// Copyright (c) 2016-2020 The Hush developers // Distributed under the GPLv3 software license, see the accompanying // file COPYING or https://www.gnu.org/licenses/gpl-3.0.en.html /****************************************************************************** * Copyright © 2014-2019 The SuperNET Developers. * * * * See the AUTHORS, DEVELOPER-AGREEMENT and LICENSE files at * * the top-level directory of this distribution for the individual copyright * * holder information and the developer policies on copyright and licensing. * * * * Unless otherwise agreed in a custom licensing agreement, no part of the * * SuperNET software, including this file may be copied, modified, propagated * * or distributed except according to the terms contained in the LICENSE file * * * * Removal or modification of this copyright notice is prohibited. * * * ******************************************************************************/ #ifndef H_HUSH25519_H #define H_HUSH25519_H // derived from curve25519_donna #include #include #include #ifdef _WIN32 #include #endif bits320 fmul(const bits320 in2,const bits320 in); bits320 fexpand(bits256 basepoint); bits256 fcontract(const bits320 input); void cmult(bits320 *resultx,bits320 *resultz,bits256 secret,const bits320 q); bits320 crecip(const bits320 z); bits256 curve25519(bits256 mysecret,bits256 basepoint); // Sum two numbers: output += in static inline bits320 fsum(bits320 output,bits320 in) { int32_t i; for (i=0; i<5; i++) output.ulongs[i] += in.ulongs[i]; return(output); } static inline void fdifference_backwards(uint64_t *out,const uint64_t *in) { static const uint64_t two54m152 = (((uint64_t)1) << 54) - 152; // 152 is 19 << 3 static const uint64_t two54m8 = (((uint64_t)1) << 54) - 8; int32_t i; out[0] = in[0] + two54m152 - out[0]; for (i=1; i<5; i++) out[i] = in[i] + two54m8 - out[i]; } void store_limb(uint8_t *out,uint64_t in) { int32_t i; for (i=0; i<8; i++,in>>=8) out[i] = (in & 0xff); } static inline uint64_t load_limb(uint8_t *in) { return ((uint64_t)in[0]) | (((uint64_t)in[1]) << 8) | (((uint64_t)in[2]) << 16) | (((uint64_t)in[3]) << 24) | (((uint64_t)in[4]) << 32) | (((uint64_t)in[5]) << 40) | (((uint64_t)in[6]) << 48) | (((uint64_t)in[7]) << 56); } // Take a little-endian, 32-byte number and expand it into polynomial form bits320 fexpand(bits256 basepoint) { bits320 out; out.ulongs[0] = load_limb(basepoint.bytes) & 0x7ffffffffffffLL; out.ulongs[1] = (load_limb(basepoint.bytes+6) >> 3) & 0x7ffffffffffffLL; out.ulongs[2] = (load_limb(basepoint.bytes+12) >> 6) & 0x7ffffffffffffLL; out.ulongs[3] = (load_limb(basepoint.bytes+19) >> 1) & 0x7ffffffffffffLL; out.ulongs[4] = (load_limb(basepoint.bytes+24) >> 12) & 0x7ffffffffffffLL; return(out); } #if defined(__x86_64__) || defined(_WIN64) || defined(__aarch64__) || defined(__amd64__) || defined(__amd64) || defined(_M_X64) || defined(_M_IA64) // donna: special gcc mode for 128-bit integers. It's implemented on 64-bit platforms only as far as I know. typedef unsigned uint128_t __attribute__((mode(TI))); // Multiply a number by a scalar: output = in * scalar static inline bits320 fscalar_product(const bits320 in,const uint64_t scalar) { int32_t i; uint128_t a = 0; bits320 output; a = ((uint128_t)in.ulongs[0]) * scalar; output.ulongs[0] = ((uint64_t)a) & 0x7ffffffffffffLL; for (i=1; i<5; i++) { a = ((uint128_t)in.ulongs[i]) * scalar + ((uint64_t) (a >> 51)); output.ulongs[i] = ((uint64_t)a) & 0x7ffffffffffffLL; } output.ulongs[0] += (a >> 51) * 19; return(output); } // Multiply two numbers: output = in2 * in // output must be distinct to both inputs. The inputs are reduced coefficient form, the output is not. // Assumes that in[i] < 2**55 and likewise for in2. On return, output[i] < 2**52 bits320 fmul(const bits320 in2,const bits320 in) { uint128_t t[5]; uint64_t r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c; bits320 out; r0 = in.ulongs[0], r1 = in.ulongs[1], r2 = in.ulongs[2], r3 = in.ulongs[3], r4 = in.ulongs[4]; s0 = in2.ulongs[0], s1 = in2.ulongs[1], s2 = in2.ulongs[2], s3 = in2.ulongs[3], s4 = in2.ulongs[4]; t[0] = ((uint128_t) r0) * s0; t[1] = ((uint128_t) r0) * s1 + ((uint128_t) r1) * s0; t[2] = ((uint128_t) r0) * s2 + ((uint128_t) r2) * s0 + ((uint128_t) r1) * s1; t[3] = ((uint128_t) r0) * s3 + ((uint128_t) r3) * s0 + ((uint128_t) r1) * s2 + ((uint128_t) r2) * s1; t[4] = ((uint128_t) r0) * s4 + ((uint128_t) r4) * s0 + ((uint128_t) r3) * s1 + ((uint128_t) r1) * s3 + ((uint128_t) r2) * s2; r4 *= 19, r1 *= 19, r2 *= 19, r3 *= 19; t[0] += ((uint128_t) r4) * s1 + ((uint128_t) r1) * s4 + ((uint128_t) r2) * s3 + ((uint128_t) r3) * s2; t[1] += ((uint128_t) r4) * s2 + ((uint128_t) r2) * s4 + ((uint128_t) r3) * s3; t[2] += ((uint128_t) r4) * s3 + ((uint128_t) r3) * s4; t[3] += ((uint128_t) r4) * s4; r0 = (uint64_t)t[0] & 0x7ffffffffffffLL; c = (uint64_t)(t[0] >> 51); t[1] += c; r1 = (uint64_t)t[1] & 0x7ffffffffffffLL; c = (uint64_t)(t[1] >> 51); t[2] += c; r2 = (uint64_t)t[2] & 0x7ffffffffffffLL; c = (uint64_t)(t[2] >> 51); t[3] += c; r3 = (uint64_t)t[3] & 0x7ffffffffffffLL; c = (uint64_t)(t[3] >> 51); t[4] += c; r4 = (uint64_t)t[4] & 0x7ffffffffffffLL; c = (uint64_t)(t[4] >> 51); r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffLL; r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffLL; r2 += c; out.ulongs[0] = r0, out.ulongs[1] = r1, out.ulongs[2] = r2, out.ulongs[3] = r3, out.ulongs[4] = r4; return(out); } bits320 fsquare_times(const bits320 in,uint64_t count) { uint128_t t[5]; uint64_t r0,r1,r2,r3,r4,c,d0,d1,d2,d4,d419; bits320 out; r0 = in.ulongs[0], r1 = in.ulongs[1], r2 = in.ulongs[2], r3 = in.ulongs[3], r4 = in.ulongs[4]; do { d0 = r0 * 2; d1 = r1 * 2; d2 = r2 * 2 * 19; d419 = r4 * 19; d4 = d419 * 2; t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3 )); t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19)); t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3 )); t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419 )); t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2 )); r0 = (uint64_t)t[0] & 0x7ffffffffffffLL; c = (uint64_t)(t[0] >> 51); t[1] += c; r1 = (uint64_t)t[1] & 0x7ffffffffffffLL; c = (uint64_t)(t[1] >> 51); t[2] += c; r2 = (uint64_t)t[2] & 0x7ffffffffffffLL; c = (uint64_t)(t[2] >> 51); t[3] += c; r3 = (uint64_t)t[3] & 0x7ffffffffffffL; c = (uint64_t)(t[3] >> 51); t[4] += c; r4 = (uint64_t)t[4] & 0x7ffffffffffffLL; c = (uint64_t)(t[4] >> 51); r0 += c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffLL; r1 += c; c = r1 >> 51; r1 = r1 & 0x7ffffffffffffLL; r2 += c; } while( --count ); out.ulongs[0] = r0, out.ulongs[1] = r1, out.ulongs[2] = r2, out.ulongs[3] = r3, out.ulongs[4] = r4; return(out); } static inline void fcontract_iter(uint128_t t[5],int32_t flag) { int32_t i; uint64_t mask = 0x7ffffffffffffLL; for (i=0; i<4; i++) t[i+1] += t[i] >> 51, t[i] &= mask; if ( flag != 0 ) t[0] += 19 * (t[4] >> 51); t[4] &= mask; } // donna: Take a fully reduced polynomial form number and contract it into a little-endian, 32-byte array bits256 fcontract(const bits320 input) { uint128_t t[5]; int32_t i; bits256 out; for (i=0; i<5; i++) t[i] = input.ulongs[i]; fcontract_iter(t,1), fcontract_iter(t,1); // donna: now t is between 0 and 2^255-1, properly carried. // donna: case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. t[0] += 19, fcontract_iter(t,1); // now between 19 and 2^255-1 in both cases, and offset by 19. t[0] += 0x8000000000000 - 19; for (i=1; i<5; i++) t[i] += 0x8000000000000 - 1; // now between 2^255 and 2^256-20, and offset by 2^255. fcontract_iter(t,0); store_limb(out.bytes,t[0] | (t[1] << 51)); store_limb(out.bytes+8,(t[1] >> 13) | (t[2] << 38)); store_limb(out.bytes+16,(t[2] >> 26) | (t[3] << 25)); store_limb(out.bytes+24,(t[3] >> 39) | (t[4] << 12)); return(out); } bits256 curve25519(bits256 mysecret,bits256 basepoint) { bits320 bp,x,z; mysecret.bytes[0] &= 0xf8, mysecret.bytes[31] &= 0x7f, mysecret.bytes[31] |= 0x40; bp = fexpand(basepoint); cmult(&x,&z,mysecret,bp); return(fcontract(fmul(x,crecip(z)))); } #else // from curve25519-donna.c typedef uint8_t u8; typedef int32_t s32; typedef int64_t limb; /* Multiply a number by a scalar: output = in * scalar */ static void fscalar_product32(limb *output, const limb *in, const limb scalar) { unsigned i; for (i = 0; i < 10; ++i) { output[i] = in[i] * scalar; } } /* Multiply two numbers: output = in2 * in * * output must be distinct to both inputs. The inputs are reduced coefficient * form, the output is not. * * output[x] <= 14 * the largest product of the input limbs. static void fproduct(limb *output, const limb *in2, const limb *in) { output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]); output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) + ((limb) ((s32) in2[1])) * ((s32) in[0]); output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) + ((limb) ((s32) in2[0])) * ((s32) in[2]) + ((limb) ((s32) in2[2])) * ((s32) in[0]); output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) + ((limb) ((s32) in2[2])) * ((s32) in[1]) + ((limb) ((s32) in2[0])) * ((s32) in[3]) + ((limb) ((s32) in2[3])) * ((s32) in[0]); output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) + 2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) + ((limb) ((s32) in2[3])) * ((s32) in[1])) + ((limb) ((s32) in2[0])) * ((s32) in[4]) + ((limb) ((s32) in2[4])) * ((s32) in[0]); output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) + ((limb) ((s32) in2[3])) * ((s32) in[2]) + ((limb) ((s32) in2[1])) * ((s32) in[4]) + ((limb) ((s32) in2[4])) * ((s32) in[1]) + ((limb) ((s32) in2[0])) * ((s32) in[5]) + ((limb) ((s32) in2[5])) * ((s32) in[0]); output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) + ((limb) ((s32) in2[1])) * ((s32) in[5]) + ((limb) ((s32) in2[5])) * ((s32) in[1])) + ((limb) ((s32) in2[2])) * ((s32) in[4]) + ((limb) ((s32) in2[4])) * ((s32) in[2]) + ((limb) ((s32) in2[0])) * ((s32) in[6]) + ((limb) ((s32) in2[6])) * ((s32) in[0]); output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) + ((limb) ((s32) in2[4])) * ((s32) in[3]) + ((limb) ((s32) in2[2])) * ((s32) in[5]) + ((limb) ((s32) in2[5])) * ((s32) in[2]) + ((limb) ((s32) in2[1])) * ((s32) in[6]) + ((limb) ((s32) in2[6])) * ((s32) in[1]) + ((limb) ((s32) in2[0])) * ((s32) in[7]) + ((limb) ((s32) in2[7])) * ((s32) in[0]); output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) + 2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) + ((limb) ((s32) in2[5])) * ((s32) in[3]) + ((limb) ((s32) in2[1])) * ((s32) in[7]) + ((limb) ((s32) in2[7])) * ((s32) in[1])) + ((limb) ((s32) in2[2])) * ((s32) in[6]) + ((limb) ((s32) in2[6])) * ((s32) in[2]) + ((limb) ((s32) in2[0])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[0]); output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) + ((limb) ((s32) in2[5])) * ((s32) in[4]) + ((limb) ((s32) in2[3])) * ((s32) in[6]) + ((limb) ((s32) in2[6])) * ((s32) in[3]) + ((limb) ((s32) in2[2])) * ((s32) in[7]) + ((limb) ((s32) in2[7])) * ((s32) in[2]) + ((limb) ((s32) in2[1])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[1]) + ((limb) ((s32) in2[0])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[0]); output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) + ((limb) ((s32) in2[3])) * ((s32) in[7]) + ((limb) ((s32) in2[7])) * ((s32) in[3]) + ((limb) ((s32) in2[1])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[1])) + ((limb) ((s32) in2[4])) * ((s32) in[6]) + ((limb) ((s32) in2[6])) * ((s32) in[4]) + ((limb) ((s32) in2[2])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[2]); output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) + ((limb) ((s32) in2[6])) * ((s32) in[5]) + ((limb) ((s32) in2[4])) * ((s32) in[7]) + ((limb) ((s32) in2[7])) * ((s32) in[4]) + ((limb) ((s32) in2[3])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[3]) + ((limb) ((s32) in2[2])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[2]); output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) + 2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) + ((limb) ((s32) in2[7])) * ((s32) in[5]) + ((limb) ((s32) in2[3])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[3])) + ((limb) ((s32) in2[4])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[4]); output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) + ((limb) ((s32) in2[7])) * ((s32) in[6]) + ((limb) ((s32) in2[5])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[5]) + ((limb) ((s32) in2[4])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[4]); output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) + ((limb) ((s32) in2[5])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[5])) + ((limb) ((s32) in2[6])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[6]); output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) + ((limb) ((s32) in2[8])) * ((s32) in[7]) + ((limb) ((s32) in2[6])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[6]); output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) + 2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[7])); output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) + ((limb) ((s32) in2[9])) * ((s32) in[8]); output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]); }*/ /* Reduce a long form to a short form by taking the input mod 2^255 - 19. * * On entry: |output[i]| < 14*2^54 * On exit: |output[0..8]| < 280*2^54 */ static void freduce_degree(limb *output) { /* Each of these shifts and adds ends up multiplying the value by 19. * * For output[0..8], the absolute entry value is < 14*2^54 and we add, at * most, 19*14*2^54 thus, on exit, |output[0..8]| < 280*2^54. */ output[8] += output[18] << 4; output[8] += output[18] << 1; output[8] += output[18]; output[7] += output[17] << 4; output[7] += output[17] << 1; output[7] += output[17]; output[6] += output[16] << 4; output[6] += output[16] << 1; output[6] += output[16]; output[5] += output[15] << 4; output[5] += output[15] << 1; output[5] += output[15]; output[4] += output[14] << 4; output[4] += output[14] << 1; output[4] += output[14]; output[3] += output[13] << 4; output[3] += output[13] << 1; output[3] += output[13]; output[2] += output[12] << 4; output[2] += output[12] << 1; output[2] += output[12]; output[1] += output[11] << 4; output[1] += output[11] << 1; output[1] += output[11]; output[0] += output[10] << 4; output[0] += output[10] << 1; output[0] += output[10]; } #if (-1 & 3) != 3 #error "This code only works on a two's complement system" #endif /* return v / 2^26, using only shifts and adds. * * On entry: v can take any value. */ static inline limb div_by_2_26(const limb v) { /* High word of v; no shift needed. */ const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32); /* Set to all 1s if v was negative; else set to 0s. */ const int32_t sign = ((int32_t) highword) >> 31; /* Set to 0x3ffffff if v was negative; else set to 0. */ const int32_t roundoff = ((uint32_t) sign) >> 6; /* Should return v / (1<<26) */ return (v + roundoff) >> 26; } /* return v / (2^25), using only shifts and adds. * * On entry: v can take any value. */ static inline limb div_by_2_25(const limb v) { /* High word of v; no shift needed*/ const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32); /* Set to all 1s if v was negative; else set to 0s. */ const int32_t sign = ((int32_t) highword) >> 31; /* Set to 0x1ffffff if v was negative; else set to 0. */ const int32_t roundoff = ((uint32_t) sign) >> 7; /* Should return v / (1<<25) */ return (v + roundoff) >> 25; } /* Reduce all coefficients of the short form input so that |x| < 2^26. * * On entry: |output[i]| < 280*2^54 */ static void freduce_coefficients(limb *output) { unsigned i; output[10] = 0; for (i = 0; i < 10; i += 2) { limb over = div_by_2_26(output[i]); /* The entry condition (that |output[i]| < 280*2^54) means that over is, at * most, 280*2^28 in the first iteration of this loop. This is added to the * next limb and we can approximate the resulting bound of that limb by * 281*2^54. */ output[i] -= over << 26; output[i+1] += over; /* For the first iteration, |output[i+1]| < 281*2^54, thus |over| < * 281*2^29. When this is added to the next limb, the resulting bound can * be approximated as 281*2^54. * * For subsequent iterations of the loop, 281*2^54 remains a conservative * bound and no overflow occurs. */ over = div_by_2_25(output[i+1]); output[i+1] -= over << 25; output[i+2] += over; } /* Now |output[10]| < 281*2^29 and all other coefficients are reduced. */ output[0] += output[10] << 4; output[0] += output[10] << 1; output[0] += output[10]; output[10] = 0; /* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19*281*2^29 * So |over| will be no more than 2^16. */ { limb over = div_by_2_26(output[0]); output[0] -= over << 26; output[1] += over; } /* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 2^16 < 2^26. The * bound on |output[1]| is sufficient to meet our needs. */ } /* A helpful wrapper around fproduct: output = in * in2. * * On entry: |in[i]| < 2^27 and |in2[i]| < 2^27. * * output must be distinct to both inputs. The output is reduced degree * (indeed, one need only provide storage for 10 limbs) and |output[i]| < 2^26. static void fmul32(limb *output, const limb *in, const limb *in2) { limb t[19]; fproduct(t, in, in2); //|t[i]| < 14*2^54 freduce_degree(t); freduce_coefficients(t); // |t[i]| < 2^26 memcpy(output, t, sizeof(limb) * 10); }*/ /* Square a number: output = in**2 * * output must be distinct from the input. The inputs are reduced coefficient * form, the output is not. * * output[x] <= 14 * the largest product of the input limbs. */ static void fsquare_inner(limb *output, const limb *in) { output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]); output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]); output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) + ((limb) ((s32) in[0])) * ((s32) in[2])); output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) + ((limb) ((s32) in[0])) * ((s32) in[3])); output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) + 4 * ((limb) ((s32) in[1])) * ((s32) in[3]) + 2 * ((limb) ((s32) in[0])) * ((s32) in[4]); output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) + ((limb) ((s32) in[1])) * ((s32) in[4]) + ((limb) ((s32) in[0])) * ((s32) in[5])); output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) + ((limb) ((s32) in[2])) * ((s32) in[4]) + ((limb) ((s32) in[0])) * ((s32) in[6]) + 2 * ((limb) ((s32) in[1])) * ((s32) in[5])); output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) + ((limb) ((s32) in[2])) * ((s32) in[5]) + ((limb) ((s32) in[1])) * ((s32) in[6]) + ((limb) ((s32) in[0])) * ((s32) in[7])); output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) + 2 * (((limb) ((s32) in[2])) * ((s32) in[6]) + ((limb) ((s32) in[0])) * ((s32) in[8]) + 2 * (((limb) ((s32) in[1])) * ((s32) in[7]) + ((limb) ((s32) in[3])) * ((s32) in[5]))); output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) + ((limb) ((s32) in[3])) * ((s32) in[6]) + ((limb) ((s32) in[2])) * ((s32) in[7]) + ((limb) ((s32) in[1])) * ((s32) in[8]) + ((limb) ((s32) in[0])) * ((s32) in[9])); output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) + ((limb) ((s32) in[4])) * ((s32) in[6]) + ((limb) ((s32) in[2])) * ((s32) in[8]) + 2 * (((limb) ((s32) in[3])) * ((s32) in[7]) + ((limb) ((s32) in[1])) * ((s32) in[9]))); output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) + ((limb) ((s32) in[4])) * ((s32) in[7]) + ((limb) ((s32) in[3])) * ((s32) in[8]) + ((limb) ((s32) in[2])) * ((s32) in[9])); output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) + 2 * (((limb) ((s32) in[4])) * ((s32) in[8]) + 2 * (((limb) ((s32) in[5])) * ((s32) in[7]) + ((limb) ((s32) in[3])) * ((s32) in[9]))); output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) + ((limb) ((s32) in[5])) * ((s32) in[8]) + ((limb) ((s32) in[4])) * ((s32) in[9])); output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) + ((limb) ((s32) in[6])) * ((s32) in[8]) + 2 * ((limb) ((s32) in[5])) * ((s32) in[9])); output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) + ((limb) ((s32) in[6])) * ((s32) in[9])); output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) + 4 * ((limb) ((s32) in[7])) * ((s32) in[9]); output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]); output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]); } /* fsquare sets output = in^2. * * On entry: The |in| argument is in reduced coefficients form and |in[i]| < * 2^27. * * On exit: The |output| argument is in reduced coefficients form (indeed, one * need only provide storage for 10 limbs) and |out[i]| < 2^26. */ static void fsquare32(limb *output, const limb *in) { limb t[19]; fsquare_inner(t, in); /* |t[i]| < 14*2^54 because the largest product of two limbs will be < * 2^(27+27) and fsquare_inner adds together, at most, 14 of those * products. */ freduce_degree(t); freduce_coefficients(t); /* |t[i]| < 2^26 */ memcpy(output, t, sizeof(limb) * 10); } #if (-32 >> 1) != -16 #error "This code only works when >> does sign-extension on negative numbers" #endif /* s32_eq returns 0xffffffff iff a == b and zero otherwise. */ static s32 s32_eq(s32 a, s32 b) { a = ~(a ^ b); a &= a << 16; a &= a << 8; a &= a << 4; a &= a << 2; a &= a << 1; return a >> 31; } /* s32_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are * both non-negative. */ static s32 s32_gte(s32 a, s32 b) { a -= b; /* a >= 0 iff a >= b. */ return ~(a >> 31); } /* Take a fully reduced polynomial form number and contract it into a * little-endian, 32-byte array. * * On entry: |input_limbs[i]| < 2^26 */ static void fcontract32(u8 *output, limb *input_limbs) { int i; int j; s32 input[10]; s32 mask; /* |input_limbs[i]| < 2^26, so it's valid to convert to an s32. */ for (i = 0; i < 10; i++) input[i] = (s32)input_limbs[i]; for (j = 0; j < 2; ++j) { for (i = 0; i < 9; ++i) { if ((i & 1) == 1) { /* This calculation is a time-invariant way to make input[i] * non-negative by borrowing from the next-larger limb. */ const s32 mask = input[i] >> 31; const s32 carry = -((input[i] & mask) >> 25); input[i] = input[i] + (carry << 25); input[i+1] = input[i+1] - carry; } else { const s32 mask = input[i] >> 31; const s32 carry = -((input[i] & mask) >> 26); input[i] = input[i] + (carry << 26); input[i+1] = input[i+1] - carry; } } /* There's no greater limb for input[9] to borrow from, but we can multiply * by 19 and borrow from input[0], which is valid mod 2^255-19. */ { const s32 mask = input[9] >> 31; const s32 carry = -((input[9] & mask) >> 25); input[9] = input[9] + (carry << 25); input[0] = input[0] - (carry * 19); } /* After the first iteration, input[1..9] are non-negative and fit within * 25 or 26 bits, depending on position. However, input[0] may be * negative. */ } /* The first borrow-propagation pass above ended with every limb except (possibly) input[0] non-negative. If input[0] was negative after the first pass, then it was because of a carry from input[9]. On entry, input[9] < 2^26 so the carry was, at most, one, since (2**26-1) >> 25 = 1. Thus input[0] >= -19. In the second pass, each limb is decreased by at most one. Thus the second borrow-propagation pass could only have wrapped around to decrease input[0] again if the first pass left input[0] negative *and* input[1] through input[9] were all zero. In that case, input[1] is now 2^25 - 1, and this last borrow-propagation step will leave input[1] non-negative. */ { const s32 mask = input[0] >> 31; const s32 carry = -((input[0] & mask) >> 26); input[0] = input[0] + (carry << 26); input[1] = input[1] - carry; } /* All input[i] are now non-negative. However, there might be values between * 2^25 and 2^26 in a limb which is, nominally, 25 bits wide. */ for (j = 0; j < 2; j++) { for (i = 0; i < 9; i++) { if ((i & 1) == 1) { const s32 carry = input[i] >> 25; input[i] &= 0x1ffffff; input[i+1] += carry; } else { const s32 carry = input[i] >> 26; input[i] &= 0x3ffffff; input[i+1] += carry; } } { const s32 carry = input[9] >> 25; input[9] &= 0x1ffffff; input[0] += 19*carry; } } /* If the first carry-chain pass, just above, ended up with a carry from * input[9], and that caused input[0] to be out-of-bounds, then input[0] was * < 2^26 + 2*19, because the carry was, at most, two. * * If the second pass carried from input[9] again then input[0] is < 2*19 and * the input[9] -> input[0] carry didn't push input[0] out of bounds. */ /* It still remains the case that input might be between 2^255-19 and 2^255. * In this case, input[1..9] must take their maximum value and input[0] must * be >= (2^255-19) & 0x3ffffff, which is 0x3ffffed. */ mask = s32_gte(input[0], 0x3ffffed); for (i = 1; i < 10; i++) { if ((i & 1) == 1) { mask &= s32_eq(input[i], 0x1ffffff); } else { mask &= s32_eq(input[i], 0x3ffffff); } } /* mask is either 0xffffffff (if input >= 2^255-19) and zero otherwise. Thus * this conditionally subtracts 2^255-19. */ input[0] -= mask & 0x3ffffed; for (i = 1; i < 10; i++) { if ((i & 1) == 1) { input[i] -= mask & 0x1ffffff; } else { input[i] -= mask & 0x3ffffff; } } input[1] <<= 2; input[2] <<= 3; input[3] <<= 5; input[4] <<= 6; input[6] <<= 1; input[7] <<= 3; input[8] <<= 4; input[9] <<= 6; #define F(i, s) \ output[s+0] |= input[i] & 0xff; \ output[s+1] = (input[i] >> 8) & 0xff; \ output[s+2] = (input[i] >> 16) & 0xff; \ output[s+3] = (input[i] >> 24) & 0xff; output[0] = 0; output[16] = 0; F(0,0); F(1,3); F(2,6); F(3,9); F(4,12); F(5,16); F(6,19); F(7,22); F(8,25); F(9,28); #undef F } bits320 bits320_limbs(limb limbs[10]) { bits320 output; int32_t i; for (i=0; i<10; i++) output.uints[i] = limbs[i]; return(output); } static inline bits320 fscalar_product(const bits320 in,const uint64_t scalar) { limb output[10],input[10]; int32_t i; for (i=0; i<10; i++) input[i] = in.uints[i]; fscalar_product32(output,input,scalar); return(bits320_limbs(output)); } static inline bits320 fsquare_times(const bits320 in,uint64_t count) { limb output[10],input[10]; int32_t i; for (i=0; i<10; i++) input[i] = in.uints[i]; for (i=0; i Output: 2Q, Q+Q' // x2 z2: long form && x3 z3: long form // x z: short form, destroyed && xprime zprime: short form, destroyed // qmqp: short form, preserved static inline void fmonty(bits320 *x2, bits320 *z2, // output 2Q bits320 *x3, bits320 *z3, // output Q + Q' bits320 *x, bits320 *z, // input Q bits320 *xprime, bits320 *zprime, // input Q' const bits320 qmqp) // input Q - Q' { bits320 origx,origxprime,zzz,xx,zz,xxprime,zzprime; origx = *x; *x = fsum(*x,*z), fdifference_backwards(z->ulongs,origx.ulongs); // does x - z origxprime = *xprime; *xprime = fsum(*xprime,*zprime), fdifference_backwards(zprime->ulongs,origxprime.ulongs); xxprime = fmul(*xprime,*z), zzprime = fmul(*x,*zprime); origxprime = xxprime; xxprime = fsum(xxprime,zzprime), fdifference_backwards(zzprime.ulongs,origxprime.ulongs); *x3 = fsquare_times(xxprime,1), *z3 = fmul(fsquare_times(zzprime,1),qmqp); xx = fsquare_times(*x,1), zz = fsquare_times(*z,1); *x2 = fmul(xx,zz); fdifference_backwards(zz.ulongs,xx.ulongs); // does zz = xx - zz zzz = fscalar_product(zz,121665); *z2 = fmul(zz,fsum(zzz,xx)); } // ----------------------------------------------------------------------------- // Maybe swap the contents of two limb arrays (@a and @b), each @len elements // long. Perform the swap iff @swap is non-zero. // This function performs the swap without leaking any side-channel information. // ----------------------------------------------------------------------------- static inline void swap_conditional(bits320 *a,bits320 *b,uint64_t iswap) { int32_t i; const uint64_t swap = -iswap; for (i=0; i<5; ++i) { const uint64_t x = swap & (a->ulongs[i] ^ b->ulongs[i]); a->ulongs[i] ^= x, b->ulongs[i] ^= x; } } // Calculates nQ where Q is the x-coordinate of a point on the curve // resultx/resultz: the x coordinate of the resulting curve point (short form) // n: a little endian, 32-byte number // q: a point of the curve (short form) void cmult(bits320 *resultx,bits320 *resultz,bits256 secret,const bits320 q) { int32_t i,j; bits320 a,b,c,d,e,f,g,h,*t; bits320 Zero320bits,One320bits, *nqpqx = &a,*nqpqz = &b,*nqx = &c,*nqz = &d,*nqpqx2 = &e,*nqpqz2 = &f,*nqx2 = &g,*nqz2 = &h; memset(&Zero320bits,0,sizeof(Zero320bits)); memset(&One320bits,0,sizeof(One320bits)), One320bits.ulongs[0] = 1; a = d = e = g = Zero320bits, b = c = f = h = One320bits; *nqpqx = q; for (i=0; i<32; i++) { uint8_t byte = secret.bytes[31 - i]; for (j=0; j<8; j++) { const uint64_t bit = byte >> 7; swap_conditional(nqx,nqpqx,bit), swap_conditional(nqz,nqpqz,bit); fmonty(nqx2,nqz2,nqpqx2,nqpqz2,nqx,nqz,nqpqx,nqpqz,q); swap_conditional(nqx2,nqpqx2,bit), swap_conditional(nqz2,nqpqz2,bit); t = nqx, nqx = nqx2, nqx2 = t; t = nqz, nqz = nqz2, nqz2 = t; t = nqpqx, nqpqx = nqpqx2, nqpqx2 = t; t = nqpqz, nqpqz = nqpqz2, nqpqz2 = t; byte <<= 1; } } *resultx = *nqx, *resultz = *nqz; } // Shamelessly copied from donna's code that copied djb's code, changed a little inline bits320 crecip(const bits320 z) { bits320 a,t0,b,c; /* 2 */ a = fsquare_times(z, 1); // a = 2 /* 8 */ t0 = fsquare_times(a, 2); /* 9 */ b = fmul(t0, z); // b = 9 /* 11 */ a = fmul(b, a); // a = 11 /* 22 */ t0 = fsquare_times(a, 1); /* 2^5 - 2^0 = 31 */ b = fmul(t0, b); /* 2^10 - 2^5 */ t0 = fsquare_times(b, 5); /* 2^10 - 2^0 */ b = fmul(t0, b); /* 2^20 - 2^10 */ t0 = fsquare_times(b, 10); /* 2^20 - 2^0 */ c = fmul(t0, b); /* 2^40 - 2^20 */ t0 = fsquare_times(c, 20); /* 2^40 - 2^0 */ t0 = fmul(t0, c); /* 2^50 - 2^10 */ t0 = fsquare_times(t0, 10); /* 2^50 - 2^0 */ b = fmul(t0, b); /* 2^100 - 2^50 */ t0 = fsquare_times(b, 50); /* 2^100 - 2^0 */ c = fmul(t0, b); /* 2^200 - 2^100 */ t0 = fsquare_times(c, 100); /* 2^200 - 2^0 */ t0 = fmul(t0, c); /* 2^250 - 2^50 */ t0 = fsquare_times(t0, 50); /* 2^250 - 2^0 */ t0 = fmul(t0, b); /* 2^255 - 2^5 */ t0 = fsquare_times(t0, 5); /* 2^255 - 21 */ return(fmul(t0, a)); } #ifndef _WIN32 void OS_randombytes(unsigned char *x,long xlen); #endif bits256 rand256(int32_t privkeyflag) { bits256 randval; #ifndef __WIN32 OS_randombytes(randval.bytes,sizeof(randval)); #else randombytes_buf(randval.bytes,sizeof(randval)); #endif if ( privkeyflag != 0 ) randval.bytes[0] &= 0xf8, randval.bytes[31] &= 0x7f, randval.bytes[31] |= 0x40; return(randval); } bits256 curve25519_basepoint9() { bits256 basepoint; memset(&basepoint,0,sizeof(basepoint)); basepoint.bytes[0] = 9; return(basepoint); } bits256 curve25519_keypair(bits256 *pubkeyp) { bits256 privkey; privkey = rand256(1); *pubkeyp = curve25519(privkey,curve25519_basepoint9()); //printf("[%llx %llx] ",privkey.txid,(*pubkeyp).txid); return(privkey); } bits256 curve25519_shared(bits256 privkey,bits256 otherpub) { bits256 shared,hash; shared = curve25519(privkey,otherpub); vcalc_sha256(0,hash.bytes,shared.bytes,sizeof(shared)); //printf("priv.%llx pub.%llx shared.%llx -> hash.%llx\n",privkey.txid,pubkey.txid,shared.txid,hash.txid); //hash.bytes[0] &= 0xf8, hash.bytes[31] &= 0x7f, hash.bytes[31] |= 64; return(hash); } int32_t curve25519_donna(uint8_t *mypublic,const uint8_t *secret,const uint8_t *basepoint) { bits256 val,p,bp; memcpy(p.bytes,secret,sizeof(p)); memcpy(bp.bytes,basepoint,sizeof(bp)); val = curve25519(p,bp); memcpy(mypublic,val.bytes,sizeof(val)); return(0); } uint64_t conv_NXTpassword(unsigned char *mysecret,unsigned char *mypublic,uint8_t *pass,int32_t passlen) { static uint8_t basepoint[32] = {9}; uint64_t addr; uint8_t hash[32]; if ( pass != 0 && passlen != 0 ) vcalc_sha256(0,mysecret,pass,passlen); mysecret[0] &= 248, mysecret[31] &= 127, mysecret[31] |= 64; curve25519_donna(mypublic,mysecret,basepoint); vcalc_sha256(0,hash,mypublic,32); memcpy(&addr,hash,sizeof(addr)); return(addr); } uint256 komodo_kvprivkey(uint256 *pubkeyp,char *passphrase) { uint256 privkey; conv_NXTpassword((uint8_t *)&privkey,(uint8_t *)pubkeyp,(uint8_t *)passphrase,(int32_t)strlen(passphrase)); return(privkey); } uint256 komodo_kvsig(uint8_t *buf,int32_t len,uint256 _privkey) { bits256 sig,hash,otherpub,checksig,pubkey,privkey; uint256 usig; memcpy(&privkey,&_privkey,sizeof(privkey)); vcalc_sha256(0,hash.bytes,buf,len); otherpub = curve25519(hash,curve25519_basepoint9()); pubkey = curve25519(privkey,curve25519_basepoint9()); sig = curve25519_shared(privkey,otherpub); checksig = curve25519_shared(hash,pubkey); /*int32_t i; for (i=0; i "); for (i=0; i<32; i++) printf("%02x",((uint8_t *)&privkey)[i]); printf(" -> "); for (i=0; i<32; i++) printf("%02x",((uint8_t *)&pubkey)[i]); printf(" pubkey\n");*/ memcpy(&usig,&sig,sizeof(usig)); return(usig); } int32_t komodo_kvsigverify(uint8_t *buf,int32_t len,uint256 _pubkey,uint256 sig) { bits256 hash,checksig,pubkey; static uint256 zeroes; memcpy(&pubkey,&_pubkey,sizeof(pubkey)); if ( memcmp(&pubkey,&zeroes,sizeof(pubkey)) != 0 ) { vcalc_sha256(0,hash.bytes,buf,len); checksig = curve25519_shared(hash,pubkey); /*int32_t i; for (i=0; i "); for (i=0; i<32; i++) printf("%02x",((uint8_t *)&hash)[i]); printf(" -> "); for (i=0; i<32; i++) printf("%02x",((uint8_t *)&pubkey)[i]); printf(" verify pubkey\n"); for (i=0; i<32; i++) printf("%02x",((uint8_t *)&sig)[i]); printf(" sig vs"); for (i=0; i<32; i++) printf("%02x",((uint8_t *)&checksig)[i]); printf(" checksig\n");*/ if ( memcmp(&checksig,&sig,sizeof(sig)) != 0 ) return(-1); //else printf("VALIDATED\n"); } return(0); } #endif