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315 lines
8.6 KiB
315 lines
8.6 KiB
/**********************************************************************
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* Copyright (c) 2013, 2014 Pieter Wuille *
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* Distributed under the MIT software license, see the accompanying *
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* file COPYING or https://www.gnu.org/licenses/gpl-3.0.en.html*
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**********************************************************************/
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#ifndef SECP256K1_FIELD_IMPL_H
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#define SECP256K1_FIELD_IMPL_H
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#if defined HAVE_CONFIG_H
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#include "libsecp256k1-config.h"
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#endif
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#include "util.h"
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#if defined(USE_FIELD_10X26)
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#include "field_10x26_impl.h"
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#elif defined(USE_FIELD_5X52)
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#include "field_5x52_impl.h"
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#else
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#error "Please select field implementation"
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#endif
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SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
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secp256k1_fe na;
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secp256k1_fe_negate(&na, a, 1);
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secp256k1_fe_add(&na, b);
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return secp256k1_fe_normalizes_to_zero(&na);
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}
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SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b) {
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secp256k1_fe na;
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secp256k1_fe_negate(&na, a, 1);
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secp256k1_fe_add(&na, b);
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return secp256k1_fe_normalizes_to_zero_var(&na);
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}
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static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a) {
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/** Given that p is congruent to 3 mod 4, we can compute the square root of
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* a mod p as the (p+1)/4'th power of a.
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*
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* As (p+1)/4 is an even number, it will have the same result for a and for
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* (-a). Only one of these two numbers actually has a square root however,
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* so we test at the end by squaring and comparing to the input.
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* Also because (p+1)/4 is an even number, the computed square root is
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* itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)).
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*/
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secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
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int j;
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/** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in
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* { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
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* 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
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*/
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secp256k1_fe_sqr(&x2, a);
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secp256k1_fe_mul(&x2, &x2, a);
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secp256k1_fe_sqr(&x3, &x2);
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secp256k1_fe_mul(&x3, &x3, a);
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x6 = x3;
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for (j=0; j<3; j++) {
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secp256k1_fe_sqr(&x6, &x6);
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}
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secp256k1_fe_mul(&x6, &x6, &x3);
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x9 = x6;
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for (j=0; j<3; j++) {
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secp256k1_fe_sqr(&x9, &x9);
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}
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secp256k1_fe_mul(&x9, &x9, &x3);
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x11 = x9;
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for (j=0; j<2; j++) {
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secp256k1_fe_sqr(&x11, &x11);
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}
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secp256k1_fe_mul(&x11, &x11, &x2);
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x22 = x11;
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for (j=0; j<11; j++) {
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secp256k1_fe_sqr(&x22, &x22);
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}
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secp256k1_fe_mul(&x22, &x22, &x11);
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x44 = x22;
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for (j=0; j<22; j++) {
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secp256k1_fe_sqr(&x44, &x44);
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}
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secp256k1_fe_mul(&x44, &x44, &x22);
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x88 = x44;
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for (j=0; j<44; j++) {
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secp256k1_fe_sqr(&x88, &x88);
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}
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secp256k1_fe_mul(&x88, &x88, &x44);
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x176 = x88;
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for (j=0; j<88; j++) {
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secp256k1_fe_sqr(&x176, &x176);
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}
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secp256k1_fe_mul(&x176, &x176, &x88);
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x220 = x176;
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for (j=0; j<44; j++) {
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secp256k1_fe_sqr(&x220, &x220);
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}
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secp256k1_fe_mul(&x220, &x220, &x44);
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x223 = x220;
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for (j=0; j<3; j++) {
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secp256k1_fe_sqr(&x223, &x223);
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}
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secp256k1_fe_mul(&x223, &x223, &x3);
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/* The final result is then assembled using a sliding window over the blocks. */
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t1 = x223;
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for (j=0; j<23; j++) {
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secp256k1_fe_sqr(&t1, &t1);
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}
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secp256k1_fe_mul(&t1, &t1, &x22);
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for (j=0; j<6; j++) {
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secp256k1_fe_sqr(&t1, &t1);
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}
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secp256k1_fe_mul(&t1, &t1, &x2);
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secp256k1_fe_sqr(&t1, &t1);
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secp256k1_fe_sqr(r, &t1);
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/* Check that a square root was actually calculated */
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secp256k1_fe_sqr(&t1, r);
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return secp256k1_fe_equal(&t1, a);
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}
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static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) {
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secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
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int j;
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/** The binary representation of (p - 2) has 5 blocks of 1s, with lengths in
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* { 1, 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
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* [1], [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
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*/
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secp256k1_fe_sqr(&x2, a);
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secp256k1_fe_mul(&x2, &x2, a);
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secp256k1_fe_sqr(&x3, &x2);
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secp256k1_fe_mul(&x3, &x3, a);
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x6 = x3;
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for (j=0; j<3; j++) {
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secp256k1_fe_sqr(&x6, &x6);
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}
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secp256k1_fe_mul(&x6, &x6, &x3);
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x9 = x6;
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for (j=0; j<3; j++) {
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secp256k1_fe_sqr(&x9, &x9);
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}
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secp256k1_fe_mul(&x9, &x9, &x3);
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x11 = x9;
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for (j=0; j<2; j++) {
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secp256k1_fe_sqr(&x11, &x11);
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}
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secp256k1_fe_mul(&x11, &x11, &x2);
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x22 = x11;
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for (j=0; j<11; j++) {
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secp256k1_fe_sqr(&x22, &x22);
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}
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secp256k1_fe_mul(&x22, &x22, &x11);
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x44 = x22;
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for (j=0; j<22; j++) {
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secp256k1_fe_sqr(&x44, &x44);
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}
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secp256k1_fe_mul(&x44, &x44, &x22);
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x88 = x44;
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for (j=0; j<44; j++) {
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secp256k1_fe_sqr(&x88, &x88);
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}
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secp256k1_fe_mul(&x88, &x88, &x44);
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x176 = x88;
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for (j=0; j<88; j++) {
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secp256k1_fe_sqr(&x176, &x176);
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}
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secp256k1_fe_mul(&x176, &x176, &x88);
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x220 = x176;
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for (j=0; j<44; j++) {
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secp256k1_fe_sqr(&x220, &x220);
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}
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secp256k1_fe_mul(&x220, &x220, &x44);
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x223 = x220;
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for (j=0; j<3; j++) {
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secp256k1_fe_sqr(&x223, &x223);
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}
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secp256k1_fe_mul(&x223, &x223, &x3);
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/* The final result is then assembled using a sliding window over the blocks. */
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t1 = x223;
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for (j=0; j<23; j++) {
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secp256k1_fe_sqr(&t1, &t1);
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}
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secp256k1_fe_mul(&t1, &t1, &x22);
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for (j=0; j<5; j++) {
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secp256k1_fe_sqr(&t1, &t1);
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}
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secp256k1_fe_mul(&t1, &t1, a);
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for (j=0; j<3; j++) {
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secp256k1_fe_sqr(&t1, &t1);
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}
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secp256k1_fe_mul(&t1, &t1, &x2);
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for (j=0; j<2; j++) {
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secp256k1_fe_sqr(&t1, &t1);
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}
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secp256k1_fe_mul(r, a, &t1);
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}
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static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) {
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#if defined(USE_FIELD_INV_BUILTIN)
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secp256k1_fe_inv(r, a);
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#elif defined(USE_FIELD_INV_NUM)
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secp256k1_num n, m;
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static const secp256k1_fe negone = SECP256K1_FE_CONST(
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0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
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0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, 0xFFFFFC2EUL
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);
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/* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
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static const unsigned char prime[32] = {
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0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
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0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
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0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
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0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
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};
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unsigned char b[32];
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int res;
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secp256k1_fe c = *a;
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secp256k1_fe_normalize_var(&c);
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secp256k1_fe_get_b32(b, &c);
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secp256k1_num_set_bin(&n, b, 32);
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secp256k1_num_set_bin(&m, prime, 32);
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secp256k1_num_mod_inverse(&n, &n, &m);
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secp256k1_num_get_bin(b, 32, &n);
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res = secp256k1_fe_set_b32(r, b);
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(void)res;
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VERIFY_CHECK(res);
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/* Verify the result is the (unique) valid inverse using non-GMP code. */
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secp256k1_fe_mul(&c, &c, r);
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secp256k1_fe_add(&c, &negone);
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CHECK(secp256k1_fe_normalizes_to_zero_var(&c));
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#else
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#error "Please select field inverse implementation"
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#endif
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}
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static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len) {
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secp256k1_fe u;
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size_t i;
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if (len < 1) {
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return;
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}
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VERIFY_CHECK((r + len <= a) || (a + len <= r));
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r[0] = a[0];
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i = 0;
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while (++i < len) {
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secp256k1_fe_mul(&r[i], &r[i - 1], &a[i]);
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}
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secp256k1_fe_inv_var(&u, &r[--i]);
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while (i > 0) {
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size_t j = i--;
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secp256k1_fe_mul(&r[j], &r[i], &u);
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secp256k1_fe_mul(&u, &u, &a[j]);
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}
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r[0] = u;
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}
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static int secp256k1_fe_is_quad_var(const secp256k1_fe *a) {
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#ifndef USE_NUM_NONE
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unsigned char b[32];
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secp256k1_num n;
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secp256k1_num m;
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/* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
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static const unsigned char prime[32] = {
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0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
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0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
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0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
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0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
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};
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secp256k1_fe c = *a;
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secp256k1_fe_normalize_var(&c);
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secp256k1_fe_get_b32(b, &c);
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secp256k1_num_set_bin(&n, b, 32);
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secp256k1_num_set_bin(&m, prime, 32);
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return secp256k1_num_jacobi(&n, &m) >= 0;
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#else
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secp256k1_fe r;
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return secp256k1_fe_sqrt(&r, a);
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#endif
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}
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#endif /* SECP256K1_FIELD_IMPL_H */
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