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/* MIT License
*
* Copyright (c) 2016-2022 INRIA, CMU and Microsoft Corporation
* Copyright (c) 2022-2023 HACL* Contributors
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
#include "Hacl_P521.h"
#include "internal/Hacl_Krmllib.h"
#include "internal/Hacl_Bignum_Base.h"
static inline uint64_t
bn_is_eq_mask(uint64_t *x, uint64_t *y)
{
uint64_t mask = 0xFFFFFFFFFFFFFFFFULL;
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
uint64_t uu____0 = FStar_UInt64_eq_mask(x[i], y[i]);
mask = uu____0 & mask;);
uint64_t mask1 = mask;
return mask1;
}
static inline void
bn_cmovznz(uint64_t *a, uint64_t b, uint64_t *c, uint64_t *d)
{
uint64_t mask = ~FStar_UInt64_eq_mask(b, 0ULL);
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
uint64_t *os = a;
uint64_t uu____0 = c[i];
uint64_t x = uu____0 ^ (mask & (d[i] ^ uu____0));
os[i] = x;);
}
static inline void
bn_add_mod(uint64_t *a, uint64_t *b, uint64_t *c, uint64_t *d)
{
uint64_t c10 = 0ULL;
KRML_MAYBE_FOR2(i,
0U,
2U,
1U,
uint64_t t1 = c[4U * i];
uint64_t t20 = d[4U * i];
uint64_t *res_i0 = a + 4U * i;
c10 = Lib_IntTypes_Intrinsics_add_carry_u64(c10, t1, t20, res_i0);
uint64_t t10 = c[4U * i + 1U];
uint64_t t21 = d[4U * i + 1U];
uint64_t *res_i1 = a + 4U * i + 1U;
c10 = Lib_IntTypes_Intrinsics_add_carry_u64(c10, t10, t21, res_i1);
uint64_t t11 = c[4U * i + 2U];
uint64_t t22 = d[4U * i + 2U];
uint64_t *res_i2 = a + 4U * i + 2U;
c10 = Lib_IntTypes_Intrinsics_add_carry_u64(c10, t11, t22, res_i2);
uint64_t t12 = c[4U * i + 3U];
uint64_t t2 = d[4U * i + 3U];
uint64_t *res_i = a + 4U * i + 3U;
c10 = Lib_IntTypes_Intrinsics_add_carry_u64(c10, t12, t2, res_i););
{
uint64_t t1 = c[8U];
uint64_t t2 = d[8U];
uint64_t *res_i = a + 8U;
c10 = Lib_IntTypes_Intrinsics_add_carry_u64(c10, t1, t2, res_i);
}
uint64_t c0 = c10;
uint64_t tmp[9U] = { 0U };
uint64_t c1 = 0ULL;
KRML_MAYBE_FOR2(i,
0U,
2U,
1U,
uint64_t t1 = a[4U * i];
uint64_t t20 = b[4U * i];
uint64_t *res_i0 = tmp + 4U * i;
c1 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c1, t1, t20, res_i0);
uint64_t t10 = a[4U * i + 1U];
uint64_t t21 = b[4U * i + 1U];
uint64_t *res_i1 = tmp + 4U * i + 1U;
c1 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c1, t10, t21, res_i1);
uint64_t t11 = a[4U * i + 2U];
uint64_t t22 = b[4U * i + 2U];
uint64_t *res_i2 = tmp + 4U * i + 2U;
c1 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c1, t11, t22, res_i2);
uint64_t t12 = a[4U * i + 3U];
uint64_t t2 = b[4U * i + 3U];
uint64_t *res_i = tmp + 4U * i + 3U;
c1 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c1, t12, t2, res_i););
{
uint64_t t1 = a[8U];
uint64_t t2 = b[8U];
uint64_t *res_i = tmp + 8U;
c1 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c1, t1, t2, res_i);
}
uint64_t c11 = c1;
uint64_t c2 = c0 - c11;
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
uint64_t *os = a;
uint64_t x = (c2 & a[i]) | (~c2 & tmp[i]);
os[i] = x;);
}
static inline uint64_t
bn_sub(uint64_t *a, uint64_t *b, uint64_t *c)
{
uint64_t c1 = 0ULL;
KRML_MAYBE_FOR2(i,
0U,
2U,
1U,
uint64_t t1 = b[4U * i];
uint64_t t20 = c[4U * i];
uint64_t *res_i0 = a + 4U * i;
c1 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c1, t1, t20, res_i0);
uint64_t t10 = b[4U * i + 1U];
uint64_t t21 = c[4U * i + 1U];
uint64_t *res_i1 = a + 4U * i + 1U;
c1 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c1, t10, t21, res_i1);
uint64_t t11 = b[4U * i + 2U];
uint64_t t22 = c[4U * i + 2U];
uint64_t *res_i2 = a + 4U * i + 2U;
c1 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c1, t11, t22, res_i2);
uint64_t t12 = b[4U * i + 3U];
uint64_t t2 = c[4U * i + 3U];
uint64_t *res_i = a + 4U * i + 3U;
c1 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c1, t12, t2, res_i););
{
uint64_t t1 = b[8U];
uint64_t t2 = c[8U];
uint64_t *res_i = a + 8U;
c1 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c1, t1, t2, res_i);
}
uint64_t c10 = c1;
return c10;
}
static inline void
bn_sub_mod(uint64_t *a, uint64_t *b, uint64_t *c, uint64_t *d)
{
uint64_t c10 = 0ULL;
KRML_MAYBE_FOR2(i,
0U,
2U,
1U,
uint64_t t1 = c[4U * i];
uint64_t t20 = d[4U * i];
uint64_t *res_i0 = a + 4U * i;
c10 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c10, t1, t20, res_i0);
uint64_t t10 = c[4U * i + 1U];
uint64_t t21 = d[4U * i + 1U];
uint64_t *res_i1 = a + 4U * i + 1U;
c10 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c10, t10, t21, res_i1);
uint64_t t11 = c[4U * i + 2U];
uint64_t t22 = d[4U * i + 2U];
uint64_t *res_i2 = a + 4U * i + 2U;
c10 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c10, t11, t22, res_i2);
uint64_t t12 = c[4U * i + 3U];
uint64_t t2 = d[4U * i + 3U];
uint64_t *res_i = a + 4U * i + 3U;
c10 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c10, t12, t2, res_i););
{
uint64_t t1 = c[8U];
uint64_t t2 = d[8U];
uint64_t *res_i = a + 8U;
c10 = Lib_IntTypes_Intrinsics_sub_borrow_u64(c10, t1, t2, res_i);
}
uint64_t c0 = c10;
uint64_t tmp[9U] = { 0U };
uint64_t c1 = 0ULL;
KRML_MAYBE_FOR2(i,
0U,
2U,
1U,
uint64_t t1 = a[4U * i];
uint64_t t20 = b[4U * i];
uint64_t *res_i0 = tmp + 4U * i;
c1 = Lib_IntTypes_Intrinsics_add_carry_u64(c1, t1, t20, res_i0);
uint64_t t10 = a[4U * i + 1U];
uint64_t t21 = b[4U * i + 1U];
uint64_t *res_i1 = tmp + 4U * i + 1U;
c1 = Lib_IntTypes_Intrinsics_add_carry_u64(c1, t10, t21, res_i1);
uint64_t t11 = a[4U * i + 2U];
uint64_t t22 = b[4U * i + 2U];
uint64_t *res_i2 = tmp + 4U * i + 2U;
c1 = Lib_IntTypes_Intrinsics_add_carry_u64(c1, t11, t22, res_i2);
uint64_t t12 = a[4U * i + 3U];
uint64_t t2 = b[4U * i + 3U];
uint64_t *res_i = tmp + 4U * i + 3U;
c1 = Lib_IntTypes_Intrinsics_add_carry_u64(c1, t12, t2, res_i););
{
uint64_t t1 = a[8U];
uint64_t t2 = b[8U];
uint64_t *res_i = tmp + 8U;
c1 = Lib_IntTypes_Intrinsics_add_carry_u64(c1, t1, t2, res_i);
}
uint64_t c11 = c1;
KRML_MAYBE_UNUSED_VAR(c11);
uint64_t c2 = 0ULL - c0;
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
uint64_t *os = a;
uint64_t x = (c2 & tmp[i]) | (~c2 & a[i]);
os[i] = x;);
}
static inline void
bn_mul(uint64_t *a, uint64_t *b, uint64_t *c)
{
memset(a, 0U, 18U * sizeof(uint64_t));
KRML_MAYBE_FOR9(
i0,
0U,
9U,
1U,
uint64_t bj = c[i0];
uint64_t *res_j = a + i0;
uint64_t c1 = 0ULL;
KRML_MAYBE_FOR2(i,
0U,
2U,
1U,
uint64_t a_i = b[4U * i];
uint64_t *res_i0 = res_j + 4U * i;
c1 = Hacl_Bignum_Base_mul_wide_add2_u64(a_i, bj, c1, res_i0);
uint64_t a_i0 = b[4U * i + 1U];
uint64_t *res_i1 = res_j + 4U * i + 1U;
c1 = Hacl_Bignum_Base_mul_wide_add2_u64(a_i0, bj, c1, res_i1);
uint64_t a_i1 = b[4U * i + 2U];
uint64_t *res_i2 = res_j + 4U * i + 2U;
c1 = Hacl_Bignum_Base_mul_wide_add2_u64(a_i1, bj, c1, res_i2);
uint64_t a_i2 = b[4U * i + 3U];
uint64_t *res_i = res_j + 4U * i + 3U;
c1 = Hacl_Bignum_Base_mul_wide_add2_u64(a_i2, bj, c1, res_i););
{
uint64_t a_i = b[8U];
uint64_t *res_i = res_j + 8U;
c1 = Hacl_Bignum_Base_mul_wide_add2_u64(a_i, bj, c1, res_i);
} uint64_t r = c1;
a[9U + i0] = r;);
}
static inline void
bn_sqr(uint64_t *a, uint64_t *b)
{
memset(a, 0U, 18U * sizeof(uint64_t));
KRML_MAYBE_FOR9(
i0,
0U,
9U,
1U,
uint64_t *ab = b;
uint64_t a_j = b[i0];
uint64_t *res_j = a + i0;
uint64_t c = 0ULL;
for (uint32_t i = 0U; i < i0 / 4U; i++) {
uint64_t a_i = ab[4U * i];
uint64_t *res_i0 = res_j + 4U * i;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i, a_j, c, res_i0);
uint64_t a_i0 = ab[4U * i + 1U];
uint64_t *res_i1 = res_j + 4U * i + 1U;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i0, a_j, c, res_i1);
uint64_t a_i1 = ab[4U * i + 2U];
uint64_t *res_i2 = res_j + 4U * i + 2U;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i1, a_j, c, res_i2);
uint64_t a_i2 = ab[4U * i + 3U];
uint64_t *res_i = res_j + 4U * i + 3U;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i2, a_j, c, res_i);
} for (uint32_t i = i0 / 4U * 4U; i < i0; i++) {
uint64_t a_i = ab[i];
uint64_t *res_i = res_j + i;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i, a_j, c, res_i);
} uint64_t r = c;
a[i0 + i0] = r;);
uint64_t c0 = Hacl_Bignum_Addition_bn_add_eq_len_u64(18U, a, a, a);
KRML_MAYBE_UNUSED_VAR(c0);
uint64_t tmp[18U] = { 0U };
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
FStar_UInt128_uint128 res = FStar_UInt128_mul_wide(b[i], b[i]);
uint64_t hi = FStar_UInt128_uint128_to_uint64(FStar_UInt128_shift_right(res, 64U));
uint64_t lo = FStar_UInt128_uint128_to_uint64(res);
tmp[2U * i] = lo;
tmp[2U * i + 1U] = hi;);
uint64_t c1 = Hacl_Bignum_Addition_bn_add_eq_len_u64(18U, a, tmp, a);
KRML_MAYBE_UNUSED_VAR(c1);
}
static inline void
bn_to_bytes_be(uint8_t *a, uint64_t *b)
{
uint8_t tmp[72U] = { 0U };
KRML_MAYBE_FOR9(i, 0U, 9U, 1U, store64_be(tmp + i * 8U, b[9U - i - 1U]););
memcpy(a, tmp + 6U, 66U * sizeof(uint8_t));
}
static inline void
bn_from_bytes_be(uint64_t *a, uint8_t *b)
{
uint8_t tmp[72U] = { 0U };
memcpy(tmp + 6U, b, 66U * sizeof(uint8_t));
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
uint64_t *os = a;
uint64_t u = load64_be(tmp + (9U - i - 1U) * 8U);
uint64_t x = u;
os[i] = x;);
}
static inline void
p521_make_prime(uint64_t *n)
{
n[0U] = 0xffffffffffffffffULL;
n[1U] = 0xffffffffffffffffULL;
n[2U] = 0xffffffffffffffffULL;
n[3U] = 0xffffffffffffffffULL;
n[4U] = 0xffffffffffffffffULL;
n[5U] = 0xffffffffffffffffULL;
n[6U] = 0xffffffffffffffffULL;
n[7U] = 0xffffffffffffffffULL;
n[8U] = 0x1ffULL;
}
static inline void
p521_make_order(uint64_t *n)
{
n[0U] = 0xbb6fb71e91386409ULL;
n[1U] = 0x3bb5c9b8899c47aeULL;
n[2U] = 0x7fcc0148f709a5d0ULL;
n[3U] = 0x51868783bf2f966bULL;
n[4U] = 0xfffffffffffffffaULL;
n[5U] = 0xffffffffffffffffULL;
n[6U] = 0xffffffffffffffffULL;
n[7U] = 0xffffffffffffffffULL;
n[8U] = 0x1ffULL;
}
static inline void
p521_make_a_coeff(uint64_t *a)
{
a[0U] = 0xfe7fffffffffffffULL;
a[1U] = 0xffffffffffffffffULL;
a[2U] = 0xffffffffffffffffULL;
a[3U] = 0xffffffffffffffffULL;
a[4U] = 0xffffffffffffffffULL;
a[5U] = 0xffffffffffffffffULL;
a[6U] = 0xffffffffffffffffULL;
a[7U] = 0xffffffffffffffffULL;
a[8U] = 0x01ffULL;
}
static inline void
p521_make_b_coeff(uint64_t *b)
{
b[0U] = 0x8014654fae586387ULL;
b[1U] = 0x78f7a28fea35a81fULL;
b[2U] = 0x839ab9efc41e961aULL;
b[3U] = 0xbd8b29605e9dd8dfULL;
b[4U] = 0xf0ab0c9ca8f63f49ULL;
b[5U] = 0xf9dc5a44c8c77884ULL;
b[6U] = 0x77516d392dccd98aULL;
b[7U] = 0x0fc94d10d05b42a0ULL;
b[8U] = 0x4dULL;
}
static inline void
p521_make_g_x(uint64_t *n)
{
n[0U] = 0xb331a16381adc101ULL;
n[1U] = 0x4dfcbf3f18e172deULL;
n[2U] = 0x6f19a459e0c2b521ULL;
n[3U] = 0x947f0ee093d17fd4ULL;
n[4U] = 0xdd50a5af3bf7f3acULL;
n[5U] = 0x90fc1457b035a69eULL;
n[6U] = 0x214e32409c829fdaULL;
n[7U] = 0xe6cf1f65b311cadaULL;
n[8U] = 0x74ULL;
}
static inline void
p521_make_g_y(uint64_t *n)
{
n[0U] = 0x28460e4a5a9e268eULL;
n[1U] = 0x20445f4a3b4fe8b3ULL;
n[2U] = 0xb09a9e3843513961ULL;
n[3U] = 0x2062a85c809fd683ULL;
n[4U] = 0x164bf7394caf7a13ULL;
n[5U] = 0x340bd7de8b939f33ULL;
n[6U] = 0xeccc7aa224abcda2ULL;
n[7U] = 0x022e452fda163e8dULL;
n[8U] = 0x1e0ULL;
}
static inline void
p521_make_fmont_R2(uint64_t *n)
{
n[0U] = 0x0ULL;
n[1U] = 0x400000000000ULL;
n[2U] = 0x0ULL;
n[3U] = 0x0ULL;
n[4U] = 0x0ULL;
n[5U] = 0x0ULL;
n[6U] = 0x0ULL;
n[7U] = 0x0ULL;
n[8U] = 0x0ULL;
}
static inline void
p521_make_fzero(uint64_t *n)
{
memset(n, 0U, 9U * sizeof(uint64_t));
n[0U] = 0ULL;
}
static inline void
p521_make_fone(uint64_t *n)
{
n[0U] = 0x80000000000000ULL;
n[1U] = 0x0ULL;
n[2U] = 0x0ULL;
n[3U] = 0x0ULL;
n[4U] = 0x0ULL;
n[5U] = 0x0ULL;
n[6U] = 0x0ULL;
n[7U] = 0x0ULL;
n[8U] = 0x0ULL;
}
static inline void
p521_make_qone(uint64_t *f)
{
f[0U] = 0xfb80000000000000ULL;
f[1U] = 0x28a2482470b763cdULL;
f[2U] = 0x17e2251b23bb31dcULL;
f[3U] = 0xca4019ff5b847b2dULL;
f[4U] = 0x2d73cbc3e206834ULL;
f[5U] = 0x0ULL;
f[6U] = 0x0ULL;
f[7U] = 0x0ULL;
f[8U] = 0x0ULL;
}
static inline void
fmont_reduction(uint64_t *res, uint64_t *x)
{
uint64_t n[9U] = { 0U };
p521_make_prime(n);
uint64_t c0 = 0ULL;
KRML_MAYBE_FOR9(
i0,
0U,
9U,
1U,
uint64_t qj = 1ULL * x[i0];
uint64_t *res_j0 = x + i0;
uint64_t c = 0ULL;
KRML_MAYBE_FOR2(i,
0U,
2U,
1U,
uint64_t a_i = n[4U * i];
uint64_t *res_i0 = res_j0 + 4U * i;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i, qj, c, res_i0);
uint64_t a_i0 = n[4U * i + 1U];
uint64_t *res_i1 = res_j0 + 4U * i + 1U;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i0, qj, c, res_i1);
uint64_t a_i1 = n[4U * i + 2U];
uint64_t *res_i2 = res_j0 + 4U * i + 2U;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i1, qj, c, res_i2);
uint64_t a_i2 = n[4U * i + 3U];
uint64_t *res_i = res_j0 + 4U * i + 3U;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i2, qj, c, res_i););
{
uint64_t a_i = n[8U];
uint64_t *res_i = res_j0 + 8U;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i, qj, c, res_i);
} uint64_t r = c;
uint64_t c1 = r;
uint64_t *resb = x + 9U + i0;
uint64_t res_j = x[9U + i0];
c0 = Lib_IntTypes_Intrinsics_add_carry_u64(c0, c1, res_j, resb););
memcpy(res, x + 9U, 9U * sizeof(uint64_t));
uint64_t c00 = c0;
uint64_t tmp[9U] = { 0U };
uint64_t c = 0ULL;
KRML_MAYBE_FOR2(i,
0U,
2U,
1U,
uint64_t t1 = res[4U * i];
uint64_t t20 = n[4U * i];
uint64_t *res_i0 = tmp + 4U * i;
c = Lib_IntTypes_Intrinsics_sub_borrow_u64(c, t1, t20, res_i0);
uint64_t t10 = res[4U * i + 1U];
uint64_t t21 = n[4U * i + 1U];
uint64_t *res_i1 = tmp + 4U * i + 1U;
c = Lib_IntTypes_Intrinsics_sub_borrow_u64(c, t10, t21, res_i1);
uint64_t t11 = res[4U * i + 2U];
uint64_t t22 = n[4U * i + 2U];
uint64_t *res_i2 = tmp + 4U * i + 2U;
c = Lib_IntTypes_Intrinsics_sub_borrow_u64(c, t11, t22, res_i2);
uint64_t t12 = res[4U * i + 3U];
uint64_t t2 = n[4U * i + 3U];
uint64_t *res_i = tmp + 4U * i + 3U;
c = Lib_IntTypes_Intrinsics_sub_borrow_u64(c, t12, t2, res_i););
{
uint64_t t1 = res[8U];
uint64_t t2 = n[8U];
uint64_t *res_i = tmp + 8U;
c = Lib_IntTypes_Intrinsics_sub_borrow_u64(c, t1, t2, res_i);
}
uint64_t c1 = c;
uint64_t c2 = c00 - c1;
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
uint64_t *os = res;
uint64_t x1 = (c2 & res[i]) | (~c2 & tmp[i]);
os[i] = x1;);
}
static inline void
qmont_reduction(uint64_t *res, uint64_t *x)
{
uint64_t n[9U] = { 0U };
p521_make_order(n);
uint64_t c0 = 0ULL;
KRML_MAYBE_FOR9(
i0,
0U,
9U,
1U,
uint64_t qj = 2103001588584519111ULL * x[i0];
uint64_t *res_j0 = x + i0;
uint64_t c = 0ULL;
KRML_MAYBE_FOR2(i,
0U,
2U,
1U,
uint64_t a_i = n[4U * i];
uint64_t *res_i0 = res_j0 + 4U * i;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i, qj, c, res_i0);
uint64_t a_i0 = n[4U * i + 1U];
uint64_t *res_i1 = res_j0 + 4U * i + 1U;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i0, qj, c, res_i1);
uint64_t a_i1 = n[4U * i + 2U];
uint64_t *res_i2 = res_j0 + 4U * i + 2U;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i1, qj, c, res_i2);
uint64_t a_i2 = n[4U * i + 3U];
uint64_t *res_i = res_j0 + 4U * i + 3U;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i2, qj, c, res_i););
{
uint64_t a_i = n[8U];
uint64_t *res_i = res_j0 + 8U;
c = Hacl_Bignum_Base_mul_wide_add2_u64(a_i, qj, c, res_i);
} uint64_t r = c;
uint64_t c1 = r;
uint64_t *resb = x + 9U + i0;
uint64_t res_j = x[9U + i0];
c0 = Lib_IntTypes_Intrinsics_add_carry_u64(c0, c1, res_j, resb););
memcpy(res, x + 9U, 9U * sizeof(uint64_t));
uint64_t c00 = c0;
uint64_t tmp[9U] = { 0U };
uint64_t c = 0ULL;
KRML_MAYBE_FOR2(i,
0U,
2U,
1U,
uint64_t t1 = res[4U * i];
uint64_t t20 = n[4U * i];
uint64_t *res_i0 = tmp + 4U * i;
c = Lib_IntTypes_Intrinsics_sub_borrow_u64(c, t1, t20, res_i0);
uint64_t t10 = res[4U * i + 1U];
uint64_t t21 = n[4U * i + 1U];
uint64_t *res_i1 = tmp + 4U * i + 1U;
c = Lib_IntTypes_Intrinsics_sub_borrow_u64(c, t10, t21, res_i1);
uint64_t t11 = res[4U * i + 2U];
uint64_t t22 = n[4U * i + 2U];
uint64_t *res_i2 = tmp + 4U * i + 2U;
c = Lib_IntTypes_Intrinsics_sub_borrow_u64(c, t11, t22, res_i2);
uint64_t t12 = res[4U * i + 3U];
uint64_t t2 = n[4U * i + 3U];
uint64_t *res_i = tmp + 4U * i + 3U;
c = Lib_IntTypes_Intrinsics_sub_borrow_u64(c, t12, t2, res_i););
{
uint64_t t1 = res[8U];
uint64_t t2 = n[8U];
uint64_t *res_i = tmp + 8U;
c = Lib_IntTypes_Intrinsics_sub_borrow_u64(c, t1, t2, res_i);
}
uint64_t c1 = c;
uint64_t c2 = c00 - c1;
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
uint64_t *os = res;
uint64_t x1 = (c2 & res[i]) | (~c2 & tmp[i]);
os[i] = x1;);
}
static inline uint64_t
bn_is_lt_prime_mask(uint64_t *f)
{
uint64_t tmp[9U] = { 0U };
p521_make_prime(tmp);
uint64_t c = bn_sub(tmp, f, tmp);
uint64_t m = FStar_UInt64_gte_mask(c, 0ULL) & ~FStar_UInt64_eq_mask(c, 0ULL);
return m;
}
static inline void
fadd0(uint64_t *a, uint64_t *b, uint64_t *c)
{
uint64_t n[9U] = { 0U };
p521_make_prime(n);
bn_add_mod(a, n, b, c);
}
static inline void
fsub0(uint64_t *a, uint64_t *b, uint64_t *c)
{
uint64_t n[9U] = { 0U };
p521_make_prime(n);
bn_sub_mod(a, n, b, c);
}
static inline void
fmul0(uint64_t *a, uint64_t *b, uint64_t *c)
{
uint64_t tmp[18U] = { 0U };
bn_mul(tmp, b, c);
fmont_reduction(a, tmp);
}
static inline void
fsqr0(uint64_t *a, uint64_t *b)
{
uint64_t tmp[18U] = { 0U };
bn_sqr(tmp, b);
fmont_reduction(a, tmp);
}
static inline void
from_mont(uint64_t *a, uint64_t *b)
{
uint64_t tmp[18U] = { 0U };
memcpy(tmp, b, 9U * sizeof(uint64_t));
fmont_reduction(a, tmp);
}
static inline void
to_mont(uint64_t *a, uint64_t *b)
{
uint64_t r2modn[9U] = { 0U };
p521_make_fmont_R2(r2modn);
uint64_t tmp[18U] = { 0U };
bn_mul(tmp, b, r2modn);
fmont_reduction(a, tmp);
}
static inline void
p521_finv(uint64_t *res, uint64_t *a)
{
uint64_t b[9U] = { 0U };
b[0U] = 0xfffffffffffffffdULL;
b[1U] = 0xffffffffffffffffULL;
b[2U] = 0xffffffffffffffffULL;
b[3U] = 0xffffffffffffffffULL;
b[4U] = 0xffffffffffffffffULL;
b[5U] = 0xffffffffffffffffULL;
b[6U] = 0xffffffffffffffffULL;
b[7U] = 0xffffffffffffffffULL;
b[8U] = 0x1ffULL;
uint64_t tmp[9U] = { 0U };
memcpy(tmp, a, 9U * sizeof(uint64_t));
uint64_t table[288U] = { 0U };
uint64_t tmp1[9U] = { 0U };
uint64_t *t0 = table;
uint64_t *t1 = table + 9U;
p521_make_fone(t0);
memcpy(t1, tmp, 9U * sizeof(uint64_t));
KRML_MAYBE_FOR15(i,
0U,
15U,
1U,
uint64_t *t11 = table + (i + 1U) * 9U;
fsqr0(tmp1, t11);
memcpy(table + (2U * i + 2U) * 9U, tmp1, 9U * sizeof(uint64_t));
uint64_t *t2 = table + (2U * i + 2U) * 9U;
fmul0(tmp1, tmp, t2);
memcpy(table + (2U * i + 3U) * 9U, tmp1, 9U * sizeof(uint64_t)););
uint32_t i0 = 520U;
uint64_t bits_c = Hacl_Bignum_Lib_bn_get_bits_u64(9U, b, i0, 5U);
memcpy(res, (uint64_t *)table, 9U * sizeof(uint64_t));
for (uint32_t i1 = 0U; i1 < 31U; i1++) {
uint64_t c = FStar_UInt64_eq_mask(bits_c, (uint64_t)(i1 + 1U));
const uint64_t *res_j = table + (i1 + 1U) * 9U;
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
uint64_t *os = res;
uint64_t x = (c & res_j[i]) | (~c & res[i]);
os[i] = x;);
}
uint64_t tmp10[9U] = { 0U };
for (uint32_t i1 = 0U; i1 < 104U; i1++) {
KRML_MAYBE_FOR5(i, 0U, 5U, 1U, fsqr0(res, res););
uint32_t k = 520U - 5U * i1 - 5U;
uint64_t bits_l = Hacl_Bignum_Lib_bn_get_bits_u64(9U, b, k, 5U);
memcpy(tmp10, (uint64_t *)table, 9U * sizeof(uint64_t));
for (uint32_t i2 = 0U; i2 < 31U; i2++) {
uint64_t c = FStar_UInt64_eq_mask(bits_l, (uint64_t)(i2 + 1U));
const uint64_t *res_j = table + (i2 + 1U) * 9U;
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
uint64_t *os = tmp10;
uint64_t x = (c & res_j[i]) | (~c & tmp10[i]);
os[i] = x;);
}
fmul0(res, res, tmp10);
}
}
static inline void
p521_fsqrt(uint64_t *res, uint64_t *a)
{
uint64_t b[9U] = { 0U };
b[0U] = 0x0ULL;
b[1U] = 0x0ULL;
b[2U] = 0x0ULL;
b[3U] = 0x0ULL;
b[4U] = 0x0ULL;
b[5U] = 0x0ULL;
b[6U] = 0x0ULL;
b[7U] = 0x0ULL;
b[8U] = 0x80ULL;
uint64_t tmp[9U] = { 0U };
memcpy(tmp, a, 9U * sizeof(uint64_t));
uint64_t table[288U] = { 0U };
uint64_t tmp1[9U] = { 0U };
uint64_t *t0 = table;
uint64_t *t1 = table + 9U;
p521_make_fone(t0);
memcpy(t1, tmp, 9U * sizeof(uint64_t));
KRML_MAYBE_FOR15(i,
0U,
15U,
1U,
uint64_t *t11 = table + (i + 1U) * 9U;
fsqr0(tmp1, t11);
memcpy(table + (2U * i + 2U) * 9U, tmp1, 9U * sizeof(uint64_t));
uint64_t *t2 = table + (2U * i + 2U) * 9U;
fmul0(tmp1, tmp, t2);
memcpy(table + (2U * i + 3U) * 9U, tmp1, 9U * sizeof(uint64_t)););
uint32_t i0 = 520U;
uint64_t bits_c = Hacl_Bignum_Lib_bn_get_bits_u64(9U, b, i0, 5U);
memcpy(res, (uint64_t *)table, 9U * sizeof(uint64_t));
for (uint32_t i1 = 0U; i1 < 31U; i1++) {
uint64_t c = FStar_UInt64_eq_mask(bits_c, (uint64_t)(i1 + 1U));
const uint64_t *res_j = table + (i1 + 1U) * 9U;
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
uint64_t *os = res;
uint64_t x = (c & res_j[i]) | (~c & res[i]);
os[i] = x;);
}
uint64_t tmp10[9U] = { 0U };
for (uint32_t i1 = 0U; i1 < 104U; i1++) {
KRML_MAYBE_FOR5(i, 0U, 5U, 1U, fsqr0(res, res););
uint32_t k = 520U - 5U * i1 - 5U;
uint64_t bits_l = Hacl_Bignum_Lib_bn_get_bits_u64(9U, b, k, 5U);
memcpy(tmp10, (uint64_t *)table, 9U * sizeof(uint64_t));
for (uint32_t i2 = 0U; i2 < 31U; i2++) {
uint64_t c = FStar_UInt64_eq_mask(bits_l, (uint64_t)(i2 + 1U));
const uint64_t *res_j = table + (i2 + 1U) * 9U;
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
uint64_t *os = tmp10;
uint64_t x = (c & res_j[i]) | (~c & tmp10[i]);
os[i] = x;);
}
fmul0(res, res, tmp10);
}
}
static inline uint64_t
load_qelem_conditional(uint64_t *a, uint8_t *b)
{
bn_from_bytes_be(a, b);
uint64_t tmp[9U] = { 0U };
p521_make_order(tmp);
uint64_t c = bn_sub(tmp, a, tmp);
uint64_t is_lt_order = FStar_UInt64_gte_mask(c, 0ULL) & ~FStar_UInt64_eq_mask(c, 0ULL);
uint64_t bn_zero[9U] = { 0U };
uint64_t res = bn_is_eq_mask(a, bn_zero);
uint64_t is_eq_zero = res;
uint64_t is_b_valid = is_lt_order & ~is_eq_zero;
uint64_t oneq[9U] = { 0U };
memset(oneq, 0U, 9U * sizeof(uint64_t));
oneq[0U] = 1ULL;
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
uint64_t *os = a;
uint64_t uu____0 = oneq[i];
uint64_t x = uu____0 ^ (is_b_valid & (a[i] ^ uu____0));
os[i] = x;);
return is_b_valid;
}
static inline void
qmod_short(uint64_t *a, uint64_t *b)
{
uint64_t tmp[9U] = { 0U };
p521_make_order(tmp);
uint64_t c = bn_sub(tmp, b, tmp);
bn_cmovznz(a, c, tmp, b);
}
static inline void
qadd(uint64_t *a, uint64_t *b, uint64_t *c)
{
uint64_t n[9U] = { 0U };
p521_make_order(n);
bn_add_mod(a, n, b, c);
}
static inline void
qmul(uint64_t *a, uint64_t *b, uint64_t *c)
{
uint64_t tmp[18U] = { 0U };
bn_mul(tmp, b, c);
qmont_reduction(a, tmp);
}
static inline void
qsqr(uint64_t *a, uint64_t *b)
{
uint64_t tmp[18U] = { 0U };
bn_sqr(tmp, b);
qmont_reduction(a, tmp);
}
static inline void
from_qmont(uint64_t *a, uint64_t *b)
{
uint64_t tmp[18U] = { 0U };
memcpy(tmp, b, 9U * sizeof(uint64_t));
qmont_reduction(a, tmp);
}
static inline void
p521_qinv(uint64_t *res, uint64_t *a)
{
uint64_t b[9U] = { 0U };
b[0U] = 0xbb6fb71e91386407ULL;
b[1U] = 0x3bb5c9b8899c47aeULL;
b[2U] = 0x7fcc0148f709a5d0ULL;
b[3U] = 0x51868783bf2f966bULL;
b[4U] = 0xfffffffffffffffaULL;
b[5U] = 0xffffffffffffffffULL;
b[6U] = 0xffffffffffffffffULL;
b[7U] = 0xffffffffffffffffULL;
b[8U] = 0x1ffULL;
uint64_t tmp[9U] = { 0U };
memcpy(tmp, a, 9U * sizeof(uint64_t));
uint64_t table[288U] = { 0U };
uint64_t tmp1[9U] = { 0U };
uint64_t *t0 = table;
uint64_t *t1 = table + 9U;
p521_make_qone(t0);
memcpy(t1, tmp, 9U * sizeof(uint64_t));
KRML_MAYBE_FOR15(i,
0U,
15U,
1U,
uint64_t *t11 = table + (i + 1U) * 9U;
qsqr(tmp1, t11);
memcpy(table + (2U * i + 2U) * 9U, tmp1, 9U * sizeof(uint64_t));
uint64_t *t2 = table + (2U * i + 2U) * 9U;
qmul(tmp1, tmp, t2);
memcpy(table + (2U * i + 3U) * 9U, tmp1, 9U * sizeof(uint64_t)););
uint32_t i0 = 520U;
uint64_t bits_c = Hacl_Bignum_Lib_bn_get_bits_u64(9U, b, i0, 5U);
memcpy(res, (uint64_t *)table, 9U * sizeof(uint64_t));
for (uint32_t i1 = 0U; i1 < 31U; i1++) {
uint64_t c = FStar_UInt64_eq_mask(bits_c, (uint64_t)(i1 + 1U));
const uint64_t *res_j = table + (i1 + 1U) * 9U;
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
uint64_t *os = res;
uint64_t x = (c & res_j[i]) | (~c & res[i]);
os[i] = x;);
}
uint64_t tmp10[9U] = { 0U };
for (uint32_t i1 = 0U; i1 < 104U; i1++) {
KRML_MAYBE_FOR5(i, 0U, 5U, 1U, qsqr(res, res););
uint32_t k = 520U - 5U * i1 - 5U;
uint64_t bits_l = Hacl_Bignum_Lib_bn_get_bits_u64(9U, b, k, 5U);
memcpy(tmp10, (uint64_t *)table, 9U * sizeof(uint64_t));
for (uint32_t i2 = 0U; i2 < 31U; i2++) {
uint64_t c = FStar_UInt64_eq_mask(bits_l, (uint64_t)(i2 + 1U));
const uint64_t *res_j = table + (i2 + 1U) * 9U;
KRML_MAYBE_FOR9(i,
0U,
9U,
1U,
uint64_t *os = tmp10;
uint64_t x = (c & res_j[i]) | (~c & tmp10[i]);
os[i] = x;);
}
qmul(res, res, tmp10);
}
}
static inline void
point_add(uint64_t *x, uint64_t *y, uint64_t *xy)
{
uint64_t tmp[81U] = { 0U };
uint64_t *t0 = tmp;
uint64_t *t1 = tmp + 54U;
uint64_t *x3 = t1;
uint64_t *y3 = t1 + 9U;
uint64_t *z3 = t1 + 18U;
uint64_t *t01 = t0;
uint64_t *t11 = t0 + 9U;
uint64_t *t2 = t0 + 18U;
uint64_t *t3 = t0 + 27U;
uint64_t *t4 = t0 + 36U;
uint64_t *t5 = t0 + 45U;
uint64_t *x1 = x;
uint64_t *y1 = x + 9U;
uint64_t *z10 = x + 18U;
uint64_t *x20 = y;
uint64_t *y20 = y + 9U;
uint64_t *z20 = y + 18U;
fmul0(t01, x1, x20);
fmul0(t11, y1, y20);
fmul0(t2, z10, z20);
fadd0(t3, x1, y1);
fadd0(t4, x20, y20);
fmul0(t3, t3, t4);
fadd0(t4, t01, t11);
uint64_t *y10 = x + 9U;
uint64_t *z11 = x + 18U;
uint64_t *y2 = y + 9U;
uint64_t *z21 = y + 18U;
fsub0(t3, t3, t4);
fadd0(t4, y10, z11);
fadd0(t5, y2, z21);
fmul0(t4, t4, t5);
fadd0(t5, t11, t2);
fsub0(t4, t4, t5);
uint64_t *x10 = x;
uint64_t *z1 = x + 18U;
uint64_t *x2 = y;
uint64_t *z2 = y + 18U;
fadd0(x3, x10, z1);
fadd0(y3, x2, z2);
fmul0(x3, x3, y3);
fadd0(y3, t01, t2);
fsub0(y3, x3, y3);
uint64_t b_coeff[9U] = { 0U };
p521_make_b_coeff(b_coeff);
fmul0(z3, b_coeff, t2);
fsub0(x3, y3, z3);
fadd0(z3, x3, x3);
fadd0(x3, x3, z3);
fsub0(z3, t11, x3);
fadd0(x3, t11, x3);
uint64_t b_coeff0[9U] = { 0U };
p521_make_b_coeff(b_coeff0);
fmul0(y3, b_coeff0, y3);
fadd0(t11, t2, t2);
fadd0(t2, t11, t2);
fsub0(y3, y3, t2);
fsub0(y3, y3, t01);
fadd0(t11, y3, y3);
fadd0(y3, t11, y3);
fadd0(t11, t01, t01);
fadd0(t01, t11, t01);
fsub0(t01, t01, t2);
fmul0(t11, t4, y3);
fmul0(t2, t01, y3);
fmul0(y3, x3, z3);
fadd0(y3, y3, t2);
fmul0(x3, t3, x3);
fsub0(x3, x3, t11);
fmul0(z3, t4, z3);
fmul0(t11, t3, t01);
fadd0(z3, z3, t11);
memcpy(xy, t1, 27U * sizeof(uint64_t));
}
static inline void
point_double(uint64_t *x, uint64_t *xx)
{
uint64_t tmp[45U] = { 0U };
uint64_t *x1 = x;
uint64_t *z = x + 18U;
uint64_t *x3 = xx;
uint64_t *y3 = xx + 9U;
uint64_t *z3 = xx + 18U;
uint64_t *t0 = tmp;
uint64_t *t1 = tmp + 9U;
uint64_t *t2 = tmp + 18U;
uint64_t *t3 = tmp + 27U;
uint64_t *t4 = tmp + 36U;
uint64_t *x2 = x;
uint64_t *y = x + 9U;
uint64_t *z1 = x + 18U;
fsqr0(t0, x2);
fsqr0(t1, y);
fsqr0(t2, z1);
fmul0(t3, x2, y);
fadd0(t3, t3, t3);
fmul0(t4, y, z1);
fmul0(z3, x1, z);
fadd0(z3, z3, z3);
uint64_t b_coeff[9U] = { 0U };
p521_make_b_coeff(b_coeff);
fmul0(y3, b_coeff, t2);
fsub0(y3, y3, z3);
fadd0(x3, y3, y3);
fadd0(y3, x3, y3);
fsub0(x3, t1, y3);
fadd0(y3, t1, y3);
fmul0(y3, x3, y3);
fmul0(x3, x3, t3);
fadd0(t3, t2, t2);
fadd0(t2, t2, t3);
uint64_t b_coeff0[9U] = { 0U };
p521_make_b_coeff(b_coeff0);
fmul0(z3, b_coeff0, z3);
fsub0(z3, z3, t2);
fsub0(z3, z3, t0);
fadd0(t3, z3, z3);
fadd0(z3, z3, t3);
fadd0(t3, t0, t0);
fadd0(t0, t3, t0);
fsub0(t0, t0, t2);
fmul0(t0, t0, z3);
fadd0(y3, y3, t0);
fadd0(t0, t4, t4);
fmul0(z3, t0, z3);
fsub0(x3, x3, z3);
fmul0(z3, t0, t1);
fadd0(z3, z3, z3);
fadd0(z3, z3, z3);
}
static inline void
point_zero(uint64_t *one)
{
uint64_t *x = one;
uint64_t *y = one + 9U;
uint64_t *z = one + 18U;
p521_make_fzero(x);
p521_make_fone(y);
p521_make_fzero(z);
}
static inline void
point_mul(uint64_t *res, uint64_t *scalar, uint64_t *p)
{
uint64_t table[432U] = { 0U };
uint64_t tmp[27U] = { 0U };
uint64_t *t0 = table;
uint64_t *t1 = table + 27U;
point_zero(t0);
memcpy(t1, p, 27U * sizeof(uint64_t));
KRML_MAYBE_FOR7(i,
0U,
7U,
1U,
uint64_t *t11 = table + (i + 1U) * 27U;
point_double(t11, tmp);
memcpy(table + (2U * i + 2U) * 27U, tmp, 27U * sizeof(uint64_t));
uint64_t *t2 = table + (2U * i + 2U) * 27U;
point_add(p, t2, tmp);
memcpy(table + (2U * i + 3U) * 27U, tmp, 27U * sizeof(uint64_t)););
uint32_t i0 = 520U;
uint64_t bits_c = Hacl_Bignum_Lib_bn_get_bits_u64(9U, scalar, i0, 4U);
memcpy(res, (uint64_t *)table, 27U * sizeof(uint64_t));
KRML_MAYBE_FOR15(
i1,
0U,
15U,
1U,
uint64_t c = FStar_UInt64_eq_mask(bits_c, (uint64_t)(i1 + 1U));
const uint64_t *res_j = table + (i1 + 1U) * 27U;
for (uint32_t i = 0U; i < 27U; i++) {
uint64_t *os = res;
uint64_t x = (c & res_j[i]) | (~c & res[i]);
os[i] = x;
});
uint64_t tmp0[27U] = { 0U };
for (uint32_t i1 = 0U; i1 < 130U; i1++) {
KRML_MAYBE_FOR4(i, 0U, 4U, 1U, point_double(res, res););
uint32_t k = 520U - 4U * i1 - 4U;
uint64_t bits_l = Hacl_Bignum_Lib_bn_get_bits_u64(9U, scalar, k, 4U);
memcpy(tmp0, (uint64_t *)table, 27U * sizeof(uint64_t));
KRML_MAYBE_FOR15(
i2,
0U,
15U,
1U,
uint64_t c = FStar_UInt64_eq_mask(bits_l, (uint64_t)(i2 + 1U));
const uint64_t *res_j = table + (i2 + 1U) * 27U;
for (uint32_t i = 0U; i < 27U; i++) {
uint64_t *os = tmp0;
uint64_t x = (c & res_j[i]) | (~c & tmp0[i]);
os[i] = x;
});
point_add(res, tmp0, res);
}
}
static inline void
point_mul_g(uint64_t *res, uint64_t *scalar)
{
uint64_t g[27U] = { 0U };
uint64_t *x = g;
uint64_t *y = g + 9U;
uint64_t *z = g + 18U;
p521_make_g_x(x);
p521_make_g_y(y);
p521_make_fone(z);
point_mul(res, scalar, g);
}
static inline void
point_mul_double_g(uint64_t *res, uint64_t *scalar1, uint64_t *scalar2, uint64_t *p)
{
uint64_t tmp[27U] = { 0U };
point_mul_g(tmp, scalar1);
point_mul(res, scalar2, p);
point_add(res, tmp, res);
}
static inline bool
ecdsa_sign_msg_as_qelem(
uint8_t *signature,
uint64_t *m_q,
uint8_t *private_key,
uint8_t *nonce)
{
uint64_t rsdk_q[36U] = { 0U };
uint64_t *r_q = rsdk_q;
uint64_t *s_q = rsdk_q + 9U;
uint64_t *d_a = rsdk_q + 18U;
uint64_t *k_q = rsdk_q + 27U;
uint64_t is_sk_valid = load_qelem_conditional(d_a, private_key);
uint64_t is_nonce_valid = load_qelem_conditional(k_q, nonce);
uint64_t are_sk_nonce_valid = is_sk_valid & is_nonce_valid;
uint64_t p[27U] = { 0U };
point_mul_g(p, k_q);
uint64_t zinv[9U] = { 0U };
uint64_t *px = p;
uint64_t *pz = p + 18U;
p521_finv(zinv, pz);
fmul0(r_q, px, zinv);
from_mont(r_q, r_q);
qmod_short(r_q, r_q);
uint64_t kinv[9U] = { 0U };
p521_qinv(kinv, k_q);
qmul(s_q, r_q, d_a);
from_qmont(m_q, m_q);
qadd(s_q, m_q, s_q);
qmul(s_q, kinv, s_q);
bn_to_bytes_be(signature, r_q);
bn_to_bytes_be(signature + 66U, s_q);
uint64_t bn_zero0[9U] = { 0U };
uint64_t res = bn_is_eq_mask(r_q, bn_zero0);
uint64_t is_r_zero = res;
uint64_t bn_zero[9U] = { 0U };
uint64_t res0 = bn_is_eq_mask(s_q, bn_zero);
uint64_t is_s_zero = res0;
uint64_t m = are_sk_nonce_valid & (~is_r_zero & ~is_s_zero);
bool res1 = m == 0xFFFFFFFFFFFFFFFFULL;
return res1;
}
static inline bool
ecdsa_verify_msg_as_qelem(
uint64_t *m_q,
uint8_t *public_key,
uint8_t *signature_r,
uint8_t *signature_s)
{
uint64_t tmp[63U] = { 0U };
uint64_t *pk = tmp;
uint64_t *r_q = tmp + 27U;
uint64_t *s_q = tmp + 36U;
uint64_t *u1 = tmp + 45U;
uint64_t *u2 = tmp + 54U;
uint64_t p_aff[18U] = { 0U };
uint8_t *p_x = public_key;
uint8_t *p_y = public_key + 66U;
uint64_t *bn_p_x = p_aff;
uint64_t *bn_p_y = p_aff + 9U;
bn_from_bytes_be(bn_p_x, p_x);
bn_from_bytes_be(bn_p_y, p_y);
uint64_t *px0 = p_aff;
uint64_t *py0 = p_aff + 9U;
uint64_t lessX = bn_is_lt_prime_mask(px0);
uint64_t lessY = bn_is_lt_prime_mask(py0);
uint64_t res0 = lessX & lessY;
bool is_xy_valid = res0 == 0xFFFFFFFFFFFFFFFFULL;
bool res;
if (!is_xy_valid) {
res = false;
} else {
uint64_t rp[9U] = { 0U };
uint64_t tx[9U] = { 0U };
uint64_t ty[9U] = { 0U };
uint64_t *px = p_aff;
uint64_t *py = p_aff + 9U;
to_mont(tx, px);
to_mont(ty, py);
uint64_t tmp1[9U] = { 0U };
fsqr0(rp, tx);
fmul0(rp, rp, tx);
p521_make_a_coeff(tmp1);
fmul0(tmp1, tmp1, tx);
fadd0(rp, tmp1, rp);
p521_make_b_coeff(tmp1);
fadd0(rp, tmp1, rp);
fsqr0(ty, ty);
uint64_t r = bn_is_eq_mask(ty, rp);
uint64_t r0 = r;
bool r1 = r0 == 0xFFFFFFFFFFFFFFFFULL;
res = r1;
}
if (res) {
uint64_t *px = p_aff;
uint64_t *py = p_aff + 9U;
uint64_t *rx = pk;
uint64_t *ry = pk + 9U;
uint64_t *rz = pk + 18U;
to_mont(rx, px);
to_mont(ry, py);
p521_make_fone(rz);
}
bool is_pk_valid = res;
bn_from_bytes_be(r_q, signature_r);
bn_from_bytes_be(s_q, signature_s);
uint64_t tmp10[9U] = { 0U };
p521_make_order(tmp10);
uint64_t c = bn_sub(tmp10, r_q, tmp10);
uint64_t is_lt_order = FStar_UInt64_gte_mask(c, 0ULL) & ~FStar_UInt64_eq_mask(c, 0ULL);
uint64_t bn_zero0[9U] = { 0U };
uint64_t res1 = bn_is_eq_mask(r_q, bn_zero0);
uint64_t is_eq_zero = res1;
uint64_t is_r_valid = is_lt_order & ~is_eq_zero;
uint64_t tmp11[9U] = { 0U };
p521_make_order(tmp11);
uint64_t c0 = bn_sub(tmp11, s_q, tmp11);
uint64_t is_lt_order0 = FStar_UInt64_gte_mask(c0, 0ULL) & ~FStar_UInt64_eq_mask(c0, 0ULL);
uint64_t bn_zero1[9U] = { 0U };
uint64_t res2 = bn_is_eq_mask(s_q, bn_zero1);
uint64_t is_eq_zero0 = res2;
uint64_t is_s_valid = is_lt_order0 & ~is_eq_zero0;
bool is_rs_valid = is_r_valid == 0xFFFFFFFFFFFFFFFFULL && is_s_valid == 0xFFFFFFFFFFFFFFFFULL;
if (!(is_pk_valid && is_rs_valid)) {
return false;
}
uint64_t sinv[9U] = { 0U };
p521_qinv(sinv, s_q);
uint64_t tmp1[9U] = { 0U };
from_qmont(tmp1, m_q);
qmul(u1, sinv, tmp1);
uint64_t tmp12[9U] = { 0U };
from_qmont(tmp12, r_q);
qmul(u2, sinv, tmp12);
uint64_t res3[27U] = { 0U };
point_mul_double_g(res3, u1, u2, pk);
uint64_t *pz0 = res3 + 18U;
uint64_t bn_zero[9U] = { 0U };
uint64_t res10 = bn_is_eq_mask(pz0, bn_zero);
uint64_t m = res10;
if (m == 0xFFFFFFFFFFFFFFFFULL) {
return false;
}
uint64_t x[9U] = { 0U };
uint64_t zinv[9U] = { 0U };
uint64_t *px = res3;
uint64_t *pz = res3 + 18U;
p521_finv(zinv, pz);
fmul0(x, px, zinv);
from_mont(x, x);
qmod_short(x, x);
uint64_t m0 = bn_is_eq_mask(x, r_q);
bool res11 = m0 == 0xFFFFFFFFFFFFFFFFULL;
return res11;
}
/*******************************************************************************
Verified C library for ECDSA and ECDH functions over the P-521 NIST curve.
This module implements signing and verification, key validation, conversions
between various point representations, and ECDH key agreement.
*******************************************************************************/
/*****************/
/* ECDSA signing */
/*****************/
/**
Create an ECDSA signature WITHOUT hashing first.
This function is intended to receive a hash of the input.
For convenience, we recommend using one of the hash-and-sign combined functions above.
The argument `msg` MUST be at least 66 bytes (i.e. `msg_len >= 66`).
NOTE: The equivalent functions in OpenSSL and Fiat-Crypto both accept inputs
smaller than 66 bytes. These libraries left-pad the input with enough zeroes to
reach the minimum 66 byte size. Clients who need behavior identical to OpenSSL
need to perform the left-padding themselves.
The function returns `true` for successful creation of an ECDSA signature and `false` otherwise.
The outparam `signature` (R || S) points to 132 bytes of valid memory, i.e., uint8_t[132].
The argument `msg` points to `msg_len` bytes of valid memory, i.e., uint8_t[msg_len].
The arguments `private_key` and `nonce` point to 66 bytes of valid memory, i.e., uint8_t[66].
The function also checks whether `private_key` and `nonce` are valid values:
• 0 < `private_key` < the order of the curve
• 0 < `nonce` < the order of the curve
*/
bool
Hacl_P521_ecdsa_sign_p521_without_hash(
uint8_t *signature,
uint32_t msg_len,
uint8_t *msg,
uint8_t *private_key,
uint8_t *nonce)
{
uint64_t m_q[9U] = { 0U };
uint8_t mHash[66U] = { 0U };
memcpy(mHash, msg, 66U * sizeof(uint8_t));
KRML_MAYBE_UNUSED_VAR(msg_len);
bn_from_bytes_be(m_q, mHash);
qmod_short(m_q, m_q);
bool res = ecdsa_sign_msg_as_qelem(signature, m_q, private_key, nonce);
return res;
}
/**********************/
/* ECDSA verification */
/**********************/
/**
Verify an ECDSA signature WITHOUT hashing first.
This function is intended to receive a hash of the input.
For convenience, we recommend using one of the hash-and-verify combined functions above.
The argument `msg` MUST be at least 66 bytes (i.e. `msg_len >= 66`).
The function returns `true` if the signature is valid and `false` otherwise.
The argument `msg` points to `msg_len` bytes of valid memory, i.e., uint8_t[msg_len].
The argument `public_key` (x || y) points to 132 bytes of valid memory, i.e., uint8_t[132].
The arguments `signature_r` and `signature_s` point to 66 bytes of valid memory, i.e., uint8_t[66].
The function also checks whether `public_key` is valid
*/
bool
Hacl_P521_ecdsa_verif_without_hash(
uint32_t msg_len,
uint8_t *msg,
uint8_t *public_key,
uint8_t *signature_r,
uint8_t *signature_s)
{
uint64_t m_q[9U] = { 0U };
uint8_t mHash[66U] = { 0U };
memcpy(mHash, msg, 66U * sizeof(uint8_t));
KRML_MAYBE_UNUSED_VAR(msg_len);
bn_from_bytes_be(m_q, mHash);
qmod_short(m_q, m_q);
bool res = ecdsa_verify_msg_as_qelem(m_q, public_key, signature_r, signature_s);
return res;
}
/******************/
/* Key validation */
/******************/
/**
Public key validation.
The function returns `true` if a public key is valid and `false` otherwise.
The argument `public_key` points to 132 bytes of valid memory, i.e., uint8_t[132].
The public key (x || y) is valid (with respect to SP 800-56A):
• the public key is not the “point at infinity”, represented as O.
• the affine x and y coordinates of the point represented by the public key are
in the range [0, p – 1] where p is the prime defining the finite field.
• y^2 = x^3 + ax + b where a and b are the coefficients of the curve equation.
The last extract is taken from: https://neilmadden.blog/2017/05/17/so-how-do-you-validate-nist-ecdh-public-keys/
*/
bool
Hacl_P521_validate_public_key(uint8_t *public_key)
{
uint64_t point_jac[27U] = { 0U };
uint64_t p_aff[18U] = { 0U };
uint8_t *p_x = public_key;
uint8_t *p_y = public_key + 66U;
uint64_t *bn_p_x = p_aff;
uint64_t *bn_p_y = p_aff + 9U;
bn_from_bytes_be(bn_p_x, p_x);
bn_from_bytes_be(bn_p_y, p_y);
uint64_t *px0 = p_aff;
uint64_t *py0 = p_aff + 9U;
uint64_t lessX = bn_is_lt_prime_mask(px0);
uint64_t lessY = bn_is_lt_prime_mask(py0);
uint64_t res0 = lessX & lessY;
bool is_xy_valid = res0 == 0xFFFFFFFFFFFFFFFFULL;
bool res;
if (!is_xy_valid) {
res = false;
} else {
uint64_t rp[9U] = { 0U };
uint64_t tx[9U] = { 0U };
uint64_t ty[9U] = { 0U };
uint64_t *px = p_aff;
uint64_t *py = p_aff + 9U;
to_mont(tx, px);
to_mont(ty, py);
uint64_t tmp[9U] = { 0U };
fsqr0(rp, tx);
fmul0(rp, rp, tx);
p521_make_a_coeff(tmp);
fmul0(tmp, tmp, tx);
fadd0(rp, tmp, rp);
p521_make_b_coeff(tmp);
fadd0(rp, tmp, rp);
fsqr0(ty, ty);
uint64_t r = bn_is_eq_mask(ty, rp);
uint64_t r0 = r;
bool r1 = r0 == 0xFFFFFFFFFFFFFFFFULL;
res = r1;
}
if (res) {
uint64_t *px = p_aff;
uint64_t *py = p_aff + 9U;
uint64_t *rx = point_jac;
uint64_t *ry = point_jac + 9U;
uint64_t *rz = point_jac + 18U;
to_mont(rx, px);
to_mont(ry, py);
p521_make_fone(rz);
}
bool res1 = res;
return res1;
}
/**
Private key validation.
The function returns `true` if a private key is valid and `false` otherwise.
The argument `private_key` points to 66 bytes of valid memory, i.e., uint8_t[66].
The private key is valid:
• 0 < `private_key` < the order of the curve
*/
bool
Hacl_P521_validate_private_key(uint8_t *private_key)
{
uint64_t bn_sk[9U] = { 0U };
bn_from_bytes_be(bn_sk, private_key);
uint64_t tmp[9U] = { 0U };
p521_make_order(tmp);
uint64_t c = bn_sub(tmp, bn_sk, tmp);
uint64_t is_lt_order = FStar_UInt64_gte_mask(c, 0ULL) & ~FStar_UInt64_eq_mask(c, 0ULL);
uint64_t bn_zero[9U] = { 0U };
uint64_t res = bn_is_eq_mask(bn_sk, bn_zero);
uint64_t is_eq_zero = res;
uint64_t res0 = is_lt_order & ~is_eq_zero;
return res0 == 0xFFFFFFFFFFFFFFFFULL;
}
/*******************************************************************************
Parsing and Serializing public keys.
A public key is a point (x, y) on the P-521 NIST curve.
The point can be represented in the following three ways.
• raw = [ x || y ], 132 bytes
• uncompressed = [ 0x04 || x || y ], 133 bytes
• compressed = [ (0x02 for even `y` and 0x03 for odd `y`) || x ], 33 bytes
*******************************************************************************/
/**
Convert a public key from uncompressed to its raw form.
The function returns `true` for successful conversion of a public key and `false` otherwise.
The outparam `pk_raw` points to 132 bytes of valid memory, i.e., uint8_t[132].
The argument `pk` points to 133 bytes of valid memory, i.e., uint8_t[133].
The function DOESN'T check whether (x, y) is a valid point.
*/
bool
Hacl_P521_uncompressed_to_raw(uint8_t *pk, uint8_t *pk_raw)
{
uint8_t pk0 = pk[0U];
if (pk0 != 0x04U) {
return false;
}
memcpy(pk_raw, pk + 1U, 132U * sizeof(uint8_t));
return true;
}
/**
Convert a public key from compressed to its raw form.
The function returns `true` for successful conversion of a public key and `false` otherwise.
The outparam `pk_raw` points to 132 bytes of valid memory, i.e., uint8_t[132].
The argument `pk` points to 33 bytes of valid memory, i.e., uint8_t[33].
The function also checks whether (x, y) is a valid point.
*/
bool
Hacl_P521_compressed_to_raw(uint8_t *pk, uint8_t *pk_raw)
{
uint64_t xa[9U] = { 0U };
uint64_t ya[9U] = { 0U };
uint8_t *pk_xb = pk + 1U;
uint8_t s0 = pk[0U];
uint8_t s01 = s0;
bool b;
if (!(s01 == 0x02U || s01 == 0x03U)) {
b = false;
} else {
uint8_t *xb = pk + 1U;
bn_from_bytes_be(xa, xb);
uint64_t is_x_valid = bn_is_lt_prime_mask(xa);
bool is_x_valid1 = is_x_valid == 0xFFFFFFFFFFFFFFFFULL;
bool is_y_odd = s01 == 0x03U;
if (!is_x_valid1) {
b = false;
} else {
uint64_t y2M[9U] = { 0U };
uint64_t xM[9U] = { 0U };
uint64_t yM[9U] = { 0U };
to_mont(xM, xa);
uint64_t tmp[9U] = { 0U };
fsqr0(y2M, xM);
fmul0(y2M, y2M, xM);
p521_make_a_coeff(tmp);
fmul0(tmp, tmp, xM);
fadd0(y2M, tmp, y2M);
p521_make_b_coeff(tmp);
fadd0(y2M, tmp, y2M);
p521_fsqrt(yM, y2M);
from_mont(ya, yM);
fsqr0(yM, yM);
uint64_t r = bn_is_eq_mask(yM, y2M);
uint64_t r0 = r;
bool is_y_valid = r0 == 0xFFFFFFFFFFFFFFFFULL;
bool is_y_valid0 = is_y_valid;
if (!is_y_valid0) {
b = false;
} else {
uint64_t is_y_odd1 = ya[0U] & 1ULL;
bool is_y_odd2 = is_y_odd1 == 1ULL;
uint64_t zero[9U] = { 0U };
if (is_y_odd2 != is_y_odd) {
fsub0(ya, zero, ya);
}
b = true;
}
}
}
if (b) {
memcpy(pk_raw, pk_xb, 66U * sizeof(uint8_t));
bn_to_bytes_be(pk_raw + 66U, ya);
}
return b;
}
/**
Convert a public key from raw to its uncompressed form.
The outparam `pk` points to 133 bytes of valid memory, i.e., uint8_t[133].
The argument `pk_raw` points to 132 bytes of valid memory, i.e., uint8_t[132].
The function DOESN'T check whether (x, y) is a valid point.
*/
void
Hacl_P521_raw_to_uncompressed(uint8_t *pk_raw, uint8_t *pk)
{
pk[0U] = 0x04U;
memcpy(pk + 1U, pk_raw, 132U * sizeof(uint8_t));
}
/**
Convert a public key from raw to its compressed form.
The outparam `pk` points to 33 bytes of valid memory, i.e., uint8_t[33].
The argument `pk_raw` points to 132 bytes of valid memory, i.e., uint8_t[132].
The function DOESN'T check whether (x, y) is a valid point.
*/
void
Hacl_P521_raw_to_compressed(uint8_t *pk_raw, uint8_t *pk)
{
uint8_t *pk_x = pk_raw;
uint8_t *pk_y = pk_raw + 66U;
uint64_t bn_f[9U] = { 0U };
bn_from_bytes_be(bn_f, pk_y);
uint64_t is_odd_f = bn_f[0U] & 1ULL;
pk[0U] = (uint32_t)(uint8_t)is_odd_f + 0x02U;
memcpy(pk + 1U, pk_x, 66U * sizeof(uint8_t));
}
/******************/
/* ECDH agreement */
/******************/
/**
Compute the public key from the private key.
The function returns `true` if a private key is valid and `false` otherwise.
The outparam `public_key` points to 132 bytes of valid memory, i.e., uint8_t[132].
The argument `private_key` points to 66 bytes of valid memory, i.e., uint8_t[66].
The private key is valid:
• 0 < `private_key` < the order of the curve.
*/
bool
Hacl_P521_dh_initiator(uint8_t *public_key, uint8_t *private_key)
{
uint64_t tmp[36U] = { 0U };
uint64_t *sk = tmp;
uint64_t *pk = tmp + 9U;
uint64_t is_sk_valid = load_qelem_conditional(sk, private_key);
point_mul_g(pk, sk);
uint64_t aff_p[18U] = { 0U };
uint64_t zinv[9U] = { 0U };
uint64_t *px = pk;
uint64_t *py0 = pk + 9U;
uint64_t *pz = pk + 18U;
uint64_t *x = aff_p;
uint64_t *y = aff_p + 9U;
p521_finv(zinv, pz);
fmul0(x, px, zinv);
fmul0(y, py0, zinv);
from_mont(x, x);
from_mont(y, y);
uint64_t *px0 = aff_p;
uint64_t *py = aff_p + 9U;
bn_to_bytes_be(public_key, px0);
bn_to_bytes_be(public_key + 66U, py);
return is_sk_valid == 0xFFFFFFFFFFFFFFFFULL;
}
/**
Execute the diffie-hellmann key exchange.
The function returns `true` for successful creation of an ECDH shared secret and
`false` otherwise.
The outparam `shared_secret` points to 132 bytes of valid memory, i.e., uint8_t[132].
The argument `their_pubkey` points to 132 bytes of valid memory, i.e., uint8_t[132].
The argument `private_key` points to 66 bytes of valid memory, i.e., uint8_t[66].
The function also checks whether `private_key` and `their_pubkey` are valid.
*/
bool
Hacl_P521_dh_responder(uint8_t *shared_secret, uint8_t *their_pubkey, uint8_t *private_key)
{
uint64_t tmp[264U] = { 0U };
uint64_t *sk = tmp;
uint64_t *pk = tmp + 9U;
uint64_t p_aff[18U] = { 0U };
uint8_t *p_x = their_pubkey;
uint8_t *p_y = their_pubkey + 66U;
uint64_t *bn_p_x = p_aff;
uint64_t *bn_p_y = p_aff + 9U;
bn_from_bytes_be(bn_p_x, p_x);
bn_from_bytes_be(bn_p_y, p_y);
uint64_t *px0 = p_aff;
uint64_t *py0 = p_aff + 9U;
uint64_t lessX = bn_is_lt_prime_mask(px0);
uint64_t lessY = bn_is_lt_prime_mask(py0);
uint64_t res0 = lessX & lessY;
bool is_xy_valid = res0 == 0xFFFFFFFFFFFFFFFFULL;
bool res;
if (!is_xy_valid) {
res = false;
} else {
uint64_t rp[9U] = { 0U };
uint64_t tx[9U] = { 0U };
uint64_t ty[9U] = { 0U };
uint64_t *px = p_aff;
uint64_t *py = p_aff + 9U;
to_mont(tx, px);
to_mont(ty, py);
uint64_t tmp1[9U] = { 0U };
fsqr0(rp, tx);
fmul0(rp, rp, tx);
p521_make_a_coeff(tmp1);
fmul0(tmp1, tmp1, tx);
fadd0(rp, tmp1, rp);
p521_make_b_coeff(tmp1);
fadd0(rp, tmp1, rp);
fsqr0(ty, ty);
uint64_t r = bn_is_eq_mask(ty, rp);
uint64_t r0 = r;
bool r1 = r0 == 0xFFFFFFFFFFFFFFFFULL;
res = r1;
}
if (res) {
uint64_t *px = p_aff;
uint64_t *py = p_aff + 9U;
uint64_t *rx = pk;
uint64_t *ry = pk + 9U;
uint64_t *rz = pk + 18U;
to_mont(rx, px);
to_mont(ry, py);
p521_make_fone(rz);
}
bool is_pk_valid = res;
uint64_t is_sk_valid = load_qelem_conditional(sk, private_key);
uint64_t ss_proj[27U] = { 0U };
if (is_pk_valid) {
point_mul(ss_proj, sk, pk);
uint64_t aff_p[18U] = { 0U };
uint64_t zinv[9U] = { 0U };
uint64_t *px = ss_proj;
uint64_t *py1 = ss_proj + 9U;
uint64_t *pz = ss_proj + 18U;
uint64_t *x = aff_p;
uint64_t *y = aff_p + 9U;
p521_finv(zinv, pz);
fmul0(x, px, zinv);
fmul0(y, py1, zinv);
from_mont(x, x);
from_mont(y, y);
uint64_t *px1 = aff_p;
uint64_t *py = aff_p + 9U;
bn_to_bytes_be(shared_secret, px1);
bn_to_bytes_be(shared_secret + 66U, py);
}
return is_sk_valid == 0xFFFFFFFFFFFFFFFFULL && is_pk_valid;
}