diff options
Diffstat (limited to 'third_party/bearssl/src/ec_c25519_m62.c')
| -rw-r--r-- | third_party/bearssl/src/ec_c25519_m62.c | 605 |
1 files changed, 605 insertions, 0 deletions
diff --git a/third_party/bearssl/src/ec_c25519_m62.c b/third_party/bearssl/src/ec_c25519_m62.c new file mode 100644 index 0000000..6b058eb --- /dev/null +++ b/third_party/bearssl/src/ec_c25519_m62.c @@ -0,0 +1,605 @@ +/* + * Copyright (c) 2018 Thomas Pornin <[email protected]> + * + * 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" + +#if BR_INT128 || BR_UMUL128 + +#if BR_UMUL128 +#include <intrin.h> +#endif + +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; +} + +/* + * A field element is encoded as five 64-bit integers, in basis 2^51. + * Limbs may be occasionally larger than 2^51, to save on carry + * propagation costs. + */ + +#define MASK51 (((uint64_t)1 << 51) - (uint64_t)1) + +/* + * Swap two field elements, conditionally on a flag. + */ +static inline void +f255_cswap(uint64_t *a, uint64_t *b, uint32_t ctl) +{ + uint64_t m, w; + + m = -(uint64_t)ctl; + w = m & (a[0] ^ b[0]); a[0] ^= w; b[0] ^= w; + w = m & (a[1] ^ b[1]); a[1] ^= w; b[1] ^= w; + w = m & (a[2] ^ b[2]); a[2] ^= w; b[2] ^= w; + w = m & (a[3] ^ b[3]); a[3] ^= w; b[3] ^= w; + w = m & (a[4] ^ b[4]); a[4] ^= w; b[4] ^= w; +} + +/* + * Addition with no carry propagation. Limbs double in size. + */ +static inline void +f255_add(uint64_t *d, const uint64_t *a, const uint64_t *b) +{ + d[0] = a[0] + b[0]; + d[1] = a[1] + b[1]; + d[2] = a[2] + b[2]; + d[3] = a[3] + b[3]; + d[4] = a[4] + b[4]; +} + +/* + * Subtraction. + * On input, limbs must fit on 60 bits each. On output, result is + * partially reduced, with max value 2^255+19456; moreover, all + * limbs will fit on 51 bits, except the low limb, which may have + * value up to 2^51+19455. + */ +static inline void +f255_sub(uint64_t *d, const uint64_t *a, const uint64_t *b) +{ + uint64_t cc, w; + + /* + * We compute d = (2^255-19)*1024 + a - b. Since the limbs + * fit on 60 bits, the maximum value of operands are slightly + * more than 2^264, but much less than 2^265-19456. This + * ensures that the result is positive. + */ + + /* + * Initial carry is 19456, since we add 2^265-19456. Each + * individual subtraction may yield a carry up to 513. + */ + w = a[0] - b[0] - 19456; + d[0] = w & MASK51; + cc = -(w >> 51) & 0x3FF; + w = a[1] - b[1] - cc; + d[1] = w & MASK51; + cc = -(w >> 51) & 0x3FF; + w = a[2] - b[2] - cc; + d[2] = w & MASK51; + cc = -(w >> 51) & 0x3FF; + w = a[3] - b[3] - cc; + d[3] = w & MASK51; + cc = -(w >> 51) & 0x3FF; + d[4] = ((uint64_t)1 << 61) + a[4] - b[4] - cc; + + /* + * Partial reduction. The intermediate result may be up to + * slightly above 2^265, but less than 2^265+2^255. When we + * truncate to 255 bits, the upper bits will be at most 1024. + */ + d[0] += 19 * (d[4] >> 51); + d[4] &= MASK51; +} + +/* + * UMUL51(hi, lo, x, y) computes: + * + * hi = floor((x * y) / (2^51)) + * lo = x * y mod 2^51 + * + * Note that lo < 2^51, but "hi" may be larger, if the input operands are + * larger. + */ +#if BR_INT128 + +#define UMUL51(hi, lo, x, y) do { \ + unsigned __int128 umul_tmp; \ + umul_tmp = (unsigned __int128)(x) * (unsigned __int128)(y); \ + (hi) = (uint64_t)(umul_tmp >> 51); \ + (lo) = (uint64_t)umul_tmp & MASK51; \ + } while (0) + +#elif BR_UMUL128 + +#define UMUL51(hi, lo, x, y) do { \ + uint64_t umul_hi, umul_lo; \ + umul_lo = _umul128((x), (y), &umul_hi); \ + (hi) = (umul_hi << 13) | (umul_lo >> 51); \ + (lo) = umul_lo & MASK51; \ + } while (0) + +#endif + +/* + * Multiplication. + * On input, limbs must fit on 54 bits each. + * On output, limb 0 is at most 2^51 + 155647, and other limbs fit + * on 51 bits each. + */ +static inline void +f255_mul(uint64_t *d, uint64_t *a, uint64_t *b) +{ + uint64_t t[10], hi, lo, w, cc; + + /* + * Perform cross products, accumulating values without carry + * propagation. + * + * Since input limbs fit on 54 bits each, each individual + * UMUL51 will produce a "hi" of less than 2^57. The maximum + * sum will be at most 5*(2^57-1) + 4*(2^51-1) (for t[5]), + * i.e. less than 324*2^51. + */ + + UMUL51(t[1], t[0], a[0], b[0]); + + UMUL51(t[2], lo, a[1], b[0]); t[1] += lo; + UMUL51(hi, lo, a[0], b[1]); t[1] += lo; t[2] += hi; + + UMUL51(t[3], lo, a[2], b[0]); t[2] += lo; + UMUL51(hi, lo, a[1], b[1]); t[2] += lo; t[3] += hi; + UMUL51(hi, lo, a[0], b[2]); t[2] += lo; t[3] += hi; + + UMUL51(t[4], lo, a[3], b[0]); t[3] += lo; + UMUL51(hi, lo, a[2], b[1]); t[3] += lo; t[4] += hi; + UMUL51(hi, lo, a[1], b[2]); t[3] += lo; t[4] += hi; + UMUL51(hi, lo, a[0], b[3]); t[3] += lo; t[4] += hi; + + UMUL51(t[5], lo, a[4], b[0]); t[4] += lo; + UMUL51(hi, lo, a[3], b[1]); t[4] += lo; t[5] += hi; + UMUL51(hi, lo, a[2], b[2]); t[4] += lo; t[5] += hi; + UMUL51(hi, lo, a[1], b[3]); t[4] += lo; t[5] += hi; + UMUL51(hi, lo, a[0], b[4]); t[4] += lo; t[5] += hi; + + UMUL51(t[6], lo, a[4], b[1]); t[5] += lo; + UMUL51(hi, lo, a[3], b[2]); t[5] += lo; t[6] += hi; + UMUL51(hi, lo, a[2], b[3]); t[5] += lo; t[6] += hi; + UMUL51(hi, lo, a[1], b[4]); t[5] += lo; t[6] += hi; + + UMUL51(t[7], lo, a[4], b[2]); t[6] += lo; + UMUL51(hi, lo, a[3], b[3]); t[6] += lo; t[7] += hi; + UMUL51(hi, lo, a[2], b[4]); t[6] += lo; t[7] += hi; + + UMUL51(t[8], lo, a[4], b[3]); t[7] += lo; + UMUL51(hi, lo, a[3], b[4]); t[7] += lo; t[8] += hi; + + UMUL51(t[9], lo, a[4], b[4]); t[8] += lo; + + /* + * The upper words t[5]..t[9] are folded back into the lower + * words, using the rule that 2^255 = 19 in the field. + * + * Since each t[i] is less than 324*2^51, the additions below + * will yield less than 6480*2^51 in each limb; this fits in + * 64 bits (6480*2^51 < 8192*2^51 = 2^64), hence there is + * no overflow. + */ + t[0] += 19 * t[5]; + t[1] += 19 * t[6]; + t[2] += 19 * t[7]; + t[3] += 19 * t[8]; + t[4] += 19 * t[9]; + + /* + * Propagate carries. + */ + w = t[0]; + d[0] = w & MASK51; + cc = w >> 51; + w = t[1] + cc; + d[1] = w & MASK51; + cc = w >> 51; + w = t[2] + cc; + d[2] = w & MASK51; + cc = w >> 51; + w = t[3] + cc; + d[3] = w & MASK51; + cc = w >> 51; + w = t[4] + cc; + d[4] = w & MASK51; + cc = w >> 51; + + /* + * Since the limbs were 64-bit values, the top carry is at + * most 8192 (in practice, that cannot be reached). We simply + * performed a partial reduction. + */ + d[0] += 19 * cc; +} + +/* + * Multiplication by A24 = 121665. + * Input must have limbs of 60 bits at most. + */ +static inline void +f255_mul_a24(uint64_t *d, const uint64_t *a) +{ + uint64_t t[5], cc, w; + + /* + * 121665 = 15 * 8111. We first multiply by 15, with carry + * propagation and partial reduction. + */ + w = a[0] * 15; + t[0] = w & MASK51; + cc = w >> 51; + w = a[1] * 15 + cc; + t[1] = w & MASK51; + cc = w >> 51; + w = a[2] * 15 + cc; + t[2] = w & MASK51; + cc = w >> 51; + w = a[3] * 15 + cc; + t[3] = w & MASK51; + cc = w >> 51; + w = a[4] * 15 + cc; + t[4] = w & MASK51; + t[0] += 19 * (w >> 51); + + /* + * Then multiplication by 8111. At that point, we known that + * t[0] is less than 2^51 + 19*8192, and other limbs are less + * than 2^51; thus, there will be no overflow. + */ + w = t[0] * 8111; + d[0] = w & MASK51; + cc = w >> 51; + w = t[1] * 8111 + cc; + d[1] = w & MASK51; + cc = w >> 51; + w = t[2] * 8111 + cc; + d[2] = w & MASK51; + cc = w >> 51; + w = t[3] * 8111 + cc; + d[3] = w & MASK51; + cc = w >> 51; + w = t[4] * 8111 + cc; + d[4] = w & MASK51; + d[0] += 19 * (w >> 51); +} + +/* + * Finalize reduction. + * On input, limbs must fit on 51 bits, except possibly the low limb, + * which may be slightly above 2^51. + */ +static inline void +f255_final_reduce(uint64_t *a) +{ + uint64_t t[5], cc, w; + + /* + * We add 19. If the result (in t[]) is below 2^255, then a[] + * is already less than 2^255-19, thus already reduced. + * Otherwise, we subtract 2^255 from t[], in which case we + * have t = a - (2^255-19), and that's our result. + */ + w = a[0] + 19; + t[0] = w & MASK51; + cc = w >> 51; + w = a[1] + cc; + t[1] = w & MASK51; + cc = w >> 51; + w = a[2] + cc; + t[2] = w & MASK51; + cc = w >> 51; + w = a[3] + cc; + t[3] = w & MASK51; + cc = w >> 51; + w = a[4] + cc; + t[4] = w & MASK51; + cc = w >> 51; + + /* + * The bit 255 of t is in cc. If that bit is 0, when a[] must + * be unchanged; otherwise, it must be replaced with t[]. + */ + cc = -cc; + a[0] ^= cc & (a[0] ^ t[0]); + a[1] ^= cc & (a[1] ^ t[1]); + a[2] ^= cc & (a[2] ^ t[2]); + a[3] ^= cc & (a[3] ^ t[3]); + a[4] ^= cc & (a[4] ^ t[4]); +} + +static uint32_t +api_mul(unsigned char *G, size_t Glen, + const unsigned char *kb, size_t kblen, int curve) +{ + unsigned char k[32]; + uint64_t x1[5], x2[5], z2[5], x3[5], z3[5]; + uint32_t swap; + int i; + + (void)curve; + + /* + * Points are encoded over exactly 32 bytes. Multipliers must fit + * in 32 bytes as well. + */ + if (Glen != 32 || kblen > 32) { + return 0; + } + + /* + * RFC 7748 mandates that the high bit of the last point byte must + * be ignored/cleared; the "& MASK51" in the initialization for + * x1[4] clears that bit. + */ + x1[0] = br_dec64le(&G[0]) & MASK51; + x1[1] = (br_dec64le(&G[6]) >> 3) & MASK51; + x1[2] = (br_dec64le(&G[12]) >> 6) & MASK51; + x1[3] = (br_dec64le(&G[19]) >> 1) & MASK51; + x1[4] = (br_dec64le(&G[24]) >> 12) & MASK51; + + /* + * We can use memset() to clear values, because exact-width types + * like uint64_t are guaranteed to have no padding bits or + * trap representations. + */ + memset(x2, 0, sizeof x2); + x2[0] = 1; + memset(z2, 0, sizeof z2); + memcpy(x3, x1, sizeof x1); + memcpy(z3, x2, sizeof x2); + + /* + * The multiplier is provided in big-endian notation, and + * possibly shorter than 32 bytes. + */ + memset(k, 0, (sizeof k) - kblen); + memcpy(k + (sizeof k) - kblen, kb, kblen); + k[31] &= 0xF8; + k[0] &= 0x7F; + k[0] |= 0x40; + + swap = 0; + + for (i = 254; i >= 0; i --) { + uint64_t a[5], aa[5], b[5], bb[5], e[5]; + uint64_t c[5], d[5], da[5], cb[5]; + uint32_t kt; + + kt = (k[31 - (i >> 3)] >> (i & 7)) & 1; + swap ^= kt; + f255_cswap(x2, x3, swap); + f255_cswap(z2, z3, swap); + swap = kt; + + /* + * At that point, limbs of x_2 and z_2 are assumed to fit + * on at most 52 bits each. + * + * Each f255_add() adds one bit to the maximum range of + * the values, but f255_sub() and f255_mul() bring back + * the limbs into 52 bits. All f255_add() outputs are + * used only as inputs for f255_mul(), which ensures + * that limbs remain in the proper range. + */ + + /* A = x_2 + z_2 -- limbs fit on 53 bits each */ + f255_add(a, x2, z2); + + /* AA = A^2 */ + f255_mul(aa, a, a); + + /* B = x_2 - z_2 */ + f255_sub(b, x2, z2); + + /* BB = B^2 */ + f255_mul(bb, b, b); + + /* E = AA - BB */ + f255_sub(e, aa, bb); + + /* C = x_3 + z_3 -- limbs fit on 53 bits each */ + f255_add(c, x3, z3); + + /* D = x_3 - z_3 */ + f255_sub(d, x3, z3); + + /* DA = D * A */ + f255_mul(da, d, a); + + /* CB = C * B */ + f255_mul(cb, c, b); + + /* x_3 = (DA + CB)^2 */ + f255_add(x3, da, cb); + f255_mul(x3, x3, x3); + + /* z_3 = x_1 * (DA - CB)^2 */ + f255_sub(z3, da, cb); + f255_mul(z3, z3, z3); + f255_mul(z3, x1, z3); + + /* x_2 = AA * BB */ + f255_mul(x2, aa, bb); + + /* z_2 = E * (AA + a24 * E) */ + f255_mul_a24(z2, e); + f255_add(z2, aa, z2); + f255_mul(z2, e, z2); + } + + f255_cswap(x2, x3, swap); + f255_cswap(z2, z3, swap); + + /* + * Compute 1/z2 = z2^(p-2). Since p = 2^255-19, we can mutualize + * most non-squarings. We use x1 and x3, now useless, as temporaries. + */ + memcpy(x1, z2, sizeof z2); + for (i = 0; i < 15; i ++) { + f255_mul(x1, x1, x1); + f255_mul(x1, x1, z2); + } + memcpy(x3, x1, sizeof x1); + for (i = 0; i < 14; i ++) { + int j; + + for (j = 0; j < 16; j ++) { + f255_mul(x3, x3, x3); + } + f255_mul(x3, x3, x1); + } + for (i = 14; i >= 0; i --) { + f255_mul(x3, x3, x3); + if ((0xFFEB >> i) & 1) { + f255_mul(x3, z2, x3); + } + } + + /* + * Compute x2/z2. We have 1/z2 in x3. + */ + f255_mul(x2, x2, x3); + f255_final_reduce(x2); + + /* + * Encode the final x2 value in little-endian. We first assemble + * the limbs into 64-bit values. + */ + x2[0] |= x2[1] << 51; + x2[1] = (x2[1] >> 13) | (x2[2] << 38); + x2[2] = (x2[2] >> 26) | (x2[3] << 25); + x2[3] = (x2[3] >> 39) | (x2[4] << 12); + br_enc64le(G, x2[0]); + br_enc64le(G + 8, x2[1]); + br_enc64le(G + 16, x2[2]); + br_enc64le(G + 24, x2[3]); + 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_m62 = { + (uint32_t)0x20000000, + &api_generator, + &api_order, + &api_xoff, + &api_mul, + &api_mulgen, + &api_muladd +}; + +/* see bearssl_ec.h */ +const br_ec_impl * +br_ec_c25519_m62_get(void) +{ + return &br_ec_c25519_m62; +} + +#else + +/* see bearssl_ec.h */ +const br_ec_impl * +br_ec_c25519_m62_get(void) +{ + return 0; +} + +#endif |