/* * Copyright (c) 2017 Thomas Pornin * * Permission is hereby granted, free of charge, to any person obtaining * a copy of this software and associated documentation files (the * "Software"), to deal in the Software without restriction, including * without limitation the rights to use, copy, modify, merge, publish, * distribute, sublicense, and/or sell copies of the Software, and to * permit persons to whom the Software is furnished to do so, subject to * the following conditions: * * The above copyright notice and this permission notice shall be * included in all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE * SOFTWARE. */ #include "inner.h" /* * Parameters for the field: * - field modulus p = 2^255-19 * - R^2 mod p (R = 2^(31k) for the smallest k such that R >= p) */ static const uint32_t C255_P[] = { 0x00000107, 0x7FFFFFED, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x0000007F }; #define P0I 0x286BCA1B static const uint32_t C255_R2[] = { 0x00000107, 0x00000000, 0x02D20000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000 }; static const uint32_t C255_A24[] = { 0x00000107, 0x53000000, 0x0000468B, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000 }; /* obsolete #include #include static void print_int_mont(const char *name, const uint32_t *x) { uint32_t y[10]; unsigned char tmp[32]; size_t u; printf("%s = ", name); memcpy(y, x, sizeof y); br_i31_from_monty(y, C255_P, P0I); br_i31_encode(tmp, sizeof tmp, y); for (u = 0; u < sizeof tmp; u ++) { printf("%02X", tmp[u]); } printf("\n"); } */ static const unsigned char GEN[] = { 0x09, 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 }; static const unsigned char ORDER[] = { 0x7F, 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 }; static const unsigned char * api_generator(int curve, size_t *len) { (void)curve; *len = 32; return GEN; } static const unsigned char * api_order(int curve, size_t *len) { (void)curve; *len = 32; return ORDER; } static size_t api_xoff(int curve, size_t *len) { (void)curve; *len = 32; return 0; } static void cswap(uint32_t *a, uint32_t *b, uint32_t ctl) { int i; ctl = -ctl; for (i = 0; i < 10; i ++) { uint32_t aw, bw, tw; aw = a[i]; bw = b[i]; tw = ctl & (aw ^ bw); a[i] = aw ^ tw; b[i] = bw ^ tw; } } static void c255_add(uint32_t *d, const uint32_t *a, const uint32_t *b) { uint32_t ctl; uint32_t t[10]; memcpy(t, a, sizeof t); ctl = br_i31_add(t, b, 1); ctl |= NOT(br_i31_sub(t, C255_P, 0)); br_i31_sub(t, C255_P, ctl); memcpy(d, t, sizeof t); } static void c255_sub(uint32_t *d, const uint32_t *a, const uint32_t *b) { uint32_t t[10]; memcpy(t, a, sizeof t); br_i31_add(t, C255_P, br_i31_sub(t, b, 1)); memcpy(d, t, sizeof t); } static void c255_mul(uint32_t *d, const uint32_t *a, const uint32_t *b) { uint32_t t[10]; br_i31_montymul(t, a, b, C255_P, P0I); memcpy(d, t, sizeof t); } static void byteswap(unsigned char *G) { int i; for (i = 0; i < 16; i ++) { unsigned char t; t = G[i]; G[i] = G[31 - i]; G[31 - i] = t; } } static uint32_t api_mul(unsigned char *G, size_t Glen, const unsigned char *kb, size_t kblen, int curve) { uint32_t x1[10], x2[10], x3[10], z2[10], z3[10]; uint32_t a[10], aa[10], b[10], bb[10]; uint32_t c[10], d[10], e[10], da[10], cb[10]; unsigned char k[32]; uint32_t swap; int i; (void)curve; /* * Points are encoded over exactly 32 bytes. Multipliers must fit * in 32 bytes as well. * RFC 7748 mandates that the high bit of the last point byte must * be ignored/cleared. */ if (Glen != 32 || kblen > 32) { return 0; } G[31] &= 0x7F; /* * Byteswap the point encoding, because it uses little-endian, and * the generic decoding routine uses big-endian. */ byteswap(G); /* * Decode the point ('u' coordinate). This should be reduced * modulo p, but we prefer to avoid the dependency on * br_i31_decode_reduce(). Instead, we use br_i31_decode_mod() * with a synthetic modulus of value 2^255 (this must work * since G was truncated to 255 bits), then use a conditional * subtraction. We use br_i31_decode_mod() and not * br_i31_decode(), because the ec_prime_i31 implementation uses * the former but not the latter. * br_i31_decode_reduce(a, G, 32, C255_P); */ br_i31_zero(b, 0x108); b[9] = 0x0080; br_i31_decode_mod(a, G, 32, b); a[0] = 0x107; br_i31_sub(a, C255_P, NOT(br_i31_sub(a, C255_P, 0))); /* * Initialise variables x1, x2, z2, x3 and z3. We set all of them * into Montgomery representation. */ br_i31_montymul(x1, a, C255_R2, C255_P, P0I); memcpy(x3, x1, sizeof x1); br_i31_zero(z2, C255_P[0]); memcpy(x2, z2, sizeof z2); x2[1] = 0x13000000; memcpy(z3, x2, sizeof x2); /* * kb[] is in big-endian notation, but possibly shorter than k[]. */ memset(k, 0, (sizeof k) - kblen); memcpy(k + (sizeof k) - kblen, kb, kblen); k[31] &= 0xF8; k[0] &= 0x7F; k[0] |= 0x40; /* obsolete print_int_mont("x1", x1); */ swap = 0; for (i = 254; i >= 0; i --) { uint32_t kt; kt = (k[31 - (i >> 3)] >> (i & 7)) & 1; swap ^= kt; cswap(x2, x3, swap); cswap(z2, z3, swap); swap = kt; /* obsolete print_int_mont("x2", x2); print_int_mont("z2", z2); print_int_mont("x3", x3); print_int_mont("z3", z3); */ c255_add(a, x2, z2); c255_mul(aa, a, a); c255_sub(b, x2, z2); c255_mul(bb, b, b); c255_sub(e, aa, bb); c255_add(c, x3, z3); c255_sub(d, x3, z3); c255_mul(da, d, a); c255_mul(cb, c, b); /* obsolete print_int_mont("a ", a); print_int_mont("aa", aa); print_int_mont("b ", b); print_int_mont("bb", bb); print_int_mont("e ", e); print_int_mont("c ", c); print_int_mont("d ", d); print_int_mont("da", da); print_int_mont("cb", cb); */ c255_add(x3, da, cb); c255_mul(x3, x3, x3); c255_sub(z3, da, cb); c255_mul(z3, z3, z3); c255_mul(z3, z3, x1); c255_mul(x2, aa, bb); c255_mul(z2, C255_A24, e); c255_add(z2, z2, aa); c255_mul(z2, e, z2); /* obsolete print_int_mont("x2", x2); print_int_mont("z2", z2); print_int_mont("x3", x3); print_int_mont("z3", z3); */ } cswap(x2, x3, swap); cswap(z2, z3, swap); /* * Inverse z2 with a modular exponentiation. This is a simple * square-and-multiply algorithm; we mutualise most non-squarings * since the exponent contains almost only ones. */ memcpy(a, z2, sizeof z2); for (i = 0; i < 15; i ++) { c255_mul(a, a, a); c255_mul(a, a, z2); } memcpy(b, a, sizeof a); for (i = 0; i < 14; i ++) { int j; for (j = 0; j < 16; j ++) { c255_mul(b, b, b); } c255_mul(b, b, a); } for (i = 14; i >= 0; i --) { c255_mul(b, b, b); if ((0xFFEB >> i) & 1) { c255_mul(b, z2, b); } } c255_mul(b, x2, b); /* * To avoid a dependency on br_i31_from_monty(), we use * a Montgomery multiplication with 1. * memcpy(x2, b, sizeof b); * br_i31_from_monty(x2, C255_P, P0I); */ br_i31_zero(a, C255_P[0]); a[1] = 1; br_i31_montymul(x2, a, b, C255_P, P0I); br_i31_encode(G, 32, x2); byteswap(G); return 1; } static size_t api_mulgen(unsigned char *R, const unsigned char *x, size_t xlen, int curve) { const unsigned char *G; size_t Glen; G = api_generator(curve, &Glen); memcpy(R, G, Glen); api_mul(R, Glen, x, xlen, curve); return Glen; } static uint32_t api_muladd(unsigned char *A, const unsigned char *B, size_t len, const unsigned char *x, size_t xlen, const unsigned char *y, size_t ylen, int curve) { /* * We don't implement this method, since it is used for ECDSA * only, and there is no ECDSA over Curve25519 (which instead * uses EdDSA). */ (void)A; (void)B; (void)len; (void)x; (void)xlen; (void)y; (void)ylen; (void)curve; return 0; } /* see bearssl_ec.h */ const br_ec_impl br_ec_c25519_i31 = { (uint32_t)0x20000000, &api_generator, &api_order, &api_xoff, &api_mul, &api_mulgen, &api_muladd };