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// 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.
#if defined(_MSC_VER)
#pragma warning(push, 3)
#endif
#include <string.h>
#if defined(_MSC_VER)
#pragma warning(pop)
#endif
#include <GFp/cpu.h>
#include <GFp/mem.h>
#include "internal.h"
#include "../../crypto/internal.h"
#if defined(_MSC_VER)
// '=': conversion from 'int64_t' to 'int32_t', possible loss of data
#pragma warning(disable: 4242)
// '=': conversion from 'int32_t' to 'uint8_t', possible loss of data
#pragma warning(disable: 4244)
#endif
#if defined(__GNUC__)
#pragma GCC diagnostic ignored "-Wconversion"
#pragma GCC diagnostic ignored "-Wsign-conversion"
#endif
// 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) {
memset(h, 0, sizeof(fe));
}
static void fe_loose_0(fe_loose *h) {
memset(h, 0, sizeof(fe_loose));
}
// h = 1
static void fe_1(fe *h) {
memset(h, 0, sizeof(fe));
h->v[0] = 1;
}
static void fe_loose_1(fe_loose *h) {
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);
}
#if defined(OPENSSL_SMALL)
static void fe_mul_llt(fe_loose *h, const fe_loose *f, const fe *g) {
fe_mul_impl(h->v, f->v, g->v);
}
#endif
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) {
memset(h, 0, sizeof(fe));
}
static void fe_loose_0(fe_loose *h) {
memset(h, 0, sizeof(fe_loose));
}
// h = 1
static void fe_1(fe *h) {
memset(h, 0, sizeof(fe));
h->v[0] = 1;
}
static void fe_loose_1(fe_loose *h) {
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) was
// removed. This comment is here to make diffs vs. BoringSSL easier to read.
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) {
memmove(h, f, sizeof(fe));
}
static void fe_copy_lt(fe_loose *h, const fe *f) {
OPENSSL_STATIC_ASSERT(sizeof(fe_loose) == sizeof(fe),
"fe and fe_loose mismatch");
memmove(h, f, sizeof(fe));
}
#if !defined(OPENSSL_SMALL)
static void fe_copy_ll(fe_loose *h, const fe_loose *f) {
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 GFp_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.
int GFp_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_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
static 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
static 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
static 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 = 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
static 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
static 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);
}
#if defined(OPENSSL_SMALL)
static 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);
}
}
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 GFp_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;