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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 "internal/Hacl_Curve25519_51.h"
#include "internal/Hacl_Krmllib.h"
#include "internal/Hacl_Bignum25519_51.h"
static const uint8_t g25519[32U] = { (uint8_t)9U };
static void
point_add_and_double(uint64_t *q, uint64_t *p01_tmp1, FStar_UInt128_uint128 *tmp2)
{
uint64_t *nq = p01_tmp1;
uint64_t *nq_p1 = p01_tmp1 + (uint32_t)10U;
uint64_t *tmp1 = p01_tmp1 + (uint32_t)20U;
uint64_t *x1 = q;
uint64_t *x2 = nq;
uint64_t *z2 = nq + (uint32_t)5U;
uint64_t *z3 = nq_p1 + (uint32_t)5U;
uint64_t *a = tmp1;
uint64_t *b = tmp1 + (uint32_t)5U;
uint64_t *ab = tmp1;
uint64_t *dc = tmp1 + (uint32_t)10U;
Hacl_Impl_Curve25519_Field51_fadd(a, x2, z2);
Hacl_Impl_Curve25519_Field51_fsub(b, x2, z2);
uint64_t *x3 = nq_p1;
uint64_t *z31 = nq_p1 + (uint32_t)5U;
uint64_t *d0 = dc;
uint64_t *c0 = dc + (uint32_t)5U;
Hacl_Impl_Curve25519_Field51_fadd(c0, x3, z31);
Hacl_Impl_Curve25519_Field51_fsub(d0, x3, z31);
Hacl_Impl_Curve25519_Field51_fmul2(dc, dc, ab, tmp2);
Hacl_Impl_Curve25519_Field51_fadd(x3, d0, c0);
Hacl_Impl_Curve25519_Field51_fsub(z31, d0, c0);
uint64_t *a1 = tmp1;
uint64_t *b1 = tmp1 + (uint32_t)5U;
uint64_t *d = tmp1 + (uint32_t)10U;
uint64_t *c = tmp1 + (uint32_t)15U;
uint64_t *ab1 = tmp1;
uint64_t *dc1 = tmp1 + (uint32_t)10U;
Hacl_Impl_Curve25519_Field51_fsqr2(dc1, ab1, tmp2);
Hacl_Impl_Curve25519_Field51_fsqr2(nq_p1, nq_p1, tmp2);
a1[0U] = c[0U];
a1[1U] = c[1U];
a1[2U] = c[2U];
a1[3U] = c[3U];
a1[4U] = c[4U];
Hacl_Impl_Curve25519_Field51_fsub(c, d, c);
Hacl_Impl_Curve25519_Field51_fmul1(b1, c, (uint64_t)121665U);
Hacl_Impl_Curve25519_Field51_fadd(b1, b1, d);
Hacl_Impl_Curve25519_Field51_fmul2(nq, dc1, ab1, tmp2);
Hacl_Impl_Curve25519_Field51_fmul(z3, z3, x1, tmp2);
}
static void
point_double(uint64_t *nq, uint64_t *tmp1, FStar_UInt128_uint128 *tmp2)
{
uint64_t *x2 = nq;
uint64_t *z2 = nq + (uint32_t)5U;
uint64_t *a = tmp1;
uint64_t *b = tmp1 + (uint32_t)5U;
uint64_t *d = tmp1 + (uint32_t)10U;
uint64_t *c = tmp1 + (uint32_t)15U;
uint64_t *ab = tmp1;
uint64_t *dc = tmp1 + (uint32_t)10U;
Hacl_Impl_Curve25519_Field51_fadd(a, x2, z2);
Hacl_Impl_Curve25519_Field51_fsub(b, x2, z2);
Hacl_Impl_Curve25519_Field51_fsqr2(dc, ab, tmp2);
a[0U] = c[0U];
a[1U] = c[1U];
a[2U] = c[2U];
a[3U] = c[3U];
a[4U] = c[4U];
Hacl_Impl_Curve25519_Field51_fsub(c, d, c);
Hacl_Impl_Curve25519_Field51_fmul1(b, c, (uint64_t)121665U);
Hacl_Impl_Curve25519_Field51_fadd(b, b, d);
Hacl_Impl_Curve25519_Field51_fmul2(nq, dc, ab, tmp2);
}
static void
montgomery_ladder(uint64_t *out, uint8_t *key, uint64_t *init)
{
FStar_UInt128_uint128 tmp2[10U];
for (uint32_t _i = 0U; _i < (uint32_t)10U; ++_i)
tmp2[_i] = FStar_UInt128_uint64_to_uint128((uint64_t)0U);
uint64_t p01_tmp1_swap[41U] = { 0U };
uint64_t *p0 = p01_tmp1_swap;
uint64_t *p01 = p01_tmp1_swap;
uint64_t *p03 = p01;
uint64_t *p11 = p01 + (uint32_t)10U;
memcpy(p11, init, (uint32_t)10U * sizeof(uint64_t));
uint64_t *x0 = p03;
uint64_t *z0 = p03 + (uint32_t)5U;
x0[0U] = (uint64_t)1U;
x0[1U] = (uint64_t)0U;
x0[2U] = (uint64_t)0U;
x0[3U] = (uint64_t)0U;
x0[4U] = (uint64_t)0U;
z0[0U] = (uint64_t)0U;
z0[1U] = (uint64_t)0U;
z0[2U] = (uint64_t)0U;
z0[3U] = (uint64_t)0U;
z0[4U] = (uint64_t)0U;
uint64_t *p01_tmp1 = p01_tmp1_swap;
uint64_t *p01_tmp11 = p01_tmp1_swap;
uint64_t *nq1 = p01_tmp1_swap;
uint64_t *nq_p11 = p01_tmp1_swap + (uint32_t)10U;
uint64_t *swap = p01_tmp1_swap + (uint32_t)40U;
Hacl_Impl_Curve25519_Field51_cswap2((uint64_t)1U, nq1, nq_p11);
point_add_and_double(init, p01_tmp11, tmp2);
swap[0U] = (uint64_t)1U;
for (uint32_t i = (uint32_t)0U; i < (uint32_t)251U; i++) {
uint64_t *p01_tmp12 = p01_tmp1_swap;
uint64_t *swap1 = p01_tmp1_swap + (uint32_t)40U;
uint64_t *nq2 = p01_tmp12;
uint64_t *nq_p12 = p01_tmp12 + (uint32_t)10U;
uint64_t
bit =
(uint64_t)(key[((uint32_t)253U - i) / (uint32_t)8U] >> ((uint32_t)253U - i) % (uint32_t)8U & (uint8_t)1U);
uint64_t sw = swap1[0U] ^ bit;
Hacl_Impl_Curve25519_Field51_cswap2(sw, nq2, nq_p12);
point_add_and_double(init, p01_tmp12, tmp2);
swap1[0U] = bit;
}
uint64_t sw = swap[0U];
Hacl_Impl_Curve25519_Field51_cswap2(sw, nq1, nq_p11);
uint64_t *nq10 = p01_tmp1;
uint64_t *tmp1 = p01_tmp1 + (uint32_t)20U;
point_double(nq10, tmp1, tmp2);
point_double(nq10, tmp1, tmp2);
point_double(nq10, tmp1, tmp2);
memcpy(out, p0, (uint32_t)10U * sizeof(uint64_t));
}
void
Hacl_Curve25519_51_fsquare_times(
uint64_t *o,
uint64_t *inp,
FStar_UInt128_uint128 *tmp,
uint32_t n)
{
Hacl_Impl_Curve25519_Field51_fsqr(o, inp, tmp);
for (uint32_t i = (uint32_t)0U; i < n - (uint32_t)1U; i++) {
Hacl_Impl_Curve25519_Field51_fsqr(o, o, tmp);
}
}
void
Hacl_Curve25519_51_finv(uint64_t *o, uint64_t *i, FStar_UInt128_uint128 *tmp)
{
uint64_t t1[20U] = { 0U };
uint64_t *a1 = t1;
uint64_t *b1 = t1 + (uint32_t)5U;
uint64_t *t010 = t1 + (uint32_t)15U;
FStar_UInt128_uint128 *tmp10 = tmp;
Hacl_Curve25519_51_fsquare_times(a1, i, tmp10, (uint32_t)1U);
Hacl_Curve25519_51_fsquare_times(t010, a1, tmp10, (uint32_t)2U);
Hacl_Impl_Curve25519_Field51_fmul(b1, t010, i, tmp);
Hacl_Impl_Curve25519_Field51_fmul(a1, b1, a1, tmp);
Hacl_Curve25519_51_fsquare_times(t010, a1, tmp10, (uint32_t)1U);
Hacl_Impl_Curve25519_Field51_fmul(b1, t010, b1, tmp);
Hacl_Curve25519_51_fsquare_times(t010, b1, tmp10, (uint32_t)5U);
Hacl_Impl_Curve25519_Field51_fmul(b1, t010, b1, tmp);
uint64_t *b10 = t1 + (uint32_t)5U;
uint64_t *c10 = t1 + (uint32_t)10U;
uint64_t *t011 = t1 + (uint32_t)15U;
FStar_UInt128_uint128 *tmp11 = tmp;
Hacl_Curve25519_51_fsquare_times(t011, b10, tmp11, (uint32_t)10U);
Hacl_Impl_Curve25519_Field51_fmul(c10, t011, b10, tmp);
Hacl_Curve25519_51_fsquare_times(t011, c10, tmp11, (uint32_t)20U);
Hacl_Impl_Curve25519_Field51_fmul(t011, t011, c10, tmp);
Hacl_Curve25519_51_fsquare_times(t011, t011, tmp11, (uint32_t)10U);
Hacl_Impl_Curve25519_Field51_fmul(b10, t011, b10, tmp);
Hacl_Curve25519_51_fsquare_times(t011, b10, tmp11, (uint32_t)50U);
Hacl_Impl_Curve25519_Field51_fmul(c10, t011, b10, tmp);
uint64_t *b11 = t1 + (uint32_t)5U;
uint64_t *c1 = t1 + (uint32_t)10U;
uint64_t *t01 = t1 + (uint32_t)15U;
FStar_UInt128_uint128 *tmp1 = tmp;
Hacl_Curve25519_51_fsquare_times(t01, c1, tmp1, (uint32_t)100U);
Hacl_Impl_Curve25519_Field51_fmul(t01, t01, c1, tmp);
Hacl_Curve25519_51_fsquare_times(t01, t01, tmp1, (uint32_t)50U);
Hacl_Impl_Curve25519_Field51_fmul(t01, t01, b11, tmp);
Hacl_Curve25519_51_fsquare_times(t01, t01, tmp1, (uint32_t)5U);
uint64_t *a = t1;
uint64_t *t0 = t1 + (uint32_t)15U;
Hacl_Impl_Curve25519_Field51_fmul(o, t0, a, tmp);
}
static void
encode_point(uint8_t *o, uint64_t *i)
{
uint64_t *x = i;
uint64_t *z = i + (uint32_t)5U;
uint64_t tmp[5U] = { 0U };
uint64_t u64s[4U] = { 0U };
FStar_UInt128_uint128 tmp_w[10U];
for (uint32_t _i = 0U; _i < (uint32_t)10U; ++_i)
tmp_w[_i] = FStar_UInt128_uint64_to_uint128((uint64_t)0U);
Hacl_Curve25519_51_finv(tmp, z, tmp_w);
Hacl_Impl_Curve25519_Field51_fmul(tmp, tmp, x, tmp_w);
Hacl_Impl_Curve25519_Field51_store_felem(u64s, tmp);
KRML_MAYBE_FOR4(i0,
(uint32_t)0U,
(uint32_t)4U,
(uint32_t)1U,
store64_le(o + i0 * (uint32_t)8U, u64s[i0]););
}
/**
Compute the scalar multiple of a point.
@param out Pointer to 32 bytes of memory, allocated by the caller, where the resulting point is written to.
@param priv Pointer to 32 bytes of memory where the secret/private key is read from.
@param pub Pointer to 32 bytes of memory where the public point is read from.
*/
void
Hacl_Curve25519_51_scalarmult(uint8_t *out, uint8_t *priv, uint8_t *pub)
{
uint64_t init[10U] = { 0U };
uint64_t tmp[4U] = { 0U };
KRML_MAYBE_FOR4(i,
(uint32_t)0U,
(uint32_t)4U,
(uint32_t)1U,
uint64_t *os = tmp;
uint8_t *bj = pub + i * (uint32_t)8U;
uint64_t u = load64_le(bj);
uint64_t r = u;
uint64_t x = r;
os[i] = x;);
uint64_t tmp3 = tmp[3U];
tmp[3U] = tmp3 & (uint64_t)0x7fffffffffffffffU;
uint64_t *x = init;
uint64_t *z = init + (uint32_t)5U;
z[0U] = (uint64_t)1U;
z[1U] = (uint64_t)0U;
z[2U] = (uint64_t)0U;
z[3U] = (uint64_t)0U;
z[4U] = (uint64_t)0U;
uint64_t f0l = tmp[0U] & (uint64_t)0x7ffffffffffffU;
uint64_t f0h = tmp[0U] >> (uint32_t)51U;
uint64_t f1l = (tmp[1U] & (uint64_t)0x3fffffffffU) << (uint32_t)13U;
uint64_t f1h = tmp[1U] >> (uint32_t)38U;
uint64_t f2l = (tmp[2U] & (uint64_t)0x1ffffffU) << (uint32_t)26U;
uint64_t f2h = tmp[2U] >> (uint32_t)25U;
uint64_t f3l = (tmp[3U] & (uint64_t)0xfffU) << (uint32_t)39U;
uint64_t f3h = tmp[3U] >> (uint32_t)12U;
x[0U] = f0l;
x[1U] = f0h | f1l;
x[2U] = f1h | f2l;
x[3U] = f2h | f3l;
x[4U] = f3h;
montgomery_ladder(init, priv, init);
encode_point(out, init);
}
/**
Calculate a public point from a secret/private key.
This computes a scalar multiplication of the secret/private key with the curve's basepoint.
@param pub Pointer to 32 bytes of memory, allocated by the caller, where the resulting point is written to.
@param priv Pointer to 32 bytes of memory where the secret/private key is read from.
*/
void
Hacl_Curve25519_51_secret_to_public(uint8_t *pub, uint8_t *priv)
{
uint8_t basepoint[32U] = { 0U };
for (uint32_t i = (uint32_t)0U; i < (uint32_t)32U; i++) {
uint8_t *os = basepoint;
uint8_t x = g25519[i];
os[i] = x;
}
Hacl_Curve25519_51_scalarmult(pub, priv, basepoint);
}
/**
Execute the diffie-hellmann key exchange.
@param out Pointer to 32 bytes of memory, allocated by the caller, where the resulting point is written to.
@param priv Pointer to 32 bytes of memory where **our** secret/private key is read from.
@param pub Pointer to 32 bytes of memory where **their** public point is read from.
*/
bool
Hacl_Curve25519_51_ecdh(uint8_t *out, uint8_t *priv, uint8_t *pub)
{
uint8_t zeros[32U] = { 0U };
Hacl_Curve25519_51_scalarmult(out, priv, pub);
uint8_t res = (uint8_t)255U;
for (uint32_t i = (uint32_t)0U; i < (uint32_t)32U; i++) {
uint8_t uu____0 = FStar_UInt8_eq_mask(out[i], zeros[i]);
res = uu____0 & res;
}
uint8_t z = res;
bool r = z == (uint8_t)255U;
return !r;
}