| // The MIT License (MIT) |
| // |
| // Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file). |
| // |
| // 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. |
| |
| // Some of this code is taken from the ref10 version of Ed25519 in SUPERCOP |
| // 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as |
| // public domain but parts have been replaced with code generated by Fiat |
| // (https://github.com/mit-plv/fiat-crypto), which is MIT licensed. |
| // |
| // The field functions are shared by Ed25519 and X25519 where possible. |
| |
| #include <openssl/curve25519.h> |
| |
| #include <assert.h> |
| #include <string.h> |
| |
| #include <openssl/cpu.h> |
| #include <openssl/mem.h> |
| #include <openssl/rand.h> |
| #include <openssl/sha.h> |
| #include <openssl/type_check.h> |
| |
| #include "internal.h" |
| #include "../../crypto/internal.h" |
| |
| |
| // Various pre-computed constants. |
| #include "./curve25519_tables.h" |
| |
| |
| // Low-level intrinsic operations (hand-written). |
| |
| static uint64_t load_3(const uint8_t *in) { |
| uint64_t result; |
| result = (uint64_t)in[0]; |
| result |= ((uint64_t)in[1]) << 8; |
| result |= ((uint64_t)in[2]) << 16; |
| return result; |
| } |
| |
| static uint64_t load_4(const uint8_t *in) { |
| uint64_t result; |
| result = (uint64_t)in[0]; |
| result |= ((uint64_t)in[1]) << 8; |
| result |= ((uint64_t)in[2]) << 16; |
| result |= ((uint64_t)in[3]) << 24; |
| return result; |
| } |
| |
| #if defined(BORINGSSL_CURVE25519_64BIT) |
| static uint64_t load_8(const uint8_t *in) { |
| uint64_t result; |
| result = (uint64_t)in[0]; |
| result |= ((uint64_t)in[1]) << 8; |
| result |= ((uint64_t)in[2]) << 16; |
| result |= ((uint64_t)in[3]) << 24; |
| result |= ((uint64_t)in[4]) << 32; |
| result |= ((uint64_t)in[5]) << 40; |
| result |= ((uint64_t)in[6]) << 48; |
| result |= ((uint64_t)in[7]) << 56; |
| return result; |
| } |
| |
| static uint8_t /*bool*/ addcarryx_u51(uint8_t /*bool*/ c, uint64_t a, |
| uint64_t b, uint64_t *low) { |
| // This function extracts 51 bits of result and 1 bit of carry (52 total), so |
| // a 64-bit intermediate is sufficient. |
| uint64_t x = a + b + c; |
| *low = x & ((UINT64_C(1) << 51) - 1); |
| return (x >> 51) & 1; |
| } |
| |
| static uint8_t /*bool*/ subborrow_u51(uint8_t /*bool*/ c, uint64_t a, |
| uint64_t b, uint64_t *low) { |
| // This function extracts 51 bits of result and 1 bit of borrow (52 total), so |
| // a 64-bit intermediate is sufficient. |
| uint64_t x = a - b - c; |
| *low = x & ((UINT64_C(1) << 51) - 1); |
| return x >> 63; |
| } |
| |
| static uint64_t cmovznz64(uint64_t t, uint64_t z, uint64_t nz) { |
| t = -!!t; // all set if nonzero, 0 if 0 |
| return (t&nz) | ((~t)&z); |
| } |
| |
| #else |
| |
| static uint8_t /*bool*/ addcarryx_u25(uint8_t /*bool*/ c, uint32_t a, |
| uint32_t b, uint32_t *low) { |
| // This function extracts 25 bits of result and 1 bit of carry (26 total), so |
| // a 32-bit intermediate is sufficient. |
| uint32_t x = a + b + c; |
| *low = x & ((1 << 25) - 1); |
| return (x >> 25) & 1; |
| } |
| |
| static uint8_t /*bool*/ addcarryx_u26(uint8_t /*bool*/ c, uint32_t a, |
| uint32_t b, uint32_t *low) { |
| // This function extracts 26 bits of result and 1 bit of carry (27 total), so |
| // a 32-bit intermediate is sufficient. |
| uint32_t x = a + b + c; |
| *low = x & ((1 << 26) - 1); |
| return (x >> 26) & 1; |
| } |
| |
| static uint8_t /*bool*/ subborrow_u25(uint8_t /*bool*/ c, uint32_t a, |
| uint32_t b, uint32_t *low) { |
| // This function extracts 25 bits of result and 1 bit of borrow (26 total), so |
| // a 32-bit intermediate is sufficient. |
| uint32_t x = a - b - c; |
| *low = x & ((1 << 25) - 1); |
| return x >> 31; |
| } |
| |
| static uint8_t /*bool*/ subborrow_u26(uint8_t /*bool*/ c, uint32_t a, |
| uint32_t b, uint32_t *low) { |
| // This function extracts 26 bits of result and 1 bit of borrow (27 total), so |
| // a 32-bit intermediate is sufficient. |
| uint32_t x = a - b - c; |
| *low = x & ((1 << 26) - 1); |
| return x >> 31; |
| } |
| |
| static uint32_t cmovznz32(uint32_t t, uint32_t z, uint32_t nz) { |
| t = -!!t; // all set if nonzero, 0 if 0 |
| return (t&nz) | ((~t)&z); |
| } |
| |
| #endif |
| |
| |
| // Field operations. |
| |
| #if defined(BORINGSSL_CURVE25519_64BIT) |
| |
| #define assert_fe(f) do { \ |
| for (unsigned _assert_fe_i = 0; _assert_fe_i< 5; _assert_fe_i++) { \ |
| assert(f[_assert_fe_i] < 1.125*(UINT64_C(1)<<51)); \ |
| } \ |
| } while (0) |
| |
| #define assert_fe_loose(f) do { \ |
| for (unsigned _assert_fe_i = 0; _assert_fe_i< 5; _assert_fe_i++) { \ |
| assert(f[_assert_fe_i] < 3.375*(UINT64_C(1)<<51)); \ |
| } \ |
| } while (0) |
| |
| #define assert_fe_frozen(f) do { \ |
| for (unsigned _assert_fe_i = 0; _assert_fe_i< 5; _assert_fe_i++) { \ |
| assert(f[_assert_fe_i] < (UINT64_C(1)<<51)); \ |
| } \ |
| } while (0) |
| |
| static void fe_frombytes_impl(uint64_t h[5], const uint8_t *s) { |
| // Ignores top bit of s. |
| uint64_t a0 = load_8(s); |
| uint64_t a1 = load_8(s+8); |
| uint64_t a2 = load_8(s+16); |
| uint64_t a3 = load_8(s+24); |
| // Use 51 bits, 64-51 = 13 left. |
| h[0] = a0 & ((UINT64_C(1) << 51) - 1); |
| // (64-51) + 38 = 13 + 38 = 51 |
| h[1] = (a0 >> 51) | ((a1 & ((UINT64_C(1) << 38) - 1)) << 13); |
| // (64-38) + 25 = 26 + 25 = 51 |
| h[2] = (a1 >> 38) | ((a2 & ((UINT64_C(1) << 25) - 1)) << 26); |
| // (64-25) + 12 = 39 + 12 = 51 |
| h[3] = (a2 >> 25) | ((a3 & ((UINT64_C(1) << 12) - 1)) << 39); |
| // (64-12) = 52, ignore top bit |
| h[4] = (a3 >> 12) & ((UINT64_C(1) << 51) - 1); |
| assert_fe(h); |
| } |
| |
| static void fe_frombytes(fe *h, const uint8_t *s) { |
| fe_frombytes_impl(h->v, s); |
| } |
| |
| static void fe_freeze(uint64_t out[5], const uint64_t in1[5]) { |
| { const uint64_t x7 = in1[4]; |
| { const uint64_t x8 = in1[3]; |
| { const uint64_t x6 = in1[2]; |
| { const uint64_t x4 = in1[1]; |
| { const uint64_t x2 = in1[0]; |
| { uint64_t x10; uint8_t/*bool*/ x11 = subborrow_u51(0x0, x2, 0x7ffffffffffed, &x10); |
| { uint64_t x13; uint8_t/*bool*/ x14 = subborrow_u51(x11, x4, 0x7ffffffffffff, &x13); |
| { uint64_t x16; uint8_t/*bool*/ x17 = subborrow_u51(x14, x6, 0x7ffffffffffff, &x16); |
| { uint64_t x19; uint8_t/*bool*/ x20 = subborrow_u51(x17, x8, 0x7ffffffffffff, &x19); |
| { uint64_t x22; uint8_t/*bool*/ x23 = subborrow_u51(x20, x7, 0x7ffffffffffff, &x22); |
| { uint64_t x24 = cmovznz64(x23, 0x0, 0xffffffffffffffffL); |
| { uint64_t x25 = (x24 & 0x7ffffffffffed); |
| { uint64_t x27; uint8_t/*bool*/ x28 = addcarryx_u51(0x0, x10, x25, &x27); |
| { uint64_t x29 = (x24 & 0x7ffffffffffff); |
| { uint64_t x31; uint8_t/*bool*/ x32 = addcarryx_u51(x28, x13, x29, &x31); |
| { uint64_t x33 = (x24 & 0x7ffffffffffff); |
| { uint64_t x35; uint8_t/*bool*/ x36 = addcarryx_u51(x32, x16, x33, &x35); |
| { uint64_t x37 = (x24 & 0x7ffffffffffff); |
| { uint64_t x39; uint8_t/*bool*/ x40 = addcarryx_u51(x36, x19, x37, &x39); |
| { uint64_t x41 = (x24 & 0x7ffffffffffff); |
| { uint64_t x43; addcarryx_u51(x40, x22, x41, &x43); |
| out[0] = x27; |
| out[1] = x31; |
| out[2] = x35; |
| out[3] = x39; |
| out[4] = x43; |
| }}}}}}}}}}}}}}}}}}}}} |
| } |
| |
| static void fe_tobytes(uint8_t s[32], const fe *f) { |
| assert_fe(f->v); |
| uint64_t h[5]; |
| fe_freeze(h, f->v); |
| assert_fe_frozen(h); |
| |
| s[0] = h[0] >> 0; |
| s[1] = h[0] >> 8; |
| s[2] = h[0] >> 16; |
| s[3] = h[0] >> 24; |
| s[4] = h[0] >> 32; |
| s[5] = h[0] >> 40; |
| s[6] = (h[0] >> 48) | (h[1] << 3); |
| s[7] = h[1] >> 5; |
| s[8] = h[1] >> 13; |
| s[9] = h[1] >> 21; |
| s[10] = h[1] >> 29; |
| s[11] = h[1] >> 37; |
| s[12] = (h[1] >> 45) | (h[2] << 6); |
| s[13] = h[2] >> 2; |
| s[14] = h[2] >> 10; |
| s[15] = h[2] >> 18; |
| s[16] = h[2] >> 26; |
| s[17] = h[2] >> 34; |
| s[18] = h[2] >> 42; |
| s[19] = (h[2] >> 50) | (h[3] << 1); |
| s[20] = h[3] >> 7; |
| s[21] = h[3] >> 15; |
| s[22] = h[3] >> 23; |
| s[23] = h[3] >> 31; |
| s[24] = h[3] >> 39; |
| s[25] = (h[3] >> 47) | (h[4] << 4); |
| s[26] = h[4] >> 4; |
| s[27] = h[4] >> 12; |
| s[28] = h[4] >> 20; |
| s[29] = h[4] >> 28; |
| s[30] = h[4] >> 36; |
| s[31] = h[4] >> 44; |
| } |
| |
| // h = 0 |
| static void fe_0(fe *h) { |
| OPENSSL_memset(h, 0, sizeof(fe)); |
| } |
| |
| static void fe_loose_0(fe_loose *h) { |
| OPENSSL_memset(h, 0, sizeof(fe_loose)); |
| } |
| |
| // h = 1 |
| static void fe_1(fe *h) { |
| OPENSSL_memset(h, 0, sizeof(fe)); |
| h->v[0] = 1; |
| } |
| |
| static void fe_loose_1(fe_loose *h) { |
| OPENSSL_memset(h, 0, sizeof(fe_loose)); |
| h->v[0] = 1; |
| } |
| |
| static void fe_add_impl(uint64_t out[5], const uint64_t in1[5], const uint64_t in2[5]) { |
| { const uint64_t x10 = in1[4]; |
| { const uint64_t x11 = in1[3]; |
| { const uint64_t x9 = in1[2]; |
| { const uint64_t x7 = in1[1]; |
| { const uint64_t x5 = in1[0]; |
| { const uint64_t x18 = in2[4]; |
| { const uint64_t x19 = in2[3]; |
| { const uint64_t x17 = in2[2]; |
| { const uint64_t x15 = in2[1]; |
| { const uint64_t x13 = in2[0]; |
| out[0] = (x5 + x13); |
| out[1] = (x7 + x15); |
| out[2] = (x9 + x17); |
| out[3] = (x11 + x19); |
| out[4] = (x10 + x18); |
| }}}}}}}}}} |
| } |
| |
| // h = f + g |
| // Can overlap h with f or g. |
| static void fe_add(fe_loose *h, const fe *f, const fe *g) { |
| assert_fe(f->v); |
| assert_fe(g->v); |
| fe_add_impl(h->v, f->v, g->v); |
| assert_fe_loose(h->v); |
| } |
| |
| static void fe_sub_impl(uint64_t out[5], const uint64_t in1[5], const uint64_t in2[5]) { |
| { const uint64_t x10 = in1[4]; |
| { const uint64_t x11 = in1[3]; |
| { const uint64_t x9 = in1[2]; |
| { const uint64_t x7 = in1[1]; |
| { const uint64_t x5 = in1[0]; |
| { const uint64_t x18 = in2[4]; |
| { const uint64_t x19 = in2[3]; |
| { const uint64_t x17 = in2[2]; |
| { const uint64_t x15 = in2[1]; |
| { const uint64_t x13 = in2[0]; |
| out[0] = ((0xfffffffffffda + x5) - x13); |
| out[1] = ((0xffffffffffffe + x7) - x15); |
| out[2] = ((0xffffffffffffe + x9) - x17); |
| out[3] = ((0xffffffffffffe + x11) - x19); |
| out[4] = ((0xffffffffffffe + x10) - x18); |
| }}}}}}}}}} |
| } |
| |
| // h = f - g |
| // Can overlap h with f or g. |
| static void fe_sub(fe_loose *h, const fe *f, const fe *g) { |
| assert_fe(f->v); |
| assert_fe(g->v); |
| fe_sub_impl(h->v, f->v, g->v); |
| assert_fe_loose(h->v); |
| } |
| |
| static void fe_carry_impl(uint64_t out[5], const uint64_t in1[5]) { |
| { const uint64_t x7 = in1[4]; |
| { const uint64_t x8 = in1[3]; |
| { const uint64_t x6 = in1[2]; |
| { const uint64_t x4 = in1[1]; |
| { const uint64_t x2 = in1[0]; |
| { uint64_t x9 = (x2 >> 0x33); |
| { uint64_t x10 = (x2 & 0x7ffffffffffff); |
| { uint64_t x11 = (x9 + x4); |
| { uint64_t x12 = (x11 >> 0x33); |
| { uint64_t x13 = (x11 & 0x7ffffffffffff); |
| { uint64_t x14 = (x12 + x6); |
| { uint64_t x15 = (x14 >> 0x33); |
| { uint64_t x16 = (x14 & 0x7ffffffffffff); |
| { uint64_t x17 = (x15 + x8); |
| { uint64_t x18 = (x17 >> 0x33); |
| { uint64_t x19 = (x17 & 0x7ffffffffffff); |
| { uint64_t x20 = (x18 + x7); |
| { uint64_t x21 = (x20 >> 0x33); |
| { uint64_t x22 = (x20 & 0x7ffffffffffff); |
| { uint64_t x23 = (x10 + (0x13 * x21)); |
| { uint64_t x24 = (x23 >> 0x33); |
| { uint64_t x25 = (x23 & 0x7ffffffffffff); |
| { uint64_t x26 = (x24 + x13); |
| { uint64_t x27 = (x26 >> 0x33); |
| { uint64_t x28 = (x26 & 0x7ffffffffffff); |
| out[0] = x25; |
| out[1] = x28; |
| out[2] = (x27 + x16); |
| out[3] = x19; |
| out[4] = x22; |
| }}}}}}}}}}}}}}}}}}}}}}}}} |
| } |
| |
| static void fe_carry(fe *h, const fe_loose* f) { |
| assert_fe_loose(f->v); |
| fe_carry_impl(h->v, f->v); |
| assert_fe(h->v); |
| } |
| |
| static void fe_mul_impl(uint64_t out[5], const uint64_t in1[5], const uint64_t in2[5]) { |
| assert_fe_loose(in1); |
| assert_fe_loose(in2); |
| { const uint64_t x10 = in1[4]; |
| { const uint64_t x11 = in1[3]; |
| { const uint64_t x9 = in1[2]; |
| { const uint64_t x7 = in1[1]; |
| { const uint64_t x5 = in1[0]; |
| { const uint64_t x18 = in2[4]; |
| { const uint64_t x19 = in2[3]; |
| { const uint64_t x17 = in2[2]; |
| { const uint64_t x15 = in2[1]; |
| { const uint64_t x13 = in2[0]; |
| { uint128_t x20 = ((uint128_t)x5 * x13); |
| { uint128_t x21 = (((uint128_t)x5 * x15) + ((uint128_t)x7 * x13)); |
| { uint128_t x22 = ((((uint128_t)x5 * x17) + ((uint128_t)x9 * x13)) + ((uint128_t)x7 * x15)); |
| { uint128_t x23 = (((((uint128_t)x5 * x19) + ((uint128_t)x11 * x13)) + ((uint128_t)x7 * x17)) + ((uint128_t)x9 * x15)); |
| { uint128_t x24 = ((((((uint128_t)x5 * x18) + ((uint128_t)x10 * x13)) + ((uint128_t)x11 * x15)) + ((uint128_t)x7 * x19)) + ((uint128_t)x9 * x17)); |
| { uint64_t x25 = (x10 * 0x13); |
| { uint64_t x26 = (x7 * 0x13); |
| { uint64_t x27 = (x9 * 0x13); |
| { uint64_t x28 = (x11 * 0x13); |
| { uint128_t x29 = ((((x20 + ((uint128_t)x25 * x15)) + ((uint128_t)x26 * x18)) + ((uint128_t)x27 * x19)) + ((uint128_t)x28 * x17)); |
| { uint128_t x30 = (((x21 + ((uint128_t)x25 * x17)) + ((uint128_t)x27 * x18)) + ((uint128_t)x28 * x19)); |
| { uint128_t x31 = ((x22 + ((uint128_t)x25 * x19)) + ((uint128_t)x28 * x18)); |
| { uint128_t x32 = (x23 + ((uint128_t)x25 * x18)); |
| { uint64_t x33 = (uint64_t) (x29 >> 0x33); |
| { uint64_t x34 = ((uint64_t)x29 & 0x7ffffffffffff); |
| { uint128_t x35 = (x33 + x30); |
| { uint64_t x36 = (uint64_t) (x35 >> 0x33); |
| { uint64_t x37 = ((uint64_t)x35 & 0x7ffffffffffff); |
| { uint128_t x38 = (x36 + x31); |
| { uint64_t x39 = (uint64_t) (x38 >> 0x33); |
| { uint64_t x40 = ((uint64_t)x38 & 0x7ffffffffffff); |
| { uint128_t x41 = (x39 + x32); |
| { uint64_t x42 = (uint64_t) (x41 >> 0x33); |
| { uint64_t x43 = ((uint64_t)x41 & 0x7ffffffffffff); |
| { uint128_t x44 = (x42 + x24); |
| { uint64_t x45 = (uint64_t) (x44 >> 0x33); |
| { uint64_t x46 = ((uint64_t)x44 & 0x7ffffffffffff); |
| { uint64_t x47 = (x34 + (0x13 * x45)); |
| { uint64_t x48 = (x47 >> 0x33); |
| { uint64_t x49 = (x47 & 0x7ffffffffffff); |
| { uint64_t x50 = (x48 + x37); |
| { uint64_t x51 = (x50 >> 0x33); |
| { uint64_t x52 = (x50 & 0x7ffffffffffff); |
| out[0] = x49; |
| out[1] = x52; |
| out[2] = (x51 + x40); |
| out[3] = x43; |
| out[4] = x46; |
| }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| assert_fe(out); |
| } |
| |
| static void fe_mul_ltt(fe_loose *h, const fe *f, const fe *g) { |
| fe_mul_impl(h->v, f->v, g->v); |
| } |
| |
| static void fe_mul_llt(fe_loose *h, const fe_loose *f, const fe *g) { |
| fe_mul_impl(h->v, f->v, g->v); |
| } |
| |
| static void fe_mul_ttt(fe *h, const fe *f, const fe *g) { |
| fe_mul_impl(h->v, f->v, g->v); |
| } |
| |
| static void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g) { |
| fe_mul_impl(h->v, f->v, g->v); |
| } |
| |
| static void fe_mul_ttl(fe *h, const fe *f, const fe_loose *g) { |
| fe_mul_impl(h->v, f->v, g->v); |
| } |
| |
| static void fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g) { |
| fe_mul_impl(h->v, f->v, g->v); |
| } |
| |
| static void fe_sqr_impl(uint64_t out[5], const uint64_t in1[5]) { |
| assert_fe_loose(in1); |
| { const uint64_t x7 = in1[4]; |
| { const uint64_t x8 = in1[3]; |
| { const uint64_t x6 = in1[2]; |
| { const uint64_t x4 = in1[1]; |
| { const uint64_t x2 = in1[0]; |
| { uint64_t x9 = (x2 * 0x2); |
| { uint64_t x10 = (x4 * 0x2); |
| { uint64_t x11 = ((x6 * 0x2) * 0x13); |
| { uint64_t x12 = (x7 * 0x13); |
| { uint64_t x13 = (x12 * 0x2); |
| { uint128_t x14 = ((((uint128_t)x2 * x2) + ((uint128_t)x13 * x4)) + ((uint128_t)x11 * x8)); |
| { uint128_t x15 = ((((uint128_t)x9 * x4) + ((uint128_t)x13 * x6)) + ((uint128_t)x8 * (x8 * 0x13))); |
| { uint128_t x16 = ((((uint128_t)x9 * x6) + ((uint128_t)x4 * x4)) + ((uint128_t)x13 * x8)); |
| { uint128_t x17 = ((((uint128_t)x9 * x8) + ((uint128_t)x10 * x6)) + ((uint128_t)x7 * x12)); |
| { uint128_t x18 = ((((uint128_t)x9 * x7) + ((uint128_t)x10 * x8)) + ((uint128_t)x6 * x6)); |
| { uint64_t x19 = (uint64_t) (x14 >> 0x33); |
| { uint64_t x20 = ((uint64_t)x14 & 0x7ffffffffffff); |
| { uint128_t x21 = (x19 + x15); |
| { uint64_t x22 = (uint64_t) (x21 >> 0x33); |
| { uint64_t x23 = ((uint64_t)x21 & 0x7ffffffffffff); |
| { uint128_t x24 = (x22 + x16); |
| { uint64_t x25 = (uint64_t) (x24 >> 0x33); |
| { uint64_t x26 = ((uint64_t)x24 & 0x7ffffffffffff); |
| { uint128_t x27 = (x25 + x17); |
| { uint64_t x28 = (uint64_t) (x27 >> 0x33); |
| { uint64_t x29 = ((uint64_t)x27 & 0x7ffffffffffff); |
| { uint128_t x30 = (x28 + x18); |
| { uint64_t x31 = (uint64_t) (x30 >> 0x33); |
| { uint64_t x32 = ((uint64_t)x30 & 0x7ffffffffffff); |
| { uint64_t x33 = (x20 + (0x13 * x31)); |
| { uint64_t x34 = (x33 >> 0x33); |
| { uint64_t x35 = (x33 & 0x7ffffffffffff); |
| { uint64_t x36 = (x34 + x23); |
| { uint64_t x37 = (x36 >> 0x33); |
| { uint64_t x38 = (x36 & 0x7ffffffffffff); |
| out[0] = x35; |
| out[1] = x38; |
| out[2] = (x37 + x26); |
| out[3] = x29; |
| out[4] = x32; |
| }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| assert_fe(out); |
| } |
| |
| static void fe_sq_tl(fe *h, const fe_loose *f) { |
| fe_sqr_impl(h->v, f->v); |
| } |
| |
| static void fe_sq_tt(fe *h, const fe *f) { |
| fe_sqr_impl(h->v, f->v); |
| } |
| |
| // Replace (f,g) with (g,f) if b == 1; |
| // replace (f,g) with (f,g) if b == 0. |
| // |
| // Preconditions: b in {0,1}. |
| static void fe_cswap(fe *f, fe *g, uint64_t b) { |
| b = 0-b; |
| for (unsigned i = 0; i < 5; i++) { |
| uint64_t x = f->v[i] ^ g->v[i]; |
| x &= b; |
| f->v[i] ^= x; |
| g->v[i] ^= x; |
| } |
| } |
| |
| // NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.. |
| static void fe_mul_121666_impl(uint64_t out[5], const uint64_t in1[5]) { |
| { const uint64_t x10 = in1[4]; |
| { const uint64_t x11 = in1[3]; |
| { const uint64_t x9 = in1[2]; |
| { const uint64_t x7 = in1[1]; |
| { const uint64_t x5 = in1[0]; |
| { const uint64_t x18 = 0; |
| { const uint64_t x19 = 0; |
| { const uint64_t x17 = 0; |
| { const uint64_t x15 = 0; |
| { const uint64_t x13 = 121666; |
| { uint128_t x20 = ((uint128_t)x5 * x13); |
| { uint128_t x21 = (((uint128_t)x5 * x15) + ((uint128_t)x7 * x13)); |
| { uint128_t x22 = ((((uint128_t)x5 * x17) + ((uint128_t)x9 * x13)) + ((uint128_t)x7 * x15)); |
| { uint128_t x23 = (((((uint128_t)x5 * x19) + ((uint128_t)x11 * x13)) + ((uint128_t)x7 * x17)) + ((uint128_t)x9 * x15)); |
| { uint128_t x24 = ((((((uint128_t)x5 * x18) + ((uint128_t)x10 * x13)) + ((uint128_t)x11 * x15)) + ((uint128_t)x7 * x19)) + ((uint128_t)x9 * x17)); |
| { uint64_t x25 = (x10 * 0x13); |
| { uint64_t x26 = (x7 * 0x13); |
| { uint64_t x27 = (x9 * 0x13); |
| { uint64_t x28 = (x11 * 0x13); |
| { uint128_t x29 = ((((x20 + ((uint128_t)x25 * x15)) + ((uint128_t)x26 * x18)) + ((uint128_t)x27 * x19)) + ((uint128_t)x28 * x17)); |
| { uint128_t x30 = (((x21 + ((uint128_t)x25 * x17)) + ((uint128_t)x27 * x18)) + ((uint128_t)x28 * x19)); |
| { uint128_t x31 = ((x22 + ((uint128_t)x25 * x19)) + ((uint128_t)x28 * x18)); |
| { uint128_t x32 = (x23 + ((uint128_t)x25 * x18)); |
| { uint64_t x33 = (uint64_t) (x29 >> 0x33); |
| { uint64_t x34 = ((uint64_t)x29 & 0x7ffffffffffff); |
| { uint128_t x35 = (x33 + x30); |
| { uint64_t x36 = (uint64_t) (x35 >> 0x33); |
| { uint64_t x37 = ((uint64_t)x35 & 0x7ffffffffffff); |
| { uint128_t x38 = (x36 + x31); |
| { uint64_t x39 = (uint64_t) (x38 >> 0x33); |
| { uint64_t x40 = ((uint64_t)x38 & 0x7ffffffffffff); |
| { uint128_t x41 = (x39 + x32); |
| { uint64_t x42 = (uint64_t) (x41 >> 0x33); |
| { uint64_t x43 = ((uint64_t)x41 & 0x7ffffffffffff); |
| { uint128_t x44 = (x42 + x24); |
| { uint64_t x45 = (uint64_t) (x44 >> 0x33); |
| { uint64_t x46 = ((uint64_t)x44 & 0x7ffffffffffff); |
| { uint64_t x47 = (x34 + (0x13 * x45)); |
| { uint64_t x48 = (x47 >> 0x33); |
| { uint64_t x49 = (x47 & 0x7ffffffffffff); |
| { uint64_t x50 = (x48 + x37); |
| { uint64_t x51 = (x50 >> 0x33); |
| { uint64_t x52 = (x50 & 0x7ffffffffffff); |
| out[0] = x49; |
| out[1] = x52; |
| out[2] = (x51 + x40); |
| out[3] = x43; |
| out[4] = x46; |
| }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| } |
| |
| static void fe_mul121666(fe *h, const fe_loose *f) { |
| assert_fe_loose(f->v); |
| fe_mul_121666_impl(h->v, f->v); |
| assert_fe(h->v); |
| } |
| |
| // Adapted from Fiat-synthesized |fe_sub_impl| with |out| = 0. |
| static void fe_neg_impl(uint64_t out[5], const uint64_t in2[5]) { |
| { const uint64_t x10 = 0; |
| { const uint64_t x11 = 0; |
| { const uint64_t x9 = 0; |
| { const uint64_t x7 = 0; |
| { const uint64_t x5 = 0; |
| { const uint64_t x18 = in2[4]; |
| { const uint64_t x19 = in2[3]; |
| { const uint64_t x17 = in2[2]; |
| { const uint64_t x15 = in2[1]; |
| { const uint64_t x13 = in2[0]; |
| out[0] = ((0xfffffffffffda + x5) - x13); |
| out[1] = ((0xffffffffffffe + x7) - x15); |
| out[2] = ((0xffffffffffffe + x9) - x17); |
| out[3] = ((0xffffffffffffe + x11) - x19); |
| out[4] = ((0xffffffffffffe + x10) - x18); |
| }}}}}}}}}} |
| } |
| |
| // h = -f |
| static void fe_neg(fe_loose *h, const fe *f) { |
| assert_fe(f->v); |
| fe_neg_impl(h->v, f->v); |
| assert_fe_loose(h->v); |
| } |
| |
| // Replace (f,g) with (g,g) if b == 1; |
| // replace (f,g) with (f,g) if b == 0. |
| // |
| // Preconditions: b in {0,1}. |
| static void fe_cmov(fe_loose *f, const fe_loose *g, uint64_t b) { |
| b = 0-b; |
| for (unsigned i = 0; i < 5; i++) { |
| uint64_t x = f->v[i] ^ g->v[i]; |
| x &= b; |
| f->v[i] ^= x; |
| } |
| } |
| |
| #else |
| |
| #define assert_fe(f) do { \ |
| for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \ |
| assert(f[_assert_fe_i] < 1.125*(1<<(26-(_assert_fe_i&1)))); \ |
| } \ |
| } while (0) |
| |
| #define assert_fe_loose(f) do { \ |
| for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \ |
| assert(f[_assert_fe_i] < 3.375*(1<<(26-(_assert_fe_i&1)))); \ |
| } \ |
| } while (0) |
| |
| #define assert_fe_frozen(f) do { \ |
| for (unsigned _assert_fe_i = 0; _assert_fe_i< 10; _assert_fe_i++) { \ |
| assert(f[_assert_fe_i] < (1u<<(26-(_assert_fe_i&1)))); \ |
| } \ |
| } while (0) |
| |
| static void fe_frombytes_impl(uint32_t h[10], const uint8_t *s) { |
| // Ignores top bit of s. |
| uint32_t a0 = load_4(s); |
| uint32_t a1 = load_4(s+4); |
| uint32_t a2 = load_4(s+8); |
| uint32_t a3 = load_4(s+12); |
| uint32_t a4 = load_4(s+16); |
| uint32_t a5 = load_4(s+20); |
| uint32_t a6 = load_4(s+24); |
| uint32_t a7 = load_4(s+28); |
| h[0] = a0&((1<<26)-1); // 26 used, 32-26 left. 26 |
| h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); // (32-26) + 19 = 6+19 = 25 |
| h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); // (32-19) + 13 = 13+13 = 26 |
| h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); // (32-13) + 6 = 19+ 6 = 25 |
| h[4] = (a3>> 6); // (32- 6) = 26 |
| h[5] = a4&((1<<25)-1); // 25 |
| h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); // (32-25) + 19 = 7+19 = 26 |
| h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); // (32-19) + 12 = 13+12 = 25 |
| h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); // (32-12) + 6 = 20+ 6 = 26 |
| h[9] = (a7>> 6)&((1<<25)-1); // 25 |
| assert_fe(h); |
| } |
| |
| static void fe_frombytes(fe *h, const uint8_t *s) { |
| fe_frombytes_impl(h->v, s); |
| } |
| |
| static void fe_freeze(uint32_t out[10], const uint32_t in1[10]) { |
| { const uint32_t x17 = in1[9]; |
| { const uint32_t x18 = in1[8]; |
| { const uint32_t x16 = in1[7]; |
| { const uint32_t x14 = in1[6]; |
| { const uint32_t x12 = in1[5]; |
| { const uint32_t x10 = in1[4]; |
| { const uint32_t x8 = in1[3]; |
| { const uint32_t x6 = in1[2]; |
| { const uint32_t x4 = in1[1]; |
| { const uint32_t x2 = in1[0]; |
| { uint32_t x20; uint8_t/*bool*/ x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20); |
| { uint32_t x23; uint8_t/*bool*/ x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23); |
| { uint32_t x26; uint8_t/*bool*/ x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26); |
| { uint32_t x29; uint8_t/*bool*/ x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29); |
| { uint32_t x32; uint8_t/*bool*/ x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32); |
| { uint32_t x35; uint8_t/*bool*/ x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35); |
| { uint32_t x38; uint8_t/*bool*/ x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38); |
| { uint32_t x41; uint8_t/*bool*/ x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41); |
| { uint32_t x44; uint8_t/*bool*/ x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44); |
| { uint32_t x47; uint8_t/*bool*/ x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47); |
| { uint32_t x49 = cmovznz32(x48, 0x0, 0xffffffff); |
| { uint32_t x50 = (x49 & 0x3ffffed); |
| { uint32_t x52; uint8_t/*bool*/ x53 = addcarryx_u26(0x0, x20, x50, &x52); |
| { uint32_t x54 = (x49 & 0x1ffffff); |
| { uint32_t x56; uint8_t/*bool*/ x57 = addcarryx_u25(x53, x23, x54, &x56); |
| { uint32_t x58 = (x49 & 0x3ffffff); |
| { uint32_t x60; uint8_t/*bool*/ x61 = addcarryx_u26(x57, x26, x58, &x60); |
| { uint32_t x62 = (x49 & 0x1ffffff); |
| { uint32_t x64; uint8_t/*bool*/ x65 = addcarryx_u25(x61, x29, x62, &x64); |
| { uint32_t x66 = (x49 & 0x3ffffff); |
| { uint32_t x68; uint8_t/*bool*/ x69 = addcarryx_u26(x65, x32, x66, &x68); |
| { uint32_t x70 = (x49 & 0x1ffffff); |
| { uint32_t x72; uint8_t/*bool*/ x73 = addcarryx_u25(x69, x35, x70, &x72); |
| { uint32_t x74 = (x49 & 0x3ffffff); |
| { uint32_t x76; uint8_t/*bool*/ x77 = addcarryx_u26(x73, x38, x74, &x76); |
| { uint32_t x78 = (x49 & 0x1ffffff); |
| { uint32_t x80; uint8_t/*bool*/ x81 = addcarryx_u25(x77, x41, x78, &x80); |
| { uint32_t x82 = (x49 & 0x3ffffff); |
| { uint32_t x84; uint8_t/*bool*/ x85 = addcarryx_u26(x81, x44, x82, &x84); |
| { uint32_t x86 = (x49 & 0x1ffffff); |
| { uint32_t x88; addcarryx_u25(x85, x47, x86, &x88); |
| out[0] = x52; |
| out[1] = x56; |
| out[2] = x60; |
| out[3] = x64; |
| out[4] = x68; |
| out[5] = x72; |
| out[6] = x76; |
| out[7] = x80; |
| out[8] = x84; |
| out[9] = x88; |
| }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| } |
| |
| static void fe_tobytes(uint8_t s[32], const fe *f) { |
| assert_fe(f->v); |
| uint32_t h[10]; |
| fe_freeze(h, f->v); |
| assert_fe_frozen(h); |
| |
| s[0] = h[0] >> 0; |
| s[1] = h[0] >> 8; |
| s[2] = h[0] >> 16; |
| s[3] = (h[0] >> 24) | (h[1] << 2); |
| s[4] = h[1] >> 6; |
| s[5] = h[1] >> 14; |
| s[6] = (h[1] >> 22) | (h[2] << 3); |
| s[7] = h[2] >> 5; |
| s[8] = h[2] >> 13; |
| s[9] = (h[2] >> 21) | (h[3] << 5); |
| s[10] = h[3] >> 3; |
| s[11] = h[3] >> 11; |
| s[12] = (h[3] >> 19) | (h[4] << 6); |
| s[13] = h[4] >> 2; |
| s[14] = h[4] >> 10; |
| s[15] = h[4] >> 18; |
| s[16] = h[5] >> 0; |
| s[17] = h[5] >> 8; |
| s[18] = h[5] >> 16; |
| s[19] = (h[5] >> 24) | (h[6] << 1); |
| s[20] = h[6] >> 7; |
| s[21] = h[6] >> 15; |
| s[22] = (h[6] >> 23) | (h[7] << 3); |
| s[23] = h[7] >> 5; |
| s[24] = h[7] >> 13; |
| s[25] = (h[7] >> 21) | (h[8] << 4); |
| s[26] = h[8] >> 4; |
| s[27] = h[8] >> 12; |
| s[28] = (h[8] >> 20) | (h[9] << 6); |
| s[29] = h[9] >> 2; |
| s[30] = h[9] >> 10; |
| s[31] = h[9] >> 18; |
| } |
| |
| // h = 0 |
| static void fe_0(fe *h) { |
| OPENSSL_memset(h, 0, sizeof(fe)); |
| } |
| |
| static void fe_loose_0(fe_loose *h) { |
| OPENSSL_memset(h, 0, sizeof(fe_loose)); |
| } |
| |
| // h = 1 |
| static void fe_1(fe *h) { |
| OPENSSL_memset(h, 0, sizeof(fe)); |
| h->v[0] = 1; |
| } |
| |
| static void fe_loose_1(fe_loose *h) { |
| OPENSSL_memset(h, 0, sizeof(fe_loose)); |
| h->v[0] = 1; |
| } |
| |
| static void fe_add_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) { |
| { const uint32_t x20 = in1[9]; |
| { const uint32_t x21 = in1[8]; |
| { const uint32_t x19 = in1[7]; |
| { const uint32_t x17 = in1[6]; |
| { const uint32_t x15 = in1[5]; |
| { const uint32_t x13 = in1[4]; |
| { const uint32_t x11 = in1[3]; |
| { const uint32_t x9 = in1[2]; |
| { const uint32_t x7 = in1[1]; |
| { const uint32_t x5 = in1[0]; |
| { const uint32_t x38 = in2[9]; |
| { const uint32_t x39 = in2[8]; |
| { const uint32_t x37 = in2[7]; |
| { const uint32_t x35 = in2[6]; |
| { const uint32_t x33 = in2[5]; |
| { const uint32_t x31 = in2[4]; |
| { const uint32_t x29 = in2[3]; |
| { const uint32_t x27 = in2[2]; |
| { const uint32_t x25 = in2[1]; |
| { const uint32_t x23 = in2[0]; |
| out[0] = (x5 + x23); |
| out[1] = (x7 + x25); |
| out[2] = (x9 + x27); |
| out[3] = (x11 + x29); |
| out[4] = (x13 + x31); |
| out[5] = (x15 + x33); |
| out[6] = (x17 + x35); |
| out[7] = (x19 + x37); |
| out[8] = (x21 + x39); |
| out[9] = (x20 + x38); |
| }}}}}}}}}}}}}}}}}}}} |
| } |
| |
| // h = f + g |
| // Can overlap h with f or g. |
| static void fe_add(fe_loose *h, const fe *f, const fe *g) { |
| assert_fe(f->v); |
| assert_fe(g->v); |
| fe_add_impl(h->v, f->v, g->v); |
| assert_fe_loose(h->v); |
| } |
| |
| static void fe_sub_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) { |
| { const uint32_t x20 = in1[9]; |
| { const uint32_t x21 = in1[8]; |
| { const uint32_t x19 = in1[7]; |
| { const uint32_t x17 = in1[6]; |
| { const uint32_t x15 = in1[5]; |
| { const uint32_t x13 = in1[4]; |
| { const uint32_t x11 = in1[3]; |
| { const uint32_t x9 = in1[2]; |
| { const uint32_t x7 = in1[1]; |
| { const uint32_t x5 = in1[0]; |
| { const uint32_t x38 = in2[9]; |
| { const uint32_t x39 = in2[8]; |
| { const uint32_t x37 = in2[7]; |
| { const uint32_t x35 = in2[6]; |
| { const uint32_t x33 = in2[5]; |
| { const uint32_t x31 = in2[4]; |
| { const uint32_t x29 = in2[3]; |
| { const uint32_t x27 = in2[2]; |
| { const uint32_t x25 = in2[1]; |
| { const uint32_t x23 = in2[0]; |
| out[0] = ((0x7ffffda + x5) - x23); |
| out[1] = ((0x3fffffe + x7) - x25); |
| out[2] = ((0x7fffffe + x9) - x27); |
| out[3] = ((0x3fffffe + x11) - x29); |
| out[4] = ((0x7fffffe + x13) - x31); |
| out[5] = ((0x3fffffe + x15) - x33); |
| out[6] = ((0x7fffffe + x17) - x35); |
| out[7] = ((0x3fffffe + x19) - x37); |
| out[8] = ((0x7fffffe + x21) - x39); |
| out[9] = ((0x3fffffe + x20) - x38); |
| }}}}}}}}}}}}}}}}}}}} |
| } |
| |
| // h = f - g |
| // Can overlap h with f or g. |
| static void fe_sub(fe_loose *h, const fe *f, const fe *g) { |
| assert_fe(f->v); |
| assert_fe(g->v); |
| fe_sub_impl(h->v, f->v, g->v); |
| assert_fe_loose(h->v); |
| } |
| |
| static void fe_carry_impl(uint32_t out[10], const uint32_t in1[10]) { |
| { const uint32_t x17 = in1[9]; |
| { const uint32_t x18 = in1[8]; |
| { const uint32_t x16 = in1[7]; |
| { const uint32_t x14 = in1[6]; |
| { const uint32_t x12 = in1[5]; |
| { const uint32_t x10 = in1[4]; |
| { const uint32_t x8 = in1[3]; |
| { const uint32_t x6 = in1[2]; |
| { const uint32_t x4 = in1[1]; |
| { const uint32_t x2 = in1[0]; |
| { uint32_t x19 = (x2 >> 0x1a); |
| { uint32_t x20 = (x2 & 0x3ffffff); |
| { uint32_t x21 = (x19 + x4); |
| { uint32_t x22 = (x21 >> 0x19); |
| { uint32_t x23 = (x21 & 0x1ffffff); |
| { uint32_t x24 = (x22 + x6); |
| { uint32_t x25 = (x24 >> 0x1a); |
| { uint32_t x26 = (x24 & 0x3ffffff); |
| { uint32_t x27 = (x25 + x8); |
| { uint32_t x28 = (x27 >> 0x19); |
| { uint32_t x29 = (x27 & 0x1ffffff); |
| { uint32_t x30 = (x28 + x10); |
| { uint32_t x31 = (x30 >> 0x1a); |
| { uint32_t x32 = (x30 & 0x3ffffff); |
| { uint32_t x33 = (x31 + x12); |
| { uint32_t x34 = (x33 >> 0x19); |
| { uint32_t x35 = (x33 & 0x1ffffff); |
| { uint32_t x36 = (x34 + x14); |
| { uint32_t x37 = (x36 >> 0x1a); |
| { uint32_t x38 = (x36 & 0x3ffffff); |
| { uint32_t x39 = (x37 + x16); |
| { uint32_t x40 = (x39 >> 0x19); |
| { uint32_t x41 = (x39 & 0x1ffffff); |
| { uint32_t x42 = (x40 + x18); |
| { uint32_t x43 = (x42 >> 0x1a); |
| { uint32_t x44 = (x42 & 0x3ffffff); |
| { uint32_t x45 = (x43 + x17); |
| { uint32_t x46 = (x45 >> 0x19); |
| { uint32_t x47 = (x45 & 0x1ffffff); |
| { uint32_t x48 = (x20 + (0x13 * x46)); |
| { uint32_t x49 = (x48 >> 0x1a); |
| { uint32_t x50 = (x48 & 0x3ffffff); |
| { uint32_t x51 = (x49 + x23); |
| { uint32_t x52 = (x51 >> 0x19); |
| { uint32_t x53 = (x51 & 0x1ffffff); |
| out[0] = x50; |
| out[1] = x53; |
| out[2] = (x52 + x26); |
| out[3] = x29; |
| out[4] = x32; |
| out[5] = x35; |
| out[6] = x38; |
| out[7] = x41; |
| out[8] = x44; |
| out[9] = x47; |
| }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| } |
| |
| static void fe_carry(fe *h, const fe_loose* f) { |
| assert_fe_loose(f->v); |
| fe_carry_impl(h->v, f->v); |
| assert_fe(h->v); |
| } |
| |
| static void fe_mul_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10]) { |
| assert_fe_loose(in1); |
| assert_fe_loose(in2); |
| { const uint32_t x20 = in1[9]; |
| { const uint32_t x21 = in1[8]; |
| { const uint32_t x19 = in1[7]; |
| { const uint32_t x17 = in1[6]; |
| { const uint32_t x15 = in1[5]; |
| { const uint32_t x13 = in1[4]; |
| { const uint32_t x11 = in1[3]; |
| { const uint32_t x9 = in1[2]; |
| { const uint32_t x7 = in1[1]; |
| { const uint32_t x5 = in1[0]; |
| { const uint32_t x38 = in2[9]; |
| { const uint32_t x39 = in2[8]; |
| { const uint32_t x37 = in2[7]; |
| { const uint32_t x35 = in2[6]; |
| { const uint32_t x33 = in2[5]; |
| { const uint32_t x31 = in2[4]; |
| { const uint32_t x29 = in2[3]; |
| { const uint32_t x27 = in2[2]; |
| { const uint32_t x25 = in2[1]; |
| { const uint32_t x23 = in2[0]; |
| { uint64_t x40 = ((uint64_t)x23 * x5); |
| { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5)); |
| { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5)); |
| { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5)); |
| { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5)); |
| { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5)); |
| { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5)); |
| { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5)); |
| { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5)); |
| { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5)); |
| { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9)); |
| { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9)); |
| { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13)); |
| { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13)); |
| { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17)); |
| { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17)); |
| { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19)))); |
| { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21)); |
| { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20); |
| { uint64_t x59 = (x48 + (x58 << 0x4)); |
| { uint64_t x60 = (x59 + (x58 << 0x1)); |
| { uint64_t x61 = (x60 + x58); |
| { uint64_t x62 = (x47 + (x57 << 0x4)); |
| { uint64_t x63 = (x62 + (x57 << 0x1)); |
| { uint64_t x64 = (x63 + x57); |
| { uint64_t x65 = (x46 + (x56 << 0x4)); |
| { uint64_t x66 = (x65 + (x56 << 0x1)); |
| { uint64_t x67 = (x66 + x56); |
| { uint64_t x68 = (x45 + (x55 << 0x4)); |
| { uint64_t x69 = (x68 + (x55 << 0x1)); |
| { uint64_t x70 = (x69 + x55); |
| { uint64_t x71 = (x44 + (x54 << 0x4)); |
| { uint64_t x72 = (x71 + (x54 << 0x1)); |
| { uint64_t x73 = (x72 + x54); |
| { uint64_t x74 = (x43 + (x53 << 0x4)); |
| { uint64_t x75 = (x74 + (x53 << 0x1)); |
| { uint64_t x76 = (x75 + x53); |
| { uint64_t x77 = (x42 + (x52 << 0x4)); |
| { uint64_t x78 = (x77 + (x52 << 0x1)); |
| { uint64_t x79 = (x78 + x52); |
| { uint64_t x80 = (x41 + (x51 << 0x4)); |
| { uint64_t x81 = (x80 + (x51 << 0x1)); |
| { uint64_t x82 = (x81 + x51); |
| { uint64_t x83 = (x40 + (x50 << 0x4)); |
| { uint64_t x84 = (x83 + (x50 << 0x1)); |
| { uint64_t x85 = (x84 + x50); |
| { uint64_t x86 = (x85 >> 0x1a); |
| { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff); |
| { uint64_t x88 = (x86 + x82); |
| { uint64_t x89 = (x88 >> 0x19); |
| { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff); |
| { uint64_t x91 = (x89 + x79); |
| { uint64_t x92 = (x91 >> 0x1a); |
| { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff); |
| { uint64_t x94 = (x92 + x76); |
| { uint64_t x95 = (x94 >> 0x19); |
| { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff); |
| { uint64_t x97 = (x95 + x73); |
| { uint64_t x98 = (x97 >> 0x1a); |
| { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff); |
| { uint64_t x100 = (x98 + x70); |
| { uint64_t x101 = (x100 >> 0x19); |
| { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff); |
| { uint64_t x103 = (x101 + x67); |
| { uint64_t x104 = (x103 >> 0x1a); |
| { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff); |
| { uint64_t x106 = (x104 + x64); |
| { uint64_t x107 = (x106 >> 0x19); |
| { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff); |
| { uint64_t x109 = (x107 + x61); |
| { uint64_t x110 = (x109 >> 0x1a); |
| { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff); |
| { uint64_t x112 = (x110 + x49); |
| { uint64_t x113 = (x112 >> 0x19); |
| { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff); |
| { uint64_t x115 = (x87 + (0x13 * x113)); |
| { uint32_t x116 = (uint32_t) (x115 >> 0x1a); |
| { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff); |
| { uint32_t x118 = (x116 + x90); |
| { uint32_t x119 = (x118 >> 0x19); |
| { uint32_t x120 = (x118 & 0x1ffffff); |
| out[0] = x117; |
| out[1] = x120; |
| out[2] = (x119 + x93); |
| out[3] = x96; |
| out[4] = x99; |
| out[5] = x102; |
| out[6] = x105; |
| out[7] = x108; |
| out[8] = x111; |
| out[9] = x114; |
| }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| assert_fe(out); |
| } |
| |
| static void fe_mul_ltt(fe_loose *h, const fe *f, const fe *g) { |
| fe_mul_impl(h->v, f->v, g->v); |
| } |
| |
| static void fe_mul_llt(fe_loose *h, const fe_loose *f, const fe *g) { |
| fe_mul_impl(h->v, f->v, g->v); |
| } |
| |
| static void fe_mul_ttt(fe *h, const fe *f, const fe *g) { |
| fe_mul_impl(h->v, f->v, g->v); |
| } |
| |
| static void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g) { |
| fe_mul_impl(h->v, f->v, g->v); |
| } |
| |
| static void fe_mul_ttl(fe *h, const fe *f, const fe_loose *g) { |
| fe_mul_impl(h->v, f->v, g->v); |
| } |
| |
| static void fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g) { |
| fe_mul_impl(h->v, f->v, g->v); |
| } |
| |
| static void fe_sqr_impl(uint32_t out[10], const uint32_t in1[10]) { |
| assert_fe_loose(in1); |
| { const uint32_t x17 = in1[9]; |
| { const uint32_t x18 = in1[8]; |
| { const uint32_t x16 = in1[7]; |
| { const uint32_t x14 = in1[6]; |
| { const uint32_t x12 = in1[5]; |
| { const uint32_t x10 = in1[4]; |
| { const uint32_t x8 = in1[3]; |
| { const uint32_t x6 = in1[2]; |
| { const uint32_t x4 = in1[1]; |
| { const uint32_t x2 = in1[0]; |
| { uint64_t x19 = ((uint64_t)x2 * x2); |
| { uint64_t x20 = ((uint64_t)(0x2 * x2) * x4); |
| { uint64_t x21 = (0x2 * (((uint64_t)x4 * x4) + ((uint64_t)x2 * x6))); |
| { uint64_t x22 = (0x2 * (((uint64_t)x4 * x6) + ((uint64_t)x2 * x8))); |
| { uint64_t x23 = ((((uint64_t)x6 * x6) + ((uint64_t)(0x4 * x4) * x8)) + ((uint64_t)(0x2 * x2) * x10)); |
| { uint64_t x24 = (0x2 * ((((uint64_t)x6 * x8) + ((uint64_t)x4 * x10)) + ((uint64_t)x2 * x12))); |
| { uint64_t x25 = (0x2 * (((((uint64_t)x8 * x8) + ((uint64_t)x6 * x10)) + ((uint64_t)x2 * x14)) + ((uint64_t)(0x2 * x4) * x12))); |
| { uint64_t x26 = (0x2 * (((((uint64_t)x8 * x10) + ((uint64_t)x6 * x12)) + ((uint64_t)x4 * x14)) + ((uint64_t)x2 * x16))); |
| { uint64_t x27 = (((uint64_t)x10 * x10) + (0x2 * ((((uint64_t)x6 * x14) + ((uint64_t)x2 * x18)) + (0x2 * (((uint64_t)x4 * x16) + ((uint64_t)x8 * x12)))))); |
| { uint64_t x28 = (0x2 * ((((((uint64_t)x10 * x12) + ((uint64_t)x8 * x14)) + ((uint64_t)x6 * x16)) + ((uint64_t)x4 * x18)) + ((uint64_t)x2 * x17))); |
| { uint64_t x29 = (0x2 * (((((uint64_t)x12 * x12) + ((uint64_t)x10 * x14)) + ((uint64_t)x6 * x18)) + (0x2 * (((uint64_t)x8 * x16) + ((uint64_t)x4 * x17))))); |
| { uint64_t x30 = (0x2 * (((((uint64_t)x12 * x14) + ((uint64_t)x10 * x16)) + ((uint64_t)x8 * x18)) + ((uint64_t)x6 * x17))); |
| { uint64_t x31 = (((uint64_t)x14 * x14) + (0x2 * (((uint64_t)x10 * x18) + (0x2 * (((uint64_t)x12 * x16) + ((uint64_t)x8 * x17)))))); |
| { uint64_t x32 = (0x2 * ((((uint64_t)x14 * x16) + ((uint64_t)x12 * x18)) + ((uint64_t)x10 * x17))); |
| { uint64_t x33 = (0x2 * ((((uint64_t)x16 * x16) + ((uint64_t)x14 * x18)) + ((uint64_t)(0x2 * x12) * x17))); |
| { uint64_t x34 = (0x2 * (((uint64_t)x16 * x18) + ((uint64_t)x14 * x17))); |
| { uint64_t x35 = (((uint64_t)x18 * x18) + ((uint64_t)(0x4 * x16) * x17)); |
| { uint64_t x36 = ((uint64_t)(0x2 * x18) * x17); |
| { uint64_t x37 = ((uint64_t)(0x2 * x17) * x17); |
| { uint64_t x38 = (x27 + (x37 << 0x4)); |
| { uint64_t x39 = (x38 + (x37 << 0x1)); |
| { uint64_t x40 = (x39 + x37); |
| { uint64_t x41 = (x26 + (x36 << 0x4)); |
| { uint64_t x42 = (x41 + (x36 << 0x1)); |
| { uint64_t x43 = (x42 + x36); |
| { uint64_t x44 = (x25 + (x35 << 0x4)); |
| { uint64_t x45 = (x44 + (x35 << 0x1)); |
| { uint64_t x46 = (x45 + x35); |
| { uint64_t x47 = (x24 + (x34 << 0x4)); |
| { uint64_t x48 = (x47 + (x34 << 0x1)); |
| { uint64_t x49 = (x48 + x34); |
| { uint64_t x50 = (x23 + (x33 << 0x4)); |
| { uint64_t x51 = (x50 + (x33 << 0x1)); |
| { uint64_t x52 = (x51 + x33); |
| { uint64_t x53 = (x22 + (x32 << 0x4)); |
| { uint64_t x54 = (x53 + (x32 << 0x1)); |
| { uint64_t x55 = (x54 + x32); |
| { uint64_t x56 = (x21 + (x31 << 0x4)); |
| { uint64_t x57 = (x56 + (x31 << 0x1)); |
| { uint64_t x58 = (x57 + x31); |
| { uint64_t x59 = (x20 + (x30 << 0x4)); |
| { uint64_t x60 = (x59 + (x30 << 0x1)); |
| { uint64_t x61 = (x60 + x30); |
| { uint64_t x62 = (x19 + (x29 << 0x4)); |
| { uint64_t x63 = (x62 + (x29 << 0x1)); |
| { uint64_t x64 = (x63 + x29); |
| { uint64_t x65 = (x64 >> 0x1a); |
| { uint32_t x66 = ((uint32_t)x64 & 0x3ffffff); |
| { uint64_t x67 = (x65 + x61); |
| { uint64_t x68 = (x67 >> 0x19); |
| { uint32_t x69 = ((uint32_t)x67 & 0x1ffffff); |
| { uint64_t x70 = (x68 + x58); |
| { uint64_t x71 = (x70 >> 0x1a); |
| { uint32_t x72 = ((uint32_t)x70 & 0x3ffffff); |
| { uint64_t x73 = (x71 + x55); |
| { uint64_t x74 = (x73 >> 0x19); |
| { uint32_t x75 = ((uint32_t)x73 & 0x1ffffff); |
| { uint64_t x76 = (x74 + x52); |
| { uint64_t x77 = (x76 >> 0x1a); |
| { uint32_t x78 = ((uint32_t)x76 & 0x3ffffff); |
| { uint64_t x79 = (x77 + x49); |
| { uint64_t x80 = (x79 >> 0x19); |
| { uint32_t x81 = ((uint32_t)x79 & 0x1ffffff); |
| { uint64_t x82 = (x80 + x46); |
| { uint64_t x83 = (x82 >> 0x1a); |
| { uint32_t x84 = ((uint32_t)x82 & 0x3ffffff); |
| { uint64_t x85 = (x83 + x43); |
| { uint64_t x86 = (x85 >> 0x19); |
| { uint32_t x87 = ((uint32_t)x85 & 0x1ffffff); |
| { uint64_t x88 = (x86 + x40); |
| { uint64_t x89 = (x88 >> 0x1a); |
| { uint32_t x90 = ((uint32_t)x88 & 0x3ffffff); |
| { uint64_t x91 = (x89 + x28); |
| { uint64_t x92 = (x91 >> 0x19); |
| { uint32_t x93 = ((uint32_t)x91 & 0x1ffffff); |
| { uint64_t x94 = (x66 + (0x13 * x92)); |
| { uint32_t x95 = (uint32_t) (x94 >> 0x1a); |
| { uint32_t x96 = ((uint32_t)x94 & 0x3ffffff); |
| { uint32_t x97 = (x95 + x69); |
| { uint32_t x98 = (x97 >> 0x19); |
| { uint32_t x99 = (x97 & 0x1ffffff); |
| out[0] = x96; |
| out[1] = x99; |
| out[2] = (x98 + x72); |
| out[3] = x75; |
| out[4] = x78; |
| out[5] = x81; |
| out[6] = x84; |
| out[7] = x87; |
| out[8] = x90; |
| out[9] = x93; |
| }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| assert_fe(out); |
| } |
| |
| static void fe_sq_tl(fe *h, const fe_loose *f) { |
| fe_sqr_impl(h->v, f->v); |
| } |
| |
| static void fe_sq_tt(fe *h, const fe *f) { |
| fe_sqr_impl(h->v, f->v); |
| } |
| |
| // Replace (f,g) with (g,f) if b == 1; |
| // replace (f,g) with (f,g) if b == 0. |
| // |
| // Preconditions: b in {0,1}. |
| static void fe_cswap(fe *f, fe *g, unsigned int b) { |
| b = 0-b; |
| unsigned i; |
| for (i = 0; i < 10; i++) { |
| uint32_t x = f->v[i] ^ g->v[i]; |
| x &= b; |
| f->v[i] ^= x; |
| g->v[i] ^= x; |
| } |
| } |
| |
| // NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.. |
| static void fe_mul_121666_impl(uint32_t out[10], const uint32_t in1[10]) { |
| { const uint32_t x20 = in1[9]; |
| { const uint32_t x21 = in1[8]; |
| { const uint32_t x19 = in1[7]; |
| { const uint32_t x17 = in1[6]; |
| { const uint32_t x15 = in1[5]; |
| { const uint32_t x13 = in1[4]; |
| { const uint32_t x11 = in1[3]; |
| { const uint32_t x9 = in1[2]; |
| { const uint32_t x7 = in1[1]; |
| { const uint32_t x5 = in1[0]; |
| { const uint32_t x38 = 0; |
| { const uint32_t x39 = 0; |
| { const uint32_t x37 = 0; |
| { const uint32_t x35 = 0; |
| { const uint32_t x33 = 0; |
| { const uint32_t x31 = 0; |
| { const uint32_t x29 = 0; |
| { const uint32_t x27 = 0; |
| { const uint32_t x25 = 0; |
| { const uint32_t x23 = 121666; |
| { uint64_t x40 = ((uint64_t)x23 * x5); |
| { uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5)); |
| { uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5)); |
| { uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5)); |
| { uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5)); |
| { uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5)); |
| { uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5)); |
| { uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5)); |
| { uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5)); |
| { uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5)); |
| { uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9)); |
| { uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9)); |
| { uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13)); |
| { uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13)); |
| { uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17)); |
| { uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17)); |
| { uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19)))); |
| { uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21)); |
| { uint64_t x58 = ((uint64_t)(0x2 * x38) * x20); |
| { uint64_t x59 = (x48 + (x58 << 0x4)); |
| { uint64_t x60 = (x59 + (x58 << 0x1)); |
| { uint64_t x61 = (x60 + x58); |
| { uint64_t x62 = (x47 + (x57 << 0x4)); |
| { uint64_t x63 = (x62 + (x57 << 0x1)); |
| { uint64_t x64 = (x63 + x57); |
| { uint64_t x65 = (x46 + (x56 << 0x4)); |
| { uint64_t x66 = (x65 + (x56 << 0x1)); |
| { uint64_t x67 = (x66 + x56); |
| { uint64_t x68 = (x45 + (x55 << 0x4)); |
| { uint64_t x69 = (x68 + (x55 << 0x1)); |
| { uint64_t x70 = (x69 + x55); |
| { uint64_t x71 = (x44 + (x54 << 0x4)); |
| { uint64_t x72 = (x71 + (x54 << 0x1)); |
| { uint64_t x73 = (x72 + x54); |
| { uint64_t x74 = (x43 + (x53 << 0x4)); |
| { uint64_t x75 = (x74 + (x53 << 0x1)); |
| { uint64_t x76 = (x75 + x53); |
| { uint64_t x77 = (x42 + (x52 << 0x4)); |
| { uint64_t x78 = (x77 + (x52 << 0x1)); |
| { uint64_t x79 = (x78 + x52); |
| { uint64_t x80 = (x41 + (x51 << 0x4)); |
| { uint64_t x81 = (x80 + (x51 << 0x1)); |
| { uint64_t x82 = (x81 + x51); |
| { uint64_t x83 = (x40 + (x50 << 0x4)); |
| { uint64_t x84 = (x83 + (x50 << 0x1)); |
| { uint64_t x85 = (x84 + x50); |
| { uint64_t x86 = (x85 >> 0x1a); |
| { uint32_t x87 = ((uint32_t)x85 & 0x3ffffff); |
| { uint64_t x88 = (x86 + x82); |
| { uint64_t x89 = (x88 >> 0x19); |
| { uint32_t x90 = ((uint32_t)x88 & 0x1ffffff); |
| { uint64_t x91 = (x89 + x79); |
| { uint64_t x92 = (x91 >> 0x1a); |
| { uint32_t x93 = ((uint32_t)x91 & 0x3ffffff); |
| { uint64_t x94 = (x92 + x76); |
| { uint64_t x95 = (x94 >> 0x19); |
| { uint32_t x96 = ((uint32_t)x94 & 0x1ffffff); |
| { uint64_t x97 = (x95 + x73); |
| { uint64_t x98 = (x97 >> 0x1a); |
| { uint32_t x99 = ((uint32_t)x97 & 0x3ffffff); |
| { uint64_t x100 = (x98 + x70); |
| { uint64_t x101 = (x100 >> 0x19); |
| { uint32_t x102 = ((uint32_t)x100 & 0x1ffffff); |
| { uint64_t x103 = (x101 + x67); |
| { uint64_t x104 = (x103 >> 0x1a); |
| { uint32_t x105 = ((uint32_t)x103 & 0x3ffffff); |
| { uint64_t x106 = (x104 + x64); |
| { uint64_t x107 = (x106 >> 0x19); |
| { uint32_t x108 = ((uint32_t)x106 & 0x1ffffff); |
| { uint64_t x109 = (x107 + x61); |
| { uint64_t x110 = (x109 >> 0x1a); |
| { uint32_t x111 = ((uint32_t)x109 & 0x3ffffff); |
| { uint64_t x112 = (x110 + x49); |
| { uint64_t x113 = (x112 >> 0x19); |
| { uint32_t x114 = ((uint32_t)x112 & 0x1ffffff); |
| { uint64_t x115 = (x87 + (0x13 * x113)); |
| { uint32_t x116 = (uint32_t) (x115 >> 0x1a); |
| { uint32_t x117 = ((uint32_t)x115 & 0x3ffffff); |
| { uint32_t x118 = (x116 + x90); |
| { uint32_t x119 = (x118 >> 0x19); |
| { uint32_t x120 = (x118 & 0x1ffffff); |
| out[0] = x117; |
| out[1] = x120; |
| out[2] = (x119 + x93); |
| out[3] = x96; |
| out[4] = x99; |
| out[5] = x102; |
| out[6] = x105; |
| out[7] = x108; |
| out[8] = x111; |
| out[9] = x114; |
| }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} |
| } |
| |
| static void fe_mul121666(fe *h, const fe_loose *f) { |
| assert_fe_loose(f->v); |
| fe_mul_121666_impl(h->v, f->v); |
| assert_fe(h->v); |
| } |
| |
| // Adapted from Fiat-synthesized |fe_sub_impl| with |out| = 0. |
| static void fe_neg_impl(uint32_t out[10], const uint32_t in2[10]) { |
| { const uint32_t x20 = 0; |
| { const uint32_t x21 = 0; |
| { const uint32_t x19 = 0; |
| { const uint32_t x17 = 0; |
| { const uint32_t x15 = 0; |
| { const uint32_t x13 = 0; |
| { const uint32_t x11 = 0; |
| { const uint32_t x9 = 0; |
| { const uint32_t x7 = 0; |
| { const uint32_t x5 = 0; |
| { const uint32_t x38 = in2[9]; |
| { const uint32_t x39 = in2[8]; |
| { const uint32_t x37 = in2[7]; |
| { const uint32_t x35 = in2[6]; |
| { const uint32_t x33 = in2[5]; |
| { const uint32_t x31 = in2[4]; |
| { const uint32_t x29 = in2[3]; |
| { const uint32_t x27 = in2[2]; |
| { const uint32_t x25 = in2[1]; |
| { const uint32_t x23 = in2[0]; |
| out[0] = ((0x7ffffda + x5) - x23); |
| out[1] = ((0x3fffffe + x7) - x25); |
| out[2] = ((0x7fffffe + x9) - x27); |
| out[3] = ((0x3fffffe + x11) - x29); |
| out[4] = ((0x7fffffe + x13) - x31); |
| out[5] = ((0x3fffffe + x15) - x33); |
| out[6] = ((0x7fffffe + x17) - x35); |
| out[7] = ((0x3fffffe + x19) - x37); |
| out[8] = ((0x7fffffe + x21) - x39); |
| out[9] = ((0x3fffffe + x20) - x38); |
| }}}}}}}}}}}}}}}}}}}} |
| } |
| |
| // h = -f |
| static void fe_neg(fe_loose *h, const fe *f) { |
| assert_fe(f->v); |
| fe_neg_impl(h->v, f->v); |
| assert_fe_loose(h->v); |
| } |
| |
| // Replace (f,g) with (g,g) if b == 1; |
| // replace (f,g) with (f,g) if b == 0. |
| // |
| // Preconditions: b in {0,1}. |
| static void fe_cmov(fe_loose *f, const fe_loose *g, unsigned b) { |
| b = 0-b; |
| unsigned i; |
| for (i = 0; i < 10; i++) { |
| uint32_t x = f->v[i] ^ g->v[i]; |
| x &= b; |
| f->v[i] ^= x; |
| } |
| } |
| |
| #endif // BORINGSSL_CURVE25519_64BIT |
| |
| // h = f |
| static void fe_copy(fe *h, const fe *f) { |
| OPENSSL_memmove(h, f, sizeof(fe)); |
| } |
| |
| static void fe_copy_lt(fe_loose *h, const fe *f) { |
| OPENSSL_COMPILE_ASSERT(sizeof(fe_loose) == sizeof(fe), |
| fe_and_fe_loose_mismatch); |
| OPENSSL_memmove(h, f, sizeof(fe)); |
| } |
| #if !defined(OPENSSL_SMALL) |
| static void fe_copy_ll(fe_loose *h, const fe_loose *f) { |
| OPENSSL_memmove(h, f, sizeof(fe_loose)); |
| } |
| #endif // !defined(OPENSSL_SMALL) |
| |
| static void fe_loose_invert(fe *out, const fe_loose *z) { |
| fe t0; |
| fe t1; |
| fe t2; |
| fe t3; |
| int i; |
| |
| fe_sq_tl(&t0, z); |
| fe_sq_tt(&t1, &t0); |
| for (i = 1; i < 2; ++i) { |
| fe_sq_tt(&t1, &t1); |
| } |
| fe_mul_tlt(&t1, z, &t1); |
| fe_mul_ttt(&t0, &t0, &t1); |
| fe_sq_tt(&t2, &t0); |
| fe_mul_ttt(&t1, &t1, &t2); |
| fe_sq_tt(&t2, &t1); |
| for (i = 1; i < 5; ++i) { |
| fe_sq_tt(&t2, &t2); |
| } |
| fe_mul_ttt(&t1, &t2, &t1); |
| fe_sq_tt(&t2, &t1); |
| for (i = 1; i < 10; ++i) { |
| fe_sq_tt(&t2, &t2); |
| } |
| fe_mul_ttt(&t2, &t2, &t1); |
| fe_sq_tt(&t3, &t2); |
| for (i = 1; i < 20; ++i) { |
| fe_sq_tt(&t3, &t3); |
| } |
| fe_mul_ttt(&t2, &t3, &t2); |
| fe_sq_tt(&t2, &t2); |
| for (i = 1; i < 10; ++i) { |
| fe_sq_tt(&t2, &t2); |
| } |
| fe_mul_ttt(&t1, &t2, &t1); |
| fe_sq_tt(&t2, &t1); |
| for (i = 1; i < 50; ++i) { |
| fe_sq_tt(&t2, &t2); |
| } |
| fe_mul_ttt(&t2, &t2, &t1); |
| fe_sq_tt(&t3, &t2); |
| for (i = 1; i < 100; ++i) { |
| fe_sq_tt(&t3, &t3); |
| } |
| fe_mul_ttt(&t2, &t3, &t2); |
| fe_sq_tt(&t2, &t2); |
| for (i = 1; i < 50; ++i) { |
| fe_sq_tt(&t2, &t2); |
| } |
| fe_mul_ttt(&t1, &t2, &t1); |
| fe_sq_tt(&t1, &t1); |
| for (i = 1; i < 5; ++i) { |
| fe_sq_tt(&t1, &t1); |
| } |
| fe_mul_ttt(out, &t1, &t0); |
| } |
| |
| static void fe_invert(fe *out, const fe *z) { |
| fe_loose l; |
| fe_copy_lt(&l, z); |
| fe_loose_invert(out, &l); |
| } |
| |
| // return 0 if f == 0 |
| // return 1 if f != 0 |
| static int fe_isnonzero(const fe_loose *f) { |
| fe tight; |
| fe_carry(&tight, f); |
| uint8_t s[32]; |
| fe_tobytes(s, &tight); |
| |
| static const uint8_t zero[32] = {0}; |
| return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0; |
| } |
| |
| // return 1 if f is in {1,3,5,...,q-2} |
| // return 0 if f is in {0,2,4,...,q-1} |
| static int fe_isnegative(const fe *f) { |
| uint8_t s[32]; |
| fe_tobytes(s, f); |
| return s[0] & 1; |
| } |
| |
| static void fe_sq2_tt(fe *h, const fe *f) { |
| // h = f^2 |
| fe_sq_tt(h, f); |
| |
| // h = h + h |
| fe_loose tmp; |
| fe_add(&tmp, h, h); |
| fe_carry(h, &tmp); |
| } |
| |
| static void fe_pow22523(fe *out, const fe *z) { |
| fe t0; |
| fe t1; |
| fe t2; |
| int i; |
| |
| fe_sq_tt(&t0, z); |
| fe_sq_tt(&t1, &t0); |
| for (i = 1; i < 2; ++i) { |
| fe_sq_tt(&t1, &t1); |
| } |
| fe_mul_ttt(&t1, z, &t1); |
| fe_mul_ttt(&t0, &t0, &t1); |
| fe_sq_tt(&t0, &t0); |
| fe_mul_ttt(&t0, &t1, &t0); |
| fe_sq_tt(&t1, &t0); |
| for (i = 1; i < 5; ++i) { |
| fe_sq_tt(&t1, &t1); |
| } |
| fe_mul_ttt(&t0, &t1, &t0); |
| fe_sq_tt(&t1, &t0); |
| for (i = 1; i < 10; ++i) { |
| fe_sq_tt(&t1, &t1); |
| } |
| fe_mul_ttt(&t1, &t1, &t0); |
| fe_sq_tt(&t2, &t1); |
| for (i = 1; i < 20; ++i) { |
| fe_sq_tt(&t2, &t2); |
| } |
| fe_mul_ttt(&t1, &t2, &t1); |
| fe_sq_tt(&t1, &t1); |
| for (i = 1; i < 10; ++i) { |
| fe_sq_tt(&t1, &t1); |
| } |
| fe_mul_ttt(&t0, &t1, &t0); |
| fe_sq_tt(&t1, &t0); |
| for (i = 1; i < 50; ++i) { |
| fe_sq_tt(&t1, &t1); |
| } |
| fe_mul_ttt(&t1, &t1, &t0); |
| fe_sq_tt(&t2, &t1); |
| for (i = 1; i < 100; ++i) { |
| fe_sq_tt(&t2, &t2); |
| } |
| fe_mul_ttt(&t1, &t2, &t1); |
| fe_sq_tt(&t1, &t1); |
| for (i = 1; i < 50; ++i) { |
| fe_sq_tt(&t1, &t1); |
| } |
| fe_mul_ttt(&t0, &t1, &t0); |
| fe_sq_tt(&t0, &t0); |
| for (i = 1; i < 2; ++i) { |
| fe_sq_tt(&t0, &t0); |
| } |
| fe_mul_ttt(out, &t0, z); |
| } |
| |
| |
| // Group operations. |
| |
| void x25519_ge_tobytes(uint8_t s[32], const ge_p2 *h) { |
| fe recip; |
| fe x; |
| fe y; |
| |
| fe_invert(&recip, &h->Z); |
| fe_mul_ttt(&x, &h->X, &recip); |
| fe_mul_ttt(&y, &h->Y, &recip); |
| fe_tobytes(s, &y); |
| s[31] ^= fe_isnegative(&x) << 7; |
| } |
| |
| static void ge_p3_tobytes(uint8_t s[32], const ge_p3 *h) { |
| fe recip; |
| fe x; |
| fe y; |
| |
| fe_invert(&recip, &h->Z); |
| fe_mul_ttt(&x, &h->X, &recip); |
| fe_mul_ttt(&y, &h->Y, &recip); |
| fe_tobytes(s, &y); |
| s[31] ^= fe_isnegative(&x) << 7; |
| } |
| |
| int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) { |
| fe u; |
| fe_loose v; |
| fe v3; |
| fe vxx; |
| fe_loose check; |
| |
| fe_frombytes(&h->Y, s); |
| fe_1(&h->Z); |
| fe_sq_tt(&v3, &h->Y); |
| fe_mul_ttt(&vxx, &v3, &d); |
| fe_sub(&v, &v3, &h->Z); // u = y^2-1 |
| fe_carry(&u, &v); |
| fe_add(&v, &vxx, &h->Z); // v = dy^2+1 |
| |
| fe_sq_tl(&v3, &v); |
| fe_mul_ttl(&v3, &v3, &v); // v3 = v^3 |
| fe_sq_tt(&h->X, &v3); |
| fe_mul_ttl(&h->X, &h->X, &v); |
| fe_mul_ttt(&h->X, &h->X, &u); // x = uv^7 |
| |
| fe_pow22523(&h->X, &h->X); // x = (uv^7)^((q-5)/8) |
| fe_mul_ttt(&h->X, &h->X, &v3); |
| fe_mul_ttt(&h->X, &h->X, &u); // x = uv^3(uv^7)^((q-5)/8) |
| |
| fe_sq_tt(&vxx, &h->X); |
| fe_mul_ttl(&vxx, &vxx, &v); |
| fe_sub(&check, &vxx, &u); |
| if (fe_isnonzero(&check)) { |
| fe_add(&check, &vxx, &u); |
| if (fe_isnonzero(&check)) { |
| return 0; |
| } |
| fe_mul_ttt(&h->X, &h->X, &sqrtm1); |
| } |
| |
| if (fe_isnegative(&h->X) != (s[31] >> 7)) { |
| fe_loose t; |
| fe_neg(&t, &h->X); |
| fe_carry(&h->X, &t); |
| } |
| |
| fe_mul_ttt(&h->T, &h->X, &h->Y); |
| return 1; |
| } |
| |
| static void ge_p2_0(ge_p2 *h) { |
| fe_0(&h->X); |
| fe_1(&h->Y); |
| fe_1(&h->Z); |
| } |
| |
| static void ge_p3_0(ge_p3 *h) { |
| fe_0(&h->X); |
| fe_1(&h->Y); |
| fe_1(&h->Z); |
| fe_0(&h->T); |
| } |
| |
| static void ge_cached_0(ge_cached *h) { |
| fe_loose_1(&h->YplusX); |
| fe_loose_1(&h->YminusX); |
| fe_loose_1(&h->Z); |
| fe_loose_0(&h->T2d); |
| } |
| |
| static void ge_precomp_0(ge_precomp *h) { |
| fe_loose_1(&h->yplusx); |
| fe_loose_1(&h->yminusx); |
| fe_loose_0(&h->xy2d); |
| } |
| |
| // r = p |
| static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { |
| fe_copy(&r->X, &p->X); |
| fe_copy(&r->Y, &p->Y); |
| fe_copy(&r->Z, &p->Z); |
| } |
| |
| // r = p |
| void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) { |
| fe_add(&r->YplusX, &p->Y, &p->X); |
| fe_sub(&r->YminusX, &p->Y, &p->X); |
| fe_copy_lt(&r->Z, &p->Z); |
| fe_mul_ltt(&r->T2d, &p->T, &d2); |
| } |
| |
| // r = p |
| void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { |
| fe_mul_tll(&r->X, &p->X, &p->T); |
| fe_mul_tll(&r->Y, &p->Y, &p->Z); |
| fe_mul_tll(&r->Z, &p->Z, &p->T); |
| } |
| |
| // r = p |
| void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { |
| fe_mul_tll(&r->X, &p->X, &p->T); |
| fe_mul_tll(&r->Y, &p->Y, &p->Z); |
| fe_mul_tll(&r->Z, &p->Z, &p->T); |
| fe_mul_tll(&r->T, &p->X, &p->Y); |
| } |
| |
| // r = p |
| static void ge_p1p1_to_cached(ge_cached *r, const ge_p1p1 *p) { |
| ge_p3 t; |
| x25519_ge_p1p1_to_p3(&t, p); |
| x25519_ge_p3_to_cached(r, &t); |
| } |
| |
| // r = 2 * p |
| static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { |
| fe trX, trZ, trT; |
| fe t0; |
| |
| fe_sq_tt(&trX, &p->X); |
| fe_sq_tt(&trZ, &p->Y); |
| fe_sq2_tt(&trT, &p->Z); |
| fe_add(&r->Y, &p->X, &p->Y); |
| fe_sq_tl(&t0, &r->Y); |
| |
| fe_add(&r->Y, &trZ, &trX); |
| fe_sub(&r->Z, &trZ, &trX); |
| fe_carry(&trZ, &r->Y); |
| fe_sub(&r->X, &t0, &trZ); |
| fe_carry(&trZ, &r->Z); |
| fe_sub(&r->T, &trT, &trZ); |
| } |
| |
| // r = 2 * p |
| static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { |
| ge_p2 q; |
| ge_p3_to_p2(&q, p); |
| ge_p2_dbl(r, &q); |
| } |
| |
| // r = p + q |
| static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { |
| fe trY, trZ, trT; |
| |
| fe_add(&r->X, &p->Y, &p->X); |
| fe_sub(&r->Y, &p->Y, &p->X); |
| fe_mul_tll(&trZ, &r->X, &q->yplusx); |
| fe_mul_tll(&trY, &r->Y, &q->yminusx); |
| fe_mul_tlt(&trT, &q->xy2d, &p->T); |
| fe_add(&r->T, &p->Z, &p->Z); |
| fe_sub(&r->X, &trZ, &trY); |
| fe_add(&r->Y, &trZ, &trY); |
| fe_carry(&trZ, &r->T); |
| fe_add(&r->Z, &trZ, &trT); |
| fe_sub(&r->T, &trZ, &trT); |
| } |
| |
| // r = p - q |
| static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { |
| fe trY, trZ, trT; |
| |
| fe_add(&r->X, &p->Y, &p->X); |
| fe_sub(&r->Y, &p->Y, &p->X); |
| fe_mul_tll(&trZ, &r->X, &q->yminusx); |
| fe_mul_tll(&trY, &r->Y, &q->yplusx); |
| fe_mul_tlt(&trT, &q->xy2d, &p->T); |
| fe_add(&r->T, &p->Z, &p->Z); |
| fe_sub(&r->X, &trZ, &trY); |
| fe_add(&r->Y, &trZ, &trY); |
| fe_carry(&trZ, &r->T); |
| fe_sub(&r->Z, &trZ, &trT); |
| fe_add(&r->T, &trZ, &trT); |
| } |
| |
| // r = p + q |
| void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { |
| fe trX, trY, trZ, trT; |
| |
| fe_add(&r->X, &p->Y, &p->X); |
| fe_sub(&r->Y, &p->Y, &p->X); |
| fe_mul_tll(&trZ, &r->X, &q->YplusX); |
| fe_mul_tll(&trY, &r->Y, &q->YminusX); |
| fe_mul_tlt(&trT, &q->T2d, &p->T); |
| fe_mul_ttl(&trX, &p->Z, &q->Z); |
| fe_add(&r->T, &trX, &trX); |
| fe_sub(&r->X, &trZ, &trY); |
| fe_add(&r->Y, &trZ, &trY); |
| fe_carry(&trZ, &r->T); |
| fe_add(&r->Z, &trZ, &trT); |
| fe_sub(&r->T, &trZ, &trT); |
| } |
| |
| // r = p - q |
| void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { |
| fe trX, trY, trZ, trT; |
| |
| fe_add(&r->X, &p->Y, &p->X); |
| fe_sub(&r->Y, &p->Y, &p->X); |
| fe_mul_tll(&trZ, &r->X, &q->YminusX); |
| fe_mul_tll(&trY, &r->Y, &q->YplusX); |
| fe_mul_tlt(&trT, &q->T2d, &p->T); |
| fe_mul_ttl(&trX, &p->Z, &q->Z); |
| fe_add(&r->T, &trX, &trX); |
| fe_sub(&r->X, &trZ, &trY); |
| fe_add(&r->Y, &trZ, &trY); |
| fe_carry(&trZ, &r->T); |
| fe_sub(&r->Z, &trZ, &trT); |
| fe_add(&r->T, &trZ, &trT); |
| } |
| |
| static uint8_t equal(signed char b, signed char c) { |
| uint8_t ub = b; |
| uint8_t uc = c; |
| uint8_t x = ub ^ uc; // 0: yes; 1..255: no |
| uint32_t y = x; // 0: yes; 1..255: no |
| y -= 1; // 4294967295: yes; 0..254: no |
| y >>= 31; // 1: yes; 0: no |
| return y; |
| } |
| |
| static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) { |
| fe_cmov(&t->yplusx, &u->yplusx, b); |
| fe_cmov(&t->yminusx, &u->yminusx, b); |
| fe_cmov(&t->xy2d, &u->xy2d, b); |
| } |
| |
| void x25519_ge_scalarmult_small_precomp( |
| ge_p3 *h, const uint8_t a[32], const uint8_t precomp_table[15 * 2 * 32]) { |
| // precomp_table is first expanded into matching |ge_precomp| |
| // elements. |
| ge_precomp multiples[15]; |
| |
| unsigned i; |
| for (i = 0; i < 15; i++) { |
| const uint8_t *bytes = &precomp_table[i*(2 * 32)]; |
| fe x, y; |
| fe_frombytes(&x, bytes); |
| fe_frombytes(&y, bytes + 32); |
| |
| ge_precomp *out = &multiples[i]; |
| fe_add(&out->yplusx, &y, &x); |
| fe_sub(&out->yminusx, &y, &x); |
| fe_mul_ltt(&out->xy2d, &x, &y); |
| fe_mul_llt(&out->xy2d, &out->xy2d, &d2); |
| } |
| |
| // See the comment above |k25519SmallPrecomp| about the structure of the |
| // precomputed elements. This loop does 64 additions and 64 doublings to |
| // calculate the result. |
| ge_p3_0(h); |
| |
| for (i = 63; i < 64; i--) { |
| unsigned j; |
| signed char index = 0; |
| |
| for (j = 0; j < 4; j++) { |
| const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7)); |
| index |= (bit << j); |
| } |
| |
| ge_precomp e; |
| ge_precomp_0(&e); |
| |
| for (j = 1; j < 16; j++) { |
| cmov(&e, &multiples[j-1], equal(index, j)); |
| } |
| |
| ge_cached cached; |
| ge_p1p1 r; |
| x25519_ge_p3_to_cached(&cached, h); |
| x25519_ge_add(&r, h, &cached); |
| x25519_ge_p1p1_to_p3(h, &r); |
| |
| ge_madd(&r, h, &e); |
| x25519_ge_p1p1_to_p3(h, &r); |
| } |
| } |
| |
| #if defined(OPENSSL_SMALL) |
| |
| void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) { |
| x25519_ge_scalarmult_small_precomp(h, a, k25519SmallPrecomp); |
| } |
| |
| #else |
| |
| static uint8_t negative(signed char b) { |
| uint32_t x = b; |
| x >>= 31; // 1: yes; 0: no |
| return x; |
| } |
| |
| static void table_select(ge_precomp *t, int pos, signed char b) { |
| ge_precomp minust; |
| uint8_t bnegative = negative(b); |
| uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); |
| |
| ge_precomp_0(t); |
| cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); |
| cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); |
| cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); |
| cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); |
| cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); |
| cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); |
| cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); |
| cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); |
| fe_copy_ll(&minust.yplusx, &t->yminusx); |
| fe_copy_ll(&minust.yminusx, &t->yplusx); |
| |
| // NOTE: the input table is canonical, but types don't encode it |
| fe tmp; |
| fe_carry(&tmp, &t->xy2d); |
| fe_neg(&minust.xy2d, &tmp); |
| |
| cmov(t, &minust, bnegative); |
| } |
| |
| // h = a * B |
| // where a = a[0]+256*a[1]+...+256^31 a[31] |
| // B is the Ed25519 base point (x,4/5) with x positive. |
| // |
| // Preconditions: |
| // a[31] <= 127 |
| void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t *a) { |
| signed char e[64]; |
| signed char carry; |
| ge_p1p1 r; |
| ge_p2 s; |
| ge_precomp t; |
| int i; |
| |
| for (i = 0; i < 32; ++i) { |
| e[2 * i + 0] = (a[i] >> 0) & 15; |
| e[2 * i + 1] = (a[i] >> 4) & 15; |
| } |
| // each e[i] is between 0 and 15 |
| // e[63] is between 0 and 7 |
| |
| carry = 0; |
| for (i = 0; i < 63; ++i) { |
| e[i] += carry; |
| carry = e[i] + 8; |
| carry >>= 4; |
| e[i] -= carry << 4; |
| } |
| e[63] += carry; |
| // each e[i] is between -8 and 8 |
| |
| ge_p3_0(h); |
| for (i = 1; i < 64; i += 2) { |
| table_select(&t, i / 2, e[i]); |
| ge_madd(&r, h, &t); |
| x25519_ge_p1p1_to_p3(h, &r); |
| } |
| |
| ge_p3_dbl(&r, h); |
| x25519_ge_p1p1_to_p2(&s, &r); |
| ge_p2_dbl(&r, &s); |
| x25519_ge_p1p1_to_p2(&s, &r); |
| ge_p2_dbl(&r, &s); |
| x25519_ge_p1p1_to_p2(&s, &r); |
| ge_p2_dbl(&r, &s); |
| x25519_ge_p1p1_to_p3(h, &r); |
| |
| for (i = 0; i < 64; i += 2) { |
| table_select(&t, i / 2, e[i]); |
| ge_madd(&r, h, &t); |
| x25519_ge_p1p1_to_p3(h, &r); |
| } |
| } |
| |
| #endif |
| |
| static void cmov_cached(ge_cached *t, ge_cached *u, uint8_t b) { |
| fe_cmov(&t->YplusX, &u->YplusX, b); |
| fe_cmov(&t->YminusX, &u->YminusX, b); |
| fe_cmov(&t->Z, &u->Z, b); |
| fe_cmov(&t->T2d, &u->T2d, b); |
| } |
| |
| // r = scalar * A. |
| // where a = a[0]+256*a[1]+...+256^31 a[31]. |
| void x25519_ge_scalarmult(ge_p2 *r, const uint8_t *scalar, const ge_p3 *A) { |
| ge_p2 Ai_p2[8]; |
| ge_cached Ai[16]; |
| ge_p1p1 t; |
| |
| ge_cached_0(&Ai[0]); |
| x25519_ge_p3_to_cached(&Ai[1], A); |
| ge_p3_to_p2(&Ai_p2[1], A); |
| |
| unsigned i; |
| for (i = 2; i < 16; i += 2) { |
| ge_p2_dbl(&t, &Ai_p2[i / 2]); |
| ge_p1p1_to_cached(&Ai[i], &t); |
| if (i < 8) { |
| x25519_ge_p1p1_to_p2(&Ai_p2[i], &t); |
| } |
| x25519_ge_add(&t, A, &Ai[i]); |
| ge_p1p1_to_cached(&Ai[i + 1], &t); |
| if (i < 7) { |
| x25519_ge_p1p1_to_p2(&Ai_p2[i + 1], &t); |
| } |
| } |
| |
| ge_p2_0(r); |
| ge_p3 u; |
| |
| for (i = 0; i < 256; i += 4) { |
| ge_p2_dbl(&t, r); |
| x25519_ge_p1p1_to_p2(r, &t); |
| ge_p2_dbl(&t, r); |
| x25519_ge_p1p1_to_p2(r, &t); |
| ge_p2_dbl(&t, r); |
| x25519_ge_p1p1_to_p2(r, &t); |
| ge_p2_dbl(&t, r); |
| x25519_ge_p1p1_to_p3(&u, &t); |
| |
| uint8_t index = scalar[31 - i/8]; |
| index >>= 4 - (i & 4); |
| index &= 0xf; |
| |
| unsigned j; |
| ge_cached selected; |
| ge_cached_0(&selected); |
| for (j = 0; j < 16; j++) { |
| cmov_cached(&selected, &Ai[j], equal(j, index)); |
| } |
| |
| x25519_ge_add(&t, &u, &selected); |
| x25519_ge_p1p1_to_p2(r, &t); |
| } |
| } |
| |
| static void slide(signed char *r, const uint8_t *a) { |
| int i; |
| int b; |
| int k; |
| |
| for (i = 0; i < 256; ++i) { |
| r[i] = 1 & (a[i >> 3] >> (i & 7)); |
| } |
| |
| for (i = 0; i < 256; ++i) { |
| if (r[i]) { |
| for (b = 1; b <= 6 && i + b < 256; ++b) { |
| if (r[i + b]) { |
| if (r[i] + (r[i + b] << b) <= 15) { |
| r[i] += r[i + b] << b; |
| r[i + b] = 0; |
| } else if (r[i] - (r[i + b] << b) >= -15) { |
| r[i] -= r[i + b] << b; |
| for (k = i + b; k < 256; ++k) { |
| if (!r[k]) { |
| r[k] = 1; |
| break; |
| } |
| r[k] = 0; |
| } |
| } else { |
| break; |
| } |
| } |
| } |
| } |
| } |
| } |
| |
| // r = a * A + b * B |
| // where a = a[0]+256*a[1]+...+256^31 a[31]. |
| // and b = b[0]+256*b[1]+...+256^31 b[31]. |
| // B is the Ed25519 base point (x,4/5) with x positive. |
| static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a, |
| const ge_p3 *A, const uint8_t *b) { |
| signed char aslide[256]; |
| signed char bslide[256]; |
| ge_cached Ai[8]; // A,3A,5A,7A,9A,11A,13A,15A |
| ge_p1p1 t; |
| ge_p3 u; |
| ge_p3 A2; |
| int i; |
| |
| slide(aslide, a); |
| slide(bslide, b); |
| |
| x25519_ge_p3_to_cached(&Ai[0], A); |
| ge_p3_dbl(&t, A); |
| x25519_ge_p1p1_to_p3(&A2, &t); |
| x25519_ge_add(&t, &A2, &Ai[0]); |
| x25519_ge_p1p1_to_p3(&u, &t); |
| x25519_ge_p3_to_cached(&Ai[1 |