 32 | (d4), ((uint64_t)(d7)) << 32 | (d6)}}
+
+#endif /* SECP256K1_SCALAR_REPR_H */
+
+#else
 /**********************************************************************
  * Copyright (c) 2014 Pieter Wuille                                   *
  * Distributed under the MIT software license, see the accompanying   *
@@ -17,3 +40,5 @@ typedef struct {
 #define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{((uint64_t)(d1)) << 32 | (d0), ((uint64_t)(d3)) << 32 | (d2), ((uint64_t)(d5)) << 32 | (d4), ((uint64_t)(d7)) << 32 | (d6)}}
 
 #endif /* SECP256K1_SCALAR_REPR_H */
+#endif
+

src/secp256k1/src/scalar_8x32.h

@@ -1,3 +1,26 @@
+#ifndef ENABLE_MODULE_MUSIG
+
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_SCALAR_REPR_H
+#define SECP256K1_SCALAR_REPR_H
+
+#include <stdint.h>
+
+/** A scalar modulo the group order of the secp256k1 curve. */
+typedef struct {
+    uint32_t d[8];
+} secp256k1_scalar;
+
+#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{(d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7)}}
+
+#endif /* SECP256K1_SCALAR_REPR_H */
+
+#else
 /**********************************************************************
  * Copyright (c) 2014 Pieter Wuille                                   *
  * Distributed under the MIT software license, see the accompanying   *
@@ -17,3 +40,4 @@ typedef struct {
 #define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{(d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7)}}
 
 #endif /* SECP256K1_SCALAR_REPR_H */
+#endif

src/secp256k1/src/scalar_8x32_impl.h

@@ -1,3 +1,5 @@
+#ifndef ENABLE_MODULE_MUSIG
+
 /**********************************************************************
  * Copyright (c) 2014 Pieter Wuille                                   *
  * Distributed under the MIT software license, see the accompanying   *
@@ -719,3 +721,839 @@ SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r,
 }
 
 #endif /* SECP256K1_SCALAR_REPR_IMPL_H */
+
+#else
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_SCALAR_REPR_IMPL_H
+#define SECP256K1_SCALAR_REPR_IMPL_H
+
+#include <string.h>
+
+/* Limbs of the secp256k1 order. */
+#define SECP256K1_N_0 ((uint32_t)0xD0364141UL)
+#define SECP256K1_N_1 ((uint32_t)0xBFD25E8CUL)
+#define SECP256K1_N_2 ((uint32_t)0xAF48A03BUL)
+#define SECP256K1_N_3 ((uint32_t)0xBAAEDCE6UL)
+#define SECP256K1_N_4 ((uint32_t)0xFFFFFFFEUL)
+#define SECP256K1_N_5 ((uint32_t)0xFFFFFFFFUL)
+#define SECP256K1_N_6 ((uint32_t)0xFFFFFFFFUL)
+#define SECP256K1_N_7 ((uint32_t)0xFFFFFFFFUL)
+
+/* Limbs of 2^256 minus the secp256k1 order. */
+#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1)
+#define SECP256K1_N_C_1 (~SECP256K1_N_1)
+#define SECP256K1_N_C_2 (~SECP256K1_N_2)
+#define SECP256K1_N_C_3 (~SECP256K1_N_3)
+#define SECP256K1_N_C_4 (1)
+
+/* Limbs of half the secp256k1 order. */
+#define SECP256K1_N_H_0 ((uint32_t)0x681B20A0UL)
+#define SECP256K1_N_H_1 ((uint32_t)0xDFE92F46UL)
+#define SECP256K1_N_H_2 ((uint32_t)0x57A4501DUL)
+#define SECP256K1_N_H_3 ((uint32_t)0x5D576E73UL)
+#define SECP256K1_N_H_4 ((uint32_t)0xFFFFFFFFUL)
+#define SECP256K1_N_H_5 ((uint32_t)0xFFFFFFFFUL)
+#define SECP256K1_N_H_6 ((uint32_t)0xFFFFFFFFUL)
+#define SECP256K1_N_H_7 ((uint32_t)0x7FFFFFFFUL)
+
+SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) {
+    r->d[0] = 0;
+    r->d[1] = 0;
+    r->d[2] = 0;
+    r->d[3] = 0;
+    r->d[4] = 0;
+    r->d[5] = 0;
+    r->d[6] = 0;
+    r->d[7] = 0;
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
+    r->d[0] = v;
+    r->d[1] = 0;
+    r->d[2] = 0;
+    r->d[3] = 0;
+    r->d[4] = 0;
+    r->d[5] = 0;
+    r->d[6] = 0;
+    r->d[7] = 0;
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_set_u64(secp256k1_scalar *r, uint64_t v) {
+    r->d[0] = v;
+    r->d[1] = v >> 32;
+    r->d[2] = 0;
+    r->d[3] = 0;
+    r->d[4] = 0;
+    r->d[5] = 0;
+    r->d[6] = 0;
+    r->d[7] = 0;
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    VERIFY_CHECK((offset + count - 1) >> 5 == offset >> 5);
+    return (a->d[offset >> 5] >> (offset & 0x1F)) & ((1 << count) - 1);
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    VERIFY_CHECK(count < 32);
+    VERIFY_CHECK(offset + count <= 256);
+    if ((offset + count - 1) >> 5 == offset >> 5) {
+        return secp256k1_scalar_get_bits(a, offset, count);
+    } else {
+        VERIFY_CHECK((offset >> 5) + 1 < 8);
+        return ((a->d[offset >> 5] >> (offset & 0x1F)) | (a->d[(offset >> 5) + 1] << (32 - (offset & 0x1F)))) & ((((uint32_t)1) << count) - 1);
+    }
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
+    int yes = 0;
+    int no = 0;
+    no |= (a->d[7] < SECP256K1_N_7); /* No need for a > check. */
+    no |= (a->d[6] < SECP256K1_N_6); /* No need for a > check. */
+    no |= (a->d[5] < SECP256K1_N_5); /* No need for a > check. */
+    no |= (a->d[4] < SECP256K1_N_4);
+    yes |= (a->d[4] > SECP256K1_N_4) & ~no;
+    no |= (a->d[3] < SECP256K1_N_3) & ~yes;
+    yes |= (a->d[3] > SECP256K1_N_3) & ~no;
+    no |= (a->d[2] < SECP256K1_N_2) & ~yes;
+    yes |= (a->d[2] > SECP256K1_N_2) & ~no;
+    no |= (a->d[1] < SECP256K1_N_1) & ~yes;
+    yes |= (a->d[1] > SECP256K1_N_1) & ~no;
+    yes |= (a->d[0] >= SECP256K1_N_0) & ~no;
+    return yes;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, uint32_t overflow) {
+    uint64_t t;
+    VERIFY_CHECK(overflow <= 1);
+    t = (uint64_t)r->d[0] + overflow * SECP256K1_N_C_0;
+    r->d[0] = t & 0xFFFFFFFFUL; t >>= 32;
+    t += (uint64_t)r->d[1] + overflow * SECP256K1_N_C_1;
+    r->d[1] = t & 0xFFFFFFFFUL; t >>= 32;
+    t += (uint64_t)r->d[2] + overflow * SECP256K1_N_C_2;
+    r->d[2] = t & 0xFFFFFFFFUL; t >>= 32;
+    t += (uint64_t)r->d[3] + overflow * SECP256K1_N_C_3;
+    r->d[3] = t & 0xFFFFFFFFUL; t >>= 32;
+    t += (uint64_t)r->d[4] + overflow * SECP256K1_N_C_4;
+    r->d[4] = t & 0xFFFFFFFFUL; t >>= 32;
+    t += (uint64_t)r->d[5];
+    r->d[5] = t & 0xFFFFFFFFUL; t >>= 32;
+    t += (uint64_t)r->d[6];
+    r->d[6] = t & 0xFFFFFFFFUL; t >>= 32;
+    t += (uint64_t)r->d[7];
+    r->d[7] = t & 0xFFFFFFFFUL;
+    return overflow;
+}
+
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    int overflow;
+    uint64_t t = (uint64_t)a->d[0] + b->d[0];
+    r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)a->d[1] + b->d[1];
+    r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)a->d[2] + b->d[2];
+    r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)a->d[3] + b->d[3];
+    r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)a->d[4] + b->d[4];
+    r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)a->d[5] + b->d[5];
+    r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)a->d[6] + b->d[6];
+    r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)a->d[7] + b->d[7];
+    r->d[7] = t & 0xFFFFFFFFULL; t >>= 32;
+    overflow = t + secp256k1_scalar_check_overflow(r);
+    VERIFY_CHECK(overflow == 0 || overflow == 1);
+    secp256k1_scalar_reduce(r, overflow);
+    return overflow;
+}
+
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
+    uint64_t t;
+    VERIFY_CHECK(bit < 256);
+    bit += ((uint32_t) flag - 1) & 0x100;  /* forcing (bit >> 5) > 7 makes this a noop */
+    t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << (bit & 0x1F));
+    r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)r->d[1] + (((uint32_t)((bit >> 5) == 1)) << (bit & 0x1F));
+    r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)r->d[2] + (((uint32_t)((bit >> 5) == 2)) << (bit & 0x1F));
+    r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)r->d[3] + (((uint32_t)((bit >> 5) == 3)) << (bit & 0x1F));
+    r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)r->d[4] + (((uint32_t)((bit >> 5) == 4)) << (bit & 0x1F));
+    r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)r->d[5] + (((uint32_t)((bit >> 5) == 5)) << (bit & 0x1F));
+    r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)r->d[6] + (((uint32_t)((bit >> 5) == 6)) << (bit & 0x1F));
+    r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
+    t += (uint64_t)r->d[7] + (((uint32_t)((bit >> 5) == 7)) << (bit & 0x1F));
+    r->d[7] = t & 0xFFFFFFFFULL;
+#ifdef VERIFY
+    VERIFY_CHECK((t >> 32) == 0);
+    VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
+#endif
+}
+
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
+    int over;
+    r->d[0] = (uint32_t)b32[31] | (uint32_t)b32[30] << 8 | (uint32_t)b32[29] << 16 | (uint32_t)b32[28] << 24;
+    r->d[1] = (uint32_t)b32[27] | (uint32_t)b32[26] << 8 | (uint32_t)b32[25] << 16 | (uint32_t)b32[24] << 24;
+    r->d[2] = (uint32_t)b32[23] | (uint32_t)b32[22] << 8 | (uint32_t)b32[21] << 16 | (uint32_t)b32[20] << 24;
+    r->d[3] = (uint32_t)b32[19] | (uint32_t)b32[18] << 8 | (uint32_t)b32[17] << 16 | (uint32_t)b32[16] << 24;
+    r->d[4] = (uint32_t)b32[15] | (uint32_t)b32[14] << 8 | (uint32_t)b32[13] << 16 | (uint32_t)b32[12] << 24;
+    r->d[5] = (uint32_t)b32[11] | (uint32_t)b32[10] << 8 | (uint32_t)b32[9] << 16 | (uint32_t)b32[8] << 24;
+    r->d[6] = (uint32_t)b32[7] | (uint32_t)b32[6] << 8 | (uint32_t)b32[5] << 16 | (uint32_t)b32[4] << 24;
+    r->d[7] = (uint32_t)b32[3] | (uint32_t)b32[2] << 8 | (uint32_t)b32[1] << 16 | (uint32_t)b32[0] << 24;
+    over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
+    if (overflow) {
+        *overflow = over;
+    }
+}
+
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
+    bin[0] = a->d[7] >> 24; bin[1] = a->d[7] >> 16; bin[2] = a->d[7] >> 8; bin[3] = a->d[7];
+    bin[4] = a->d[6] >> 24; bin[5] = a->d[6] >> 16; bin[6] = a->d[6] >> 8; bin[7] = a->d[6];
+    bin[8] = a->d[5] >> 24; bin[9] = a->d[5] >> 16; bin[10] = a->d[5] >> 8; bin[11] = a->d[5];
+    bin[12] = a->d[4] >> 24; bin[13] = a->d[4] >> 16; bin[14] = a->d[4] >> 8; bin[15] = a->d[4];
+    bin[16] = a->d[3] >> 24; bin[17] = a->d[3] >> 16; bin[18] = a->d[3] >> 8; bin[19] = a->d[3];
+    bin[20] = a->d[2] >> 24; bin[21] = a->d[2] >> 16; bin[22] = a->d[2] >> 8; bin[23] = a->d[2];
+    bin[24] = a->d[1] >> 24; bin[25] = a->d[1] >> 16; bin[26] = a->d[1] >> 8; bin[27] = a->d[1];
+    bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0];
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
+    return (a->d[0] | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
+}
+
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(a) == 0);
+    uint64_t t = (uint64_t)(~a->d[0]) + SECP256K1_N_0 + 1;
+    r->d[0] = t & nonzero; t >>= 32;
+    t += (uint64_t)(~a->d[1]) + SECP256K1_N_1;
+    r->d[1] = t & nonzero; t >>= 32;
+    t += (uint64_t)(~a->d[2]) + SECP256K1_N_2;
+    r->d[2] = t & nonzero; t >>= 32;
+    t += (uint64_t)(~a->d[3]) + SECP256K1_N_3;
+    r->d[3] = t & nonzero; t >>= 32;
+    t += (uint64_t)(~a->d[4]) + SECP256K1_N_4;
+    r->d[4] = t & nonzero; t >>= 32;
+    t += (uint64_t)(~a->d[5]) + SECP256K1_N_5;
+    r->d[5] = t & nonzero; t >>= 32;
+    t += (uint64_t)(~a->d[6]) + SECP256K1_N_6;
+    r->d[6] = t & nonzero; t >>= 32;
+    t += (uint64_t)(~a->d[7]) + SECP256K1_N_7;
+    r->d[7] = t & nonzero;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
+    return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
+}
+
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
+    int yes = 0;
+    int no = 0;
+    no |= (a->d[7] < SECP256K1_N_H_7);
+    yes |= (a->d[7] > SECP256K1_N_H_7) & ~no;
+    no |= (a->d[6] < SECP256K1_N_H_6) & ~yes; /* No need for a > check. */
+    no |= (a->d[5] < SECP256K1_N_H_5) & ~yes; /* No need for a > check. */
+    no |= (a->d[4] < SECP256K1_N_H_4) & ~yes; /* No need for a > check. */
+    no |= (a->d[3] < SECP256K1_N_H_3) & ~yes;
+    yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
+    no |= (a->d[2] < SECP256K1_N_H_2) & ~yes;
+    yes |= (a->d[2] > SECP256K1_N_H_2) & ~no;
+    no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
+    yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
+    yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
+    return yes;
+}
+
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
+    /* If we are flag = 0, mask = 00...00 and this is a no-op;
+     * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
+    uint32_t mask = !flag - 1;
+    uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(r) == 0);
+    uint64_t t = (uint64_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
+    r->d[0] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
+    r->d[1] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
+    r->d[2] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
+    r->d[3] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[4] ^ mask) + (SECP256K1_N_4 & mask);
+    r->d[4] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[5] ^ mask) + (SECP256K1_N_5 & mask);
+    r->d[5] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[6] ^ mask) + (SECP256K1_N_6 & mask);
+    r->d[6] = t & nonzero; t >>= 32;
+    t += (uint64_t)(r->d[7] ^ mask) + (SECP256K1_N_7 & mask);
+    r->d[7] = t & nonzero;
+    return 2 * (mask == 0) - 1;
+}
+
+
+/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
+
+/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
+#define muladd(a,b) { \
+uint32_t tl, th; \
+{ \
+uint64_t t = (uint64_t)a * b; \
+th = t >> 32;         /* at most 0xFFFFFFFE */ \
+tl = t; \
+} \
+c0 += tl;                 /* overflow is handled on the next line */ \
+th += (c0 < tl) ? 1 : 0;  /* at most 0xFFFFFFFF */ \
+c1 += th;                 /* overflow is handled on the next line */ \
+c2 += (c1 < th) ? 1 : 0;  /* never overflows by contract (verified in the next line) */ \
+VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
+}
+
+/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */
+#define muladd_fast(a,b) { \
+uint32_t tl, th; \
+{ \
+uint64_t t = (uint64_t)a * b; \
+th = t >> 32;         /* at most 0xFFFFFFFE */ \
+tl = t; \
+} \
+c0 += tl;                 /* overflow is handled on the next line */ \
+th += (c0 < tl) ? 1 : 0;  /* at most 0xFFFFFFFF */ \
+c1 += th;                 /* never overflows by contract (verified in the next line) */ \
+VERIFY_CHECK(c1 >= th); \
+}
+
+/** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */
+#define muladd2(a,b) { \
+uint32_t tl, th, th2, tl2; \
+{ \
+uint64_t t = (uint64_t)a * b; \
+th = t >> 32;               /* at most 0xFFFFFFFE */ \
+tl = t; \
+} \
+th2 = th + th;                  /* at most 0xFFFFFFFE (in case th was 0x7FFFFFFF) */ \
+c2 += (th2 < th) ? 1 : 0;       /* never overflows by contract (verified the next line) */ \
+VERIFY_CHECK((th2 >= th) || (c2 != 0)); \
+tl2 = tl + tl;                  /* at most 0xFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFF) */ \
+th2 += (tl2 < tl) ? 1 : 0;      /* at most 0xFFFFFFFF */ \
+c0 += tl2;                      /* overflow is handled on the next line */ \
+th2 += (c0 < tl2) ? 1 : 0;      /* second overflow is handled on the next line */ \
+c2 += (c0 < tl2) & (th2 == 0);  /* never overflows by contract (verified the next line) */ \
+VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \
+c1 += th2;                      /* overflow is handled on the next line */ \
+c2 += (c1 < th2) ? 1 : 0;       /* never overflows by contract (verified the next line) */ \
+VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \
+}
+
+/** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */
+#define sumadd(a) { \
+unsigned int over; \
+c0 += (a);                  /* overflow is handled on the next line */ \
+over = (c0 < (a)) ? 1 : 0; \
+c1 += over;                 /* overflow is handled on the next line */ \
+c2 += (c1 < over) ? 1 : 0;  /* never overflows by contract */ \
+}
+
+/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */
+#define sumadd_fast(a) { \
+c0 += (a);                 /* overflow is handled on the next line */ \
+c1 += (c0 < (a)) ? 1 : 0;  /* never overflows by contract (verified the next line) */ \
+VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
+VERIFY_CHECK(c2 == 0); \
+}
+
+/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. */
+#define extract(n) { \
+(n) = c0; \
+c0 = c1; \
+c1 = c2; \
+c2 = 0; \
+}
+
+/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. c2 is required to be zero. */
+#define extract_fast(n) { \
+(n) = c0; \
+c0 = c1; \
+c1 = 0; \
+VERIFY_CHECK(c2 == 0); \
+}
+
+static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint32_t *l) {
+    uint64_t c;
+    uint32_t n0 = l[8], n1 = l[9], n2 = l[10], n3 = l[11], n4 = l[12], n5 = l[13], n6 = l[14], n7 = l[15];
+    uint32_t m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12;
+    uint32_t p0, p1, p2, p3, p4, p5, p6, p7, p8;
+    
+    /* 96 bit accumulator. */
+    uint32_t c0, c1, c2;
+    
+    /* Reduce 512 bits into 385. */
+    /* m[0..12] = l[0..7] + n[0..7] * SECP256K1_N_C. */
+    c0 = l[0]; c1 = 0; c2 = 0;
+    muladd_fast(n0, SECP256K1_N_C_0);
+    extract_fast(m0);
+    sumadd_fast(l[1]);
+    muladd(n1, SECP256K1_N_C_0);
+    muladd(n0, SECP256K1_N_C_1);
+    extract(m1);
+    sumadd(l[2]);
+    muladd(n2, SECP256K1_N_C_0);
+    muladd(n1, SECP256K1_N_C_1);
+    muladd(n0, SECP256K1_N_C_2);
+    extract(m2);
+    sumadd(l[3]);
+    muladd(n3, SECP256K1_N_C_0);
+    muladd(n2, SECP256K1_N_C_1);
+    muladd(n1, SECP256K1_N_C_2);
+    muladd(n0, SECP256K1_N_C_3);
+    extract(m3);
+    sumadd(l[4]);
+    muladd(n4, SECP256K1_N_C_0);
+    muladd(n3, SECP256K1_N_C_1);
+    muladd(n2, SECP256K1_N_C_2);
+    muladd(n1, SECP256K1_N_C_3);
+    sumadd(n0);
+    extract(m4);
+    sumadd(l[5]);
+    muladd(n5, SECP256K1_N_C_0);
+    muladd(n4, SECP256K1_N_C_1);
+    muladd(n3, SECP256K1_N_C_2);
+    muladd(n2, SECP256K1_N_C_3);
+    sumadd(n1);
+    extract(m5);
+    sumadd(l[6]);
+    muladd(n6, SECP256K1_N_C_0);
+    muladd(n5, SECP256K1_N_C_1);
+    muladd(n4, SECP256K1_N_C_2);
+    muladd(n3, SECP256K1_N_C_3);
+    sumadd(n2);
+    extract(m6);
+    sumadd(l[7]);
+    muladd(n7, SECP256K1_N_C_0);
+    muladd(n6, SECP256K1_N_C_1);
+    muladd(n5, SECP256K1_N_C_2);
+    muladd(n4, SECP256K1_N_C_3);
+    sumadd(n3);
+    extract(m7);
+    muladd(n7, SECP256K1_N_C_1);
+    muladd(n6, SECP256K1_N_C_2);
+    muladd(n5, SECP256K1_N_C_3);
+    sumadd(n4);
+    extract(m8);
+    muladd(n7, SECP256K1_N_C_2);
+    muladd(n6, SECP256K1_N_C_3);
+    sumadd(n5);
+    extract(m9);
+    muladd(n7, SECP256K1_N_C_3);
+    sumadd(n6);
+    extract(m10);
+    sumadd_fast(n7);
+    extract_fast(m11);
+    VERIFY_CHECK(c0 <= 1);
+    m12 = c0;
+    
+    /* Reduce 385 bits into 258. */
+    /* p[0..8] = m[0..7] + m[8..12] * SECP256K1_N_C. */
+    c0 = m0; c1 = 0; c2 = 0;
+    muladd_fast(m8, SECP256K1_N_C_0);
+    extract_fast(p0);
+    sumadd_fast(m1);
+    muladd(m9, SECP256K1_N_C_0);
+    muladd(m8, SECP256K1_N_C_1);
+    extract(p1);
+    sumadd(m2);
+    muladd(m10, SECP256K1_N_C_0);
+    muladd(m9, SECP256K1_N_C_1);
+    muladd(m8, SECP256K1_N_C_2);
+    extract(p2);
+    sumadd(m3);
+    muladd(m11, SECP256K1_N_C_0);
+    muladd(m10, SECP256K1_N_C_1);
+    muladd(m9, SECP256K1_N_C_2);
+    muladd(m8, SECP256K1_N_C_3);
+    extract(p3);
+    sumadd(m4);
+    muladd(m12, SECP256K1_N_C_0);
+    muladd(m11, SECP256K1_N_C_1);
+    muladd(m10, SECP256K1_N_C_2);
+    muladd(m9, SECP256K1_N_C_3);
+    sumadd(m8);
+    extract(p4);
+    sumadd(m5);
+    muladd(m12, SECP256K1_N_C_1);
+    muladd(m11, SECP256K1_N_C_2);
+    muladd(m10, SECP256K1_N_C_3);
+    sumadd(m9);
+    extract(p5);
+    sumadd(m6);
+    muladd(m12, SECP256K1_N_C_2);
+    muladd(m11, SECP256K1_N_C_3);
+    sumadd(m10);
+    extract(p6);
+    sumadd_fast(m7);
+    muladd_fast(m12, SECP256K1_N_C_3);
+    sumadd_fast(m11);
+    extract_fast(p7);
+    p8 = c0 + m12;
+    VERIFY_CHECK(p8 <= 2);
+    
+    /* Reduce 258 bits into 256. */
+    /* r[0..7] = p[0..7] + p[8] * SECP256K1_N_C. */
+    c = p0 + (uint64_t)SECP256K1_N_C_0 * p8;
+    r->d[0] = c & 0xFFFFFFFFUL; c >>= 32;
+    c += p1 + (uint64_t)SECP256K1_N_C_1 * p8;
+    r->d[1] = c & 0xFFFFFFFFUL; c >>= 32;
+    c += p2 + (uint64_t)SECP256K1_N_C_2 * p8;
+    r->d[2] = c & 0xFFFFFFFFUL; c >>= 32;
+    c += p3 + (uint64_t)SECP256K1_N_C_3 * p8;
+    r->d[3] = c & 0xFFFFFFFFUL; c >>= 32;
+    c += p4 + (uint64_t)p8;
+    r->d[4] = c & 0xFFFFFFFFUL; c >>= 32;
+    c += p5;
+    r->d[5] = c & 0xFFFFFFFFUL; c >>= 32;
+    c += p6;
+    r->d[6] = c & 0xFFFFFFFFUL; c >>= 32;
+    c += p7;
+    r->d[7] = c & 0xFFFFFFFFUL; c >>= 32;
+    
+    /* Final reduction of r. */
+    secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
+}
+
+static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    /* 96 bit accumulator. */
+    uint32_t c0 = 0, c1 = 0, c2 = 0;
+    
+    /* l[0..15] = a[0..7] * b[0..7]. */
+    muladd_fast(a->d[0], b->d[0]);
+    extract_fast(l[0]);
+    muladd(a->d[0], b->d[1]);
+    muladd(a->d[1], b->d[0]);
+    extract(l[1]);
+    muladd(a->d[0], b->d[2]);
+    muladd(a->d[1], b->d[1]);
+    muladd(a->d[2], b->d[0]);
+    extract(l[2]);
+    muladd(a->d[0], b->d[3]);
+    muladd(a->d[1], b->d[2]);
+    muladd(a->d[2], b->d[1]);
+    muladd(a->d[3], b->d[0]);
+    extract(l[3]);
+    muladd(a->d[0], b->d[4]);
+    muladd(a->d[1], b->d[3]);
+    muladd(a->d[2], b->d[2]);
+    muladd(a->d[3], b->d[1]);
+    muladd(a->d[4], b->d[0]);
+    extract(l[4]);
+    muladd(a->d[0], b->d[5]);
+    muladd(a->d[1], b->d[4]);
+    muladd(a->d[2], b->d[3]);
+    muladd(a->d[3], b->d[2]);
+    muladd(a->d[4], b->d[1]);
+    muladd(a->d[5], b->d[0]);
+    extract(l[5]);
+    muladd(a->d[0], b->d[6]);
+    muladd(a->d[1], b->d[5]);
+    muladd(a->d[2], b->d[4]);
+    muladd(a->d[3], b->d[3]);
+    muladd(a->d[4], b->d[2]);
+    muladd(a->d[5], b->d[1]);
+    muladd(a->d[6], b->d[0]);
+    extract(l[6]);
+    muladd(a->d[0], b->d[7]);
+    muladd(a->d[1], b->d[6]);
+    muladd(a->d[2], b->d[5]);
+    muladd(a->d[3], b->d[4]);
+    muladd(a->d[4], b->d[3]);
+    muladd(a->d[5], b->d[2]);
+    muladd(a->d[6], b->d[1]);
+    muladd(a->d[7], b->d[0]);
+    extract(l[7]);
+    muladd(a->d[1], b->d[7]);
+    muladd(a->d[2], b->d[6]);
+    muladd(a->d[3], b->d[5]);
+    muladd(a->d[4], b->d[4]);
+    muladd(a->d[5], b->d[3]);
+    muladd(a->d[6], b->d[2]);
+    muladd(a->d[7], b->d[1]);
+    extract(l[8]);
+    muladd(a->d[2], b->d[7]);
+    muladd(a->d[3], b->d[6]);
+    muladd(a->d[4], b->d[5]);
+    muladd(a->d[5], b->d[4]);
+    muladd(a->d[6], b->d[3]);
+    muladd(a->d[7], b->d[2]);
+    extract(l[9]);
+    muladd(a->d[3], b->d[7]);
+    muladd(a->d[4], b->d[6]);
+    muladd(a->d[5], b->d[5]);
+    muladd(a->d[6], b->d[4]);
+    muladd(a->d[7], b->d[3]);
+    extract(l[10]);
+    muladd(a->d[4], b->d[7]);
+    muladd(a->d[5], b->d[6]);
+    muladd(a->d[6], b->d[5]);
+    muladd(a->d[7], b->d[4]);
+    extract(l[11]);
+    muladd(a->d[5], b->d[7]);
+    muladd(a->d[6], b->d[6]);
+    muladd(a->d[7], b->d[5]);
+    extract(l[12]);
+    muladd(a->d[6], b->d[7]);
+    muladd(a->d[7], b->d[6]);
+    extract(l[13]);
+    muladd_fast(a->d[7], b->d[7]);
+    extract_fast(l[14]);
+    VERIFY_CHECK(c1 == 0);
+    l[15] = c0;
+}
+
+static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar *a) {
+    /* 96 bit accumulator. */
+    uint32_t c0 = 0, c1 = 0, c2 = 0;
+    
+    /* l[0..15] = a[0..7]^2. */
+    muladd_fast(a->d[0], a->d[0]);
+    extract_fast(l[0]);
+    muladd2(a->d[0], a->d[1]);
+    extract(l[1]);
+    muladd2(a->d[0], a->d[2]);
+    muladd(a->d[1], a->d[1]);
+    extract(l[2]);
+    muladd2(a->d[0], a->d[3]);
+    muladd2(a->d[1], a->d[2]);
+    extract(l[3]);
+    muladd2(a->d[0], a->d[4]);
+    muladd2(a->d[1], a->d[3]);
+    muladd(a->d[2], a->d[2]);
+    extract(l[4]);
+    muladd2(a->d[0], a->d[5]);
+    muladd2(a->d[1], a->d[4]);
+    muladd2(a->d[2], a->d[3]);
+    extract(l[5]);
+    muladd2(a->d[0], a->d[6]);
+    muladd2(a->d[1], a->d[5]);
+    muladd2(a->d[2], a->d[4]);
+    muladd(a->d[3], a->d[3]);
+    extract(l[6]);
+    muladd2(a->d[0], a->d[7]);
+    muladd2(a->d[1], a->d[6]);
+    muladd2(a->d[2], a->d[5]);
+    muladd2(a->d[3], a->d[4]);
+    extract(l[7]);
+    muladd2(a->d[1], a->d[7]);
+    muladd2(a->d[2], a->d[6]);
+    muladd2(a->d[3], a->d[5]);
+    muladd(a->d[4], a->d[4]);
+    extract(l[8]);
+    muladd2(a->d[2], a->d[7]);
+    muladd2(a->d[3], a->d[6]);
+    muladd2(a->d[4], a->d[5]);
+    extract(l[9]);
+    muladd2(a->d[3], a->d[7]);
+    muladd2(a->d[4], a->d[6]);
+    muladd(a->d[5], a->d[5]);
+    extract(l[10]);
+    muladd2(a->d[4], a->d[7]);
+    muladd2(a->d[5], a->d[6]);
+    extract(l[11]);
+    muladd2(a->d[5], a->d[7]);
+    muladd(a->d[6], a->d[6]);
+    extract(l[12]);
+    muladd2(a->d[6], a->d[7]);
+    extract(l[13]);
+    muladd_fast(a->d[7], a->d[7]);
+    extract_fast(l[14]);
+    VERIFY_CHECK(c1 == 0);
+    l[15] = c0;
+}
+
+#undef sumadd
+#undef sumadd_fast
+#undef muladd
+#undef muladd_fast
+#undef muladd2
+#undef extract
+#undef extract_fast
+
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    uint32_t l[16];
+    secp256k1_scalar_mul_512(l, a, b);
+    secp256k1_scalar_reduce_512(r, l);
+}
+
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
+    int ret;
+    VERIFY_CHECK(n > 0);
+    VERIFY_CHECK(n < 16);
+    ret = r->d[0] & ((1 << n) - 1);
+    r->d[0] = (r->d[0] >> n) + (r->d[1] << (32 - n));
+    r->d[1] = (r->d[1] >> n) + (r->d[2] << (32 - n));
+    r->d[2] = (r->d[2] >> n) + (r->d[3] << (32 - n));
+    r->d[3] = (r->d[3] >> n) + (r->d[4] << (32 - n));
+    r->d[4] = (r->d[4] >> n) + (r->d[5] << (32 - n));
+    r->d[5] = (r->d[5] >> n) + (r->d[6] << (32 - n));
+    r->d[6] = (r->d[6] >> n) + (r->d[7] << (32 - n));
+    r->d[7] = (r->d[7] >> n);
+    return ret;
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    uint32_t l[16];
+    secp256k1_scalar_sqr_512(l, a);
+    secp256k1_scalar_reduce_512(r, l);
+}
+
+#ifdef USE_ENDOMORPHISM
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    r1->d[0] = a->d[0];
+    r1->d[1] = a->d[1];
+    r1->d[2] = a->d[2];
+    r1->d[3] = a->d[3];
+    r1->d[4] = 0;
+    r1->d[5] = 0;
+    r1->d[6] = 0;
+    r1->d[7] = 0;
+    r2->d[0] = a->d[4];
+    r2->d[1] = a->d[5];
+    r2->d[2] = a->d[6];
+    r2->d[3] = a->d[7];
+    r2->d[4] = 0;
+    r2->d[5] = 0;
+    r2->d[6] = 0;
+    r2->d[7] = 0;
+}
+#endif
+
+SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3]) | (a->d[4] ^ b->d[4]) | (a->d[5] ^ b->d[5]) | (a->d[6] ^ b->d[6]) | (a->d[7] ^ b->d[7])) == 0;
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
+    uint32_t l[16];
+    unsigned int shiftlimbs;
+    unsigned int shiftlow;
+    unsigned int shifthigh;
+    VERIFY_CHECK(shift >= 256);
+    secp256k1_scalar_mul_512(l, a, b);
+    shiftlimbs = shift >> 5;
+    shiftlow = shift & 0x1F;
+    shifthigh = 32 - shiftlow;
+    r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 480 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[1] = shift < 480 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[2] = shift < 448 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 416 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[3] = shift < 416 ? (l[3 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[4 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[4] = shift < 384 ? (l[4 + shiftlimbs] >> shiftlow | (shift < 352 && shiftlow ? (l[5 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[5] = shift < 352 ? (l[5 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[6 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[6] = shift < 320 ? (l[6 + shiftlimbs] >> shiftlow | (shift < 288 && shiftlow ? (l[7 + shiftlimbs] << shifthigh) : 0)) : 0;
+    r->d[7] = shift < 288 ? (l[7 + shiftlimbs] >> shiftlow)  : 0;
+    secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1);
+}
+
+#define ROTL32(x,n) ((x) << (n) | (x) >> (32-(n)))
+#define QUARTERROUND(a,b,c,d) \
+a += b; d = ROTL32(d ^ a, 16); \
+c += d; b = ROTL32(b ^ c, 12); \
+a += b; d = ROTL32(d ^ a, 8); \
+c += d; b = ROTL32(b ^ c, 7);
+
+#ifdef WORDS_BIGENDIAN
+#define LE32(p) ((((p) & 0xFF) << 24) | (((p) & 0xFF00) << 8) | (((p) & 0xFF0000) >> 8) | (((p) & 0xFF000000) >> 24))
+#define BE32(p) (p)
+#else
+#define BE32(p) ((((p) & 0xFF) << 24) | (((p) & 0xFF00) << 8) | (((p) & 0xFF0000) >> 8) | (((p) & 0xFF000000) >> 24))
+#define LE32(p) (p)
+#endif
+
+static void secp256k1_scalar_chacha20(secp256k1_scalar *r1, secp256k1_scalar *r2, const unsigned char *seed, uint64_t idx) {
+    size_t n;
+    size_t over_count = 0;
+    uint32_t seed32[8];
+    uint32_t x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15;
+    int over1, over2;
+    
+    memcpy((void *) seed32, (const void *) seed, 32);
+    do {
+        x0 = 0x61707865;
+        x1 = 0x3320646e;
+        x2 = 0x79622d32;
+        x3 = 0x6b206574;
+        x4 = LE32(seed32[0]);
+        x5 = LE32(seed32[1]);
+        x6 = LE32(seed32[2]);
+        x7 = LE32(seed32[3]);
+        x8 = LE32(seed32[4]);
+        x9 = LE32(seed32[5]);
+        x10 = LE32(seed32[6]);
+        x11 = LE32(seed32[7]);
+        x12 = idx;
+        x13 = idx >> 32;
+        x14 = 0;
+        x15 = over_count;
+        
+        n = 10;
+        while (n--) {
+            QUARTERROUND(x0, x4, x8,x12)
+            QUARTERROUND(x1, x5, x9,x13)
+            QUARTERROUND(x2, x6,x10,x14)
+            QUARTERROUND(x3, x7,x11,x15)
+            QUARTERROUND(x0, x5,x10,x15)
+            QUARTERROUND(x1, x6,x11,x12)
+            QUARTERROUND(x2, x7, x8,x13)
+            QUARTERROUND(x3, x4, x9,x14)
+        }
+        
+        x0 += 0x61707865;
+        x1 += 0x3320646e;
+        x2 += 0x79622d32;
+        x3 += 0x6b206574;
+        x4 += LE32(seed32[0]);
+        x5 += LE32(seed32[1]);
+        x6 += LE32(seed32[2]);
+        x7 += LE32(seed32[3]);
+        x8 += LE32(seed32[4]);
+        x9 += LE32(seed32[5]);
+        x10 += LE32(seed32[6]);
+        x11 += LE32(seed32[7]);
+        x12 += idx;
+        x13 += idx >> 32;
+        x14 += 0;
+        x15 += over_count;
+        
+        r1->d[7] = LE32(x0);
+        r1->d[6] = LE32(x1);
+        r1->d[5] = LE32(x2);
+        r1->d[4] = LE32(x3);
+        r1->d[3] = LE32(x4);
+        r1->d[2] = LE32(x5);
+        r1->d[1] = LE32(x6);
+        r1->d[0] = LE32(x7);
+        r2->d[7] = LE32(x8);
+        r2->d[6] = LE32(x9);
+        r2->d[5] = LE32(x10);
+        r2->d[4] = LE32(x11);
+        r2->d[3] = LE32(x12);
+        r2->d[2] = LE32(x13);
+        r2->d[1] = LE32(x14);
+        r2->d[0] = LE32(x15);
+        
+        over1 = secp256k1_scalar_check_overflow(r1);
+        over2 = secp256k1_scalar_check_overflow(r2);
+        over_count++;
+    } while (over1 | over2);
+}
+
+#undef ROTL32
+#undef QUARTERROUND
+#undef BE32
+#undef LE32
+
+#endif /* SECP256K1_SCALAR_REPR_IMPL_H */
+#endif
+

src/secp256k1/src/scalar_impl.h

@@ -1,3 +1,5 @@
+#ifndef ENABLE_MODULE_MUSIG
+
 /**********************************************************************
  * Copyright (c) 2014 Pieter Wuille                                   *
  * Distributed under the MIT software license, see the accompanying   *
@@ -331,3 +333,341 @@ static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar
 #endif
 
 #endif /* SECP256K1_SCALAR_IMPL_H */
+
+
+#else
+/**********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                   *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_SCALAR_IMPL_H
+#define SECP256K1_SCALAR_IMPL_H
+
+#include "group.h"
+#include "scalar.h"
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+#include "scalar_low_impl.h"
+#elif defined(USE_SCALAR_4X64)
+#include "scalar_4x64_impl.h"
+#elif defined(USE_SCALAR_8X32)
+#include "scalar_8x32_impl.h"
+#else
+#error "Please select scalar implementation"
+#endif
+
+#ifndef USE_NUM_NONE
+static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a) {
+    unsigned char c[32];
+    secp256k1_scalar_get_b32(c, a);
+    secp256k1_num_set_bin(r, c, 32);
+}
+
+/** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */
+static void secp256k1_scalar_order_get_num(secp256k1_num *r) {
+#if defined(EXHAUSTIVE_TEST_ORDER)
+    static const unsigned char order[32] = {
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,0,
+        0,0,0,0,0,0,0,EXHAUSTIVE_TEST_ORDER
+    };
+#else
+    static const unsigned char order[32] = {
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
+        0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
+        0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
+    };
+#endif
+    secp256k1_num_set_bin(r, order, 32);
+}
+#endif
+
+static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) {
+#if defined(EXHAUSTIVE_TEST_ORDER)
+    int i;
+    *r = 0;
+    for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++)
+        if ((i * *x) % EXHAUSTIVE_TEST_ORDER == 1)
+            *r = i;
+    /* If this VERIFY_CHECK triggers we were given a noninvertible scalar (and thus
+     * have a composite group order; fix it in exhaustive_tests.c). */
+    VERIFY_CHECK(*r != 0);
+}
+#else
+secp256k1_scalar *t;
+int i;
+/* First compute xN as x ^ (2^N - 1) for some values of N,
+ * and uM as x ^ M for some values of M. */
+secp256k1_scalar x2, x3, x6, x8, x14, x28, x56, x112, x126;
+secp256k1_scalar u2, u5, u9, u11, u13;
+
+secp256k1_scalar_sqr(&u2, x);
+secp256k1_scalar_mul(&x2, &u2,  x);
+secp256k1_scalar_mul(&u5, &u2, &x2);
+secp256k1_scalar_mul(&x3, &u5,  &u2);
+secp256k1_scalar_mul(&u9, &x3, &u2);
+secp256k1_scalar_mul(&u11, &u9, &u2);
+secp256k1_scalar_mul(&u13, &u11, &u2);
+
+secp256k1_scalar_sqr(&x6, &u13);
+secp256k1_scalar_sqr(&x6, &x6);
+secp256k1_scalar_mul(&x6, &x6, &u11);
+
+secp256k1_scalar_sqr(&x8, &x6);
+secp256k1_scalar_sqr(&x8, &x8);
+secp256k1_scalar_mul(&x8, &x8,  &x2);
+
+secp256k1_scalar_sqr(&x14, &x8);
+for (i = 0; i < 5; i++) {
+    secp256k1_scalar_sqr(&x14, &x14);
+}
+secp256k1_scalar_mul(&x14, &x14, &x6);
+
+secp256k1_scalar_sqr(&x28, &x14);
+for (i = 0; i < 13; i++) {
+    secp256k1_scalar_sqr(&x28, &x28);
+}
+secp256k1_scalar_mul(&x28, &x28, &x14);
+
+secp256k1_scalar_sqr(&x56, &x28);
+for (i = 0; i < 27; i++) {
+    secp256k1_scalar_sqr(&x56, &x56);
+}
+secp256k1_scalar_mul(&x56, &x56, &x28);
+
+secp256k1_scalar_sqr(&x112, &x56);
+for (i = 0; i < 55; i++) {
+    secp256k1_scalar_sqr(&x112, &x112);
+}
+secp256k1_scalar_mul(&x112, &x112, &x56);
+
+secp256k1_scalar_sqr(&x126, &x112);
+for (i = 0; i < 13; i++) {
+    secp256k1_scalar_sqr(&x126, &x126);
+}
+secp256k1_scalar_mul(&x126, &x126, &x14);
+
+/* Then accumulate the final result (t starts at x126). */
+t = &x126;
+for (i = 0; i < 3; i++) {
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &u5); /* 101 */
+for (i = 0; i < 4; i++) { /* 0 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &x3); /* 111 */
+for (i = 0; i < 4; i++) { /* 0 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &u5); /* 101 */
+for (i = 0; i < 5; i++) { /* 0 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &u11); /* 1011 */
+for (i = 0; i < 4; i++) {
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &u11); /* 1011 */
+for (i = 0; i < 4; i++) { /* 0 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &x3); /* 111 */
+for (i = 0; i < 5; i++) { /* 00 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &x3); /* 111 */
+for (i = 0; i < 6; i++) { /* 00 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &u13); /* 1101 */
+for (i = 0; i < 4; i++) { /* 0 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &u5); /* 101 */
+for (i = 0; i < 3; i++) {
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &x3); /* 111 */
+for (i = 0; i < 5; i++) { /* 0 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &u9); /* 1001 */
+for (i = 0; i < 6; i++) { /* 000 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &u5); /* 101 */
+for (i = 0; i < 10; i++) { /* 0000000 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &x3); /* 111 */
+for (i = 0; i < 4; i++) { /* 0 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &x3); /* 111 */
+for (i = 0; i < 9; i++) { /* 0 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &x8); /* 11111111 */
+for (i = 0; i < 5; i++) { /* 0 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &u9); /* 1001 */
+for (i = 0; i < 6; i++) { /* 00 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &u11); /* 1011 */
+for (i = 0; i < 4; i++) {
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &u13); /* 1101 */
+for (i = 0; i < 5; i++) {
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &x2); /* 11 */
+for (i = 0; i < 6; i++) { /* 00 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &u13); /* 1101 */
+for (i = 0; i < 10; i++) { /* 000000 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &u13); /* 1101 */
+for (i = 0; i < 4; i++) {
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, &u9); /* 1001 */
+for (i = 0; i < 6; i++) { /* 00000 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(t, t, x); /* 1 */
+for (i = 0; i < 8; i++) { /* 00 */
+    secp256k1_scalar_sqr(t, t);
+}
+secp256k1_scalar_mul(r, t, &x6); /* 111111 */
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) {
+    return !(a->d[0] & 1);
+}
+#endif
+
+static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) {
+#if defined(USE_SCALAR_INV_BUILTIN)
+    secp256k1_scalar_inverse(r, x);
+#elif defined(USE_SCALAR_INV_NUM)
+    unsigned char b[32];
+    secp256k1_num n, m;
+    secp256k1_scalar t = *x;
+    secp256k1_scalar_get_b32(b, &t);
+    secp256k1_num_set_bin(&n, b, 32);
+    secp256k1_scalar_order_get_num(&m);
+    secp256k1_num_mod_inverse(&n, &n, &m);
+    secp256k1_num_get_bin(b, 32, &n);
+    secp256k1_scalar_set_b32(r, b, NULL);
+    /* Verify that the inverse was computed correctly, without GMP code. */
+    secp256k1_scalar_mul(&t, &t, r);
+    CHECK(secp256k1_scalar_is_one(&t));
+#else
+#error "Please select scalar inverse implementation"
+#endif
+}
+
+#ifdef USE_ENDOMORPHISM
+#if defined(EXHAUSTIVE_TEST_ORDER)
+/**
+ * Find k1 and k2 given k, such that k1 + k2 * lambda == k mod n; unlike in the
+ * full case we don't bother making k1 and k2 be small, we just want them to be
+ * nontrivial to get full test coverage for the exhaustive tests. We therefore
+ * (arbitrarily) set k2 = k + 5 and k1 = k - k2 * lambda.
+ */
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    *r2 = (*a + 5) % EXHAUSTIVE_TEST_ORDER;
+    *r1 = (*a + (EXHAUSTIVE_TEST_ORDER - *r2) * EXHAUSTIVE_TEST_LAMBDA) % EXHAUSTIVE_TEST_ORDER;
+}
+#else
+/**
+ * The Secp256k1 curve has an endomorphism, where lambda * (x, y) = (beta * x, y), where
+ * lambda is {0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a,
+ *            0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72}
+ *
+ * "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm
+ * (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1
+ * and k2 have a small size.
+ * It relies on constants a1, b1, a2, b2. These constants for the value of lambda above are:
+ *
+ * - a1 =      {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
+ * - b1 =     -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3}
+ * - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8}
+ * - b2 =      {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
+ *
+ * The algorithm then computes c1 = round(b1 * k / n) and c2 = round(b2 * k / n), and gives
+ * k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and
+ * compute k1 as k - k2 * lambda, avoiding the need for constants a1 and a2.
+ *
+ * g1, g2 are precomputed constants used to replace division with a rounded multiplication
+ * when decomposing the scalar for an endomorphism-based point multiplication.
+ *
+ * The possibility of using precomputed estimates is mentioned in "Guide to Elliptic Curve
+ * Cryptography" (Hankerson, Menezes, Vanstone) in section 3.5.
+ *
+ * The derivation is described in the paper "Efficient Software Implementation of Public-Key
+ * Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez),
+ * Section 4.3 (here we use a somewhat higher-precision estimate):
+ * d = a1*b2 - b1*a2
+ * g1 = round((2^272)*b2/d)
+ * g2 = round((2^272)*b1/d)
+ *
+ * (Note that 'd' is also equal to the curve order here because [a1,b1] and [a2,b2] are found
+ * as outputs of the Extended Euclidean Algorithm on inputs 'order' and 'lambda').
+ *
+ * The function below splits a in r1 and r2, such that r1 + lambda * r2 == a (mod order).
+ */
+
+static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    secp256k1_scalar c1, c2;
+    static const secp256k1_scalar minus_lambda = SECP256K1_SCALAR_CONST(
+                                                                        0xAC9C52B3UL, 0x3FA3CF1FUL, 0x5AD9E3FDUL, 0x77ED9BA4UL,
+                                                                        0xA880B9FCUL, 0x8EC739C2UL, 0xE0CFC810UL, 0xB51283CFUL
+                                                                        );
+    static const secp256k1_scalar minus_b1 = SECP256K1_SCALAR_CONST(
+                                                                    0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
+                                                                    0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL
+                                                                    );
+    static const secp256k1_scalar minus_b2 = SECP256K1_SCALAR_CONST(
+                                                                    0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
+                                                                    0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL
+                                                                    );
+    static const secp256k1_scalar g1 = SECP256K1_SCALAR_CONST(
+                                                              0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00003086UL,
+                                                              0xD221A7D4UL, 0x6BCDE86CUL, 0x90E49284UL, 0xEB153DABUL
+                                                              );
+    static const secp256k1_scalar g2 = SECP256K1_SCALAR_CONST(
+                                                              0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0000E443UL,
+                                                              0x7ED6010EUL, 0x88286F54UL, 0x7FA90ABFUL, 0xE4C42212UL
+                                                              );
+    VERIFY_CHECK(r1 != a);
+    VERIFY_CHECK(r2 != a);
+    /* these _var calls are constant time since the shift amount is constant */
+    secp256k1_scalar_mul_shift_var(&c1, a, &g1, 272);
+    secp256k1_scalar_mul_shift_var(&c2, a, &g2, 272);
+    secp256k1_scalar_mul(&c1, &c1, &minus_b1);
+    secp256k1_scalar_mul(&c2, &c2, &minus_b2);
+    secp256k1_scalar_add(r2, &c1, &c2);
+    secp256k1_scalar_mul(r1, r2, &minus_lambda);
+    secp256k1_scalar_add(r1, r1, a);
+}
+#endif
+#endif
+
+#endif /* SECP256K1_SCALAR_IMPL_H */
+#endif
+

src/secp256k1/src/scalar_low.h

@@ -1,3 +1,22 @@
+#ifndef ENABLE_MODULE_MUSIG
+
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_SCALAR_REPR_H
+#define SECP256K1_SCALAR_REPR_H
+
+#include <stdint.h>
+
+/** A scalar modulo the group order of the secp256k1 curve. */
+typedef uint32_t secp256k1_scalar;
+
+#endif /* SECP256K1_SCALAR_REPR_H */
+
+#else
 /**********************************************************************
  * Copyright (c) 2015 Andrew Poelstra                                 *
  * Distributed under the MIT software license, see the accompanying   *
@@ -13,3 +32,4 @@
 typedef uint32_t secp256k1_scalar;
 
 #endif /* SECP256K1_SCALAR_REPR_H */
+#endif

src/secp256k1/src/scalar_low_impl.h

@@ -1,3 +1,5 @@
+#ifndef ENABLE_MODULE_MUSIG
+
 /**********************************************************************
  * Copyright (c) 2015 Andrew Poelstra                                 *
  * Distributed under the MIT software license, see the accompanying   *
@@ -112,3 +114,127 @@ SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const
 }
 
 #endif /* SECP256K1_SCALAR_REPR_IMPL_H */
+
+#else
+/**********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_SCALAR_REPR_IMPL_H
+#define SECP256K1_SCALAR_REPR_IMPL_H
+
+#include "scalar.h"
+
+#include <string.h>
+
+SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) {
+    return !(*a & 1);
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) { *r = 0; }
+SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) { *r = v; }
+SECP256K1_INLINE static void secp256k1_scalar_set_u64(secp256k1_scalar *r, uint64_t v) { *r = v % EXHAUSTIVE_TEST_ORDER; }
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    if (offset < 32)
+        return ((*a >> offset) & ((((uint32_t)1) << count) - 1));
+    else
+        return 0;
+}
+
+SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
+    return secp256k1_scalar_get_bits(a, offset, count);
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) { return *a >= EXHAUSTIVE_TEST_ORDER; }
+
+static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    *r = (*a + *b) % EXHAUSTIVE_TEST_ORDER;
+    return *r < *b;
+}
+
+static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
+    if (flag && bit < 32)
+        *r += (1 << bit);
+#ifdef VERIFY
+    VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0);
+#endif
+}
+
+static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
+    const int base = 0x100 % EXHAUSTIVE_TEST_ORDER;
+    int i;
+    *r = 0;
+    for (i = 0; i < 32; i++) {
+        *r = ((*r * base) + b32[i]) % EXHAUSTIVE_TEST_ORDER;
+    }
+    /* just deny overflow, it basically always happens */
+    if (overflow) *overflow = 0;
+}
+
+static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
+    memset(bin, 0, 32);
+    bin[28] = *a >> 24; bin[29] = *a >> 16; bin[30] = *a >> 8; bin[31] = *a;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
+    return *a == 0;
+}
+
+static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    if (*a == 0) {
+        *r = 0;
+    } else {
+        *r = EXHAUSTIVE_TEST_ORDER - *a;
+    }
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
+    return *a == 1;
+}
+
+static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
+    return *a > EXHAUSTIVE_TEST_ORDER / 2;
+}
+
+static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
+    if (flag) secp256k1_scalar_negate(r, r);
+    return flag ? -1 : 1;
+}
+
+static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    *r = (*a * *b) % EXHAUSTIVE_TEST_ORDER;
+}
+
+static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) {
+    int ret;
+    VERIFY_CHECK(n > 0);
+    VERIFY_CHECK(n < 16);
+    ret = *r & ((1 << n) - 1);
+    *r >>= n;
+    return ret;
+}
+
+static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) {
+    *r = (*a * *a) % EXHAUSTIVE_TEST_ORDER;
+}
+
+static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) {
+    *r1 = *a;
+    *r2 = 0;
+}
+
+SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
+    return *a == *b;
+}
+
+SECP256K1_INLINE static void secp256k1_scalar_chacha20(secp256k1_scalar *r1, secp256k1_scalar *r2, const unsigned char *seed, uint64_t n) {
+    *r1 = (seed[0] + n) % EXHAUSTIVE_TEST_ORDER;
+    *r2 = (seed[1] + n) % EXHAUSTIVE_TEST_ORDER;
+}
+
+#endif /* SECP256K1_SCALAR_REPR_IMPL_H */
+#endif
+

src/secp256k1/src/scratch.h

@@ -0,0 +1,40 @@
+/**********************************************************************
+ * Copyright (c) 2017 Andrew Poelstra	                              *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCRATCH_
+#define _SECP256K1_SCRATCH_
+
+#define SECP256K1_SCRATCH_MAX_FRAMES	5
+
+/* The typedef is used internally; the struct name is used in the public API
+ * (where it is exposed as a different typedef) */
+typedef struct secp256k1_scratch_space_struct {
+    void *data[SECP256K1_SCRATCH_MAX_FRAMES];
+    size_t offset[SECP256K1_SCRATCH_MAX_FRAMES];
+    size_t frame_size[SECP256K1_SCRATCH_MAX_FRAMES];
+    size_t frame;
+    size_t max_size;
+    const secp256k1_callback* error_callback;
+} secp256k1_scratch;
+
+static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* error_callback, size_t max_size);
+
+static void secp256k1_scratch_destroy(secp256k1_scratch* scratch);
+
+/** Attempts to allocate a new stack frame with `n` available bytes. Returns 1 on success, 0 on failure */
+static int secp256k1_scratch_allocate_frame(secp256k1_scratch* scratch, size_t n, size_t objects);
+
+/** Deallocates a stack frame */
+static void secp256k1_scratch_deallocate_frame(secp256k1_scratch* scratch);
+
+/** Returns the maximum allocation the scratch space will allow */
+static size_t secp256k1_scratch_max_allocation(const secp256k1_scratch* scratch, size_t n_objects);
+
+/** Returns a pointer into the most recently allocated frame, or NULL if there is insufficient available space */
+static void *secp256k1_scratch_alloc(secp256k1_scratch* scratch, size_t n);
+
+#endif
+

src/secp256k1/src/scratch_impl.h

@@ -0,0 +1,87 @@
+/**********************************************************************
+ * Copyright (c) 2017 Andrew Poelstra                                 *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_SCRATCH_IMPL_H_
+#define _SECP256K1_SCRATCH_IMPL_H_
+
+#include "scratch.h"
+
+/* Using 16 bytes alignment because common architectures never have alignment
+ * requirements above 8 for any of the types we care about. In addition we
+ * leave some room because currently we don't care about a few bytes.
+ * TODO: Determine this at configure time. */
+#define ALIGNMENT 16
+
+static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* error_callback, size_t max_size) {
+    secp256k1_scratch* ret = (secp256k1_scratch*)checked_malloc(error_callback, sizeof(*ret));
+    if (ret != NULL) {
+        memset(ret, 0, sizeof(*ret));
+        ret->max_size = max_size;
+        ret->error_callback = error_callback;
+    }
+    return ret;
+}
+
+static void secp256k1_scratch_destroy(secp256k1_scratch* scratch) {
+    if (scratch != NULL) {
+        VERIFY_CHECK(scratch->frame == 0);
+        free(scratch);
+    }
+}
+
+static size_t secp256k1_scratch_max_allocation(const secp256k1_scratch* scratch, size_t objects) {
+    size_t i = 0;
+    size_t allocated = 0;
+    for (i = 0; i < scratch->frame; i++) {
+        allocated += scratch->frame_size[i];
+    }
+    if (scratch->max_size - allocated <= objects * ALIGNMENT) {
+        return 0;
+    }
+    return scratch->max_size - allocated - objects * ALIGNMENT;
+}
+
+static int secp256k1_scratch_allocate_frame(secp256k1_scratch* scratch, size_t n, size_t objects) {
+    VERIFY_CHECK(scratch->frame < SECP256K1_SCRATCH_MAX_FRAMES);
+
+    if (n <= secp256k1_scratch_max_allocation(scratch, objects)) {
+        n += objects * ALIGNMENT;
+        scratch->data[scratch->frame] = checked_malloc(scratch->error_callback, n);
+        if (scratch->data[scratch->frame] == NULL) {
+            return 0;
+        }
+        scratch->frame_size[scratch->frame] = n;
+        scratch->offset[scratch->frame] = 0;
+        scratch->frame++;
+        return 1;
+    } else {
+        return 0;
+    }
+}
+
+static void secp256k1_scratch_deallocate_frame(secp256k1_scratch* scratch) {
+    VERIFY_CHECK(scratch->frame > 0);
+    scratch->frame -= 1;
+    free(scratch->data[scratch->frame]);
+}
+
+static void *secp256k1_scratch_alloc(secp256k1_scratch* scratch, size_t size) {
+    void *ret;
+    size_t frame = scratch->frame - 1;
+    size = ((size + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT;
+
+    if (scratch->frame == 0 || size + scratch->offset[frame] > scratch->frame_size[frame]) {
+        return NULL;
+    }
+    ret = (void *) ((unsigned char *) scratch->data[frame] + scratch->offset[frame]);
+    memset(ret, 0, size);
+    scratch->offset[frame] += size;
+
+    return ret;
+}
+
+#endif
+

src/secp256k1/src/secp256k1.c

@@ -17,6 +17,7 @@
 #include "ecdsa_impl.h"
 #include "eckey_impl.h"
 #include "hash_impl.h"
+#include "scratch_impl.h"
 
 #define ARG_CHECK(cond) do { \
     if (EXPECT(!(cond), 0)) { \

src/secp256k1/src/tests.c

@@ -2405,7 +2405,7 @@ void ecmult_const_random_mult(void) {
         0xb84e4e1b, 0xfb77e21f, 0x96baae2a, 0x63dec956
     );
     secp256k1_gej b;
-    secp256k1_ecmult_const(&b, &a, &xn);
+    secp256k1_ecmult_const(&b, &a, &xn,256);
 
     CHECK(secp256k1_ge_is_valid_var(&a));
     ge_equals_gej(&expected_b, &b);
@@ -2421,12 +2421,12 @@ void ecmult_const_commutativity(void) {
     random_scalar_order_test(&a);
     random_scalar_order_test(&b);
 
-    secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a);
-    secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b);
+    secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a,256);
+    secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b,256);
     secp256k1_ge_set_gej(&mid1, &res1);
     secp256k1_ge_set_gej(&mid2, &res2);
-    secp256k1_ecmult_const(&res1, &mid1, &b);
-    secp256k1_ecmult_const(&res2, &mid2, &a);
+    secp256k1_ecmult_const(&res1, &mid1, &b,256);
+    secp256k1_ecmult_const(&res2, &mid2, &a,256);
     secp256k1_ge_set_gej(&mid1, &res1);
     secp256k1_ge_set_gej(&mid2, &res2);
     ge_equals_ge(&mid1, &mid2);
@@ -2442,13 +2442,13 @@ void ecmult_const_mult_zero_one(void) {
     secp256k1_scalar_negate(&negone, &one);
 
     random_group_element_test(&point);
-    secp256k1_ecmult_const(&res1, &point, &zero);
+    secp256k1_ecmult_const(&res1, &point, &zero,256);
     secp256k1_ge_set_gej(&res2, &res1);
     CHECK(secp256k1_ge_is_infinity(&res2));
-    secp256k1_ecmult_const(&res1, &point, &one);
+    secp256k1_ecmult_const(&res1, &point, &one,256);
     secp256k1_ge_set_gej(&res2, &res1);
     ge_equals_ge(&res2, &point);
-    secp256k1_ecmult_const(&res1, &point, &negone);
+    secp256k1_ecmult_const(&res1, &point, &negone,256);
     secp256k1_gej_neg(&res1, &res1);
     secp256k1_ge_set_gej(&res2, &res1);
     ge_equals_ge(&res2, &point);
@@ -2474,7 +2474,7 @@ void ecmult_const_chain_multiply(void) {
     for (i = 0; i < 100; ++i) {
         secp256k1_ge tmp;
         secp256k1_ge_set_gej(&tmp, &point);
-        secp256k1_ecmult_const(&point, &tmp, &scalar);
+        secp256k1_ecmult_const(&point, &tmp, &scalar,256);
     }
     secp256k1_ge_set_gej(&res, &point);
     ge_equals_gej(&res, &expected_point);

src/secp256k1/src/tests_exhaustive.c

@@ -174,7 +174,7 @@ void test_exhaustive_ecmult(const secp256k1_context *ctx, const secp256k1_ge *gr
                 ge_equals_gej(&group[(i * r_log + j) % order], &tmp);
 
                 if (i > 0) {
-                    secp256k1_ecmult_const(&tmp, &group[i], &ng);
+                    secp256k1_ecmult_const(&tmp, &group[i], &ng,256);
                     ge_equals_gej(&group[(i * j) % order], &tmp);
                 }
             }