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/* Copyright (c) 2014, Intel Corporation.
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
/* Developers and authors:
* Shay Gueron (1, 2), and Vlad Krasnov (1)
* (1) Intel Corporation, Israel Development Center
* (2) University of Haifa
* Reference:
* Shay Gueron and Vlad Krasnov
* "Fast Prime Field Elliptic Curve Cryptography with 256 Bit Primes"
* http://eprint.iacr.org/2013/816 */
#include "ecp_nistz.h"
#if defined(__GNUC__)
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wsign-conversion"
#endif
/* Avoid -Wmissing-prototypes warnings. */
void GFp_nistz384_point_mul(P384_POINT *r, const BN_ULONG p_scalar[P384_LIMBS],
const BN_ULONG p_x[P384_LIMBS],
const BN_ULONG p_y[P384_LIMBS]);
static BN_ULONG is_zero(const BN_ULONG a[P384_LIMBS]) {
BN_ULONG acc = 0;
for (size_t i = 0; i < P384_LIMBS; ++i) {
acc |= a[i];
}
return constant_time_is_zero_w(acc);
}
/* Point double: r = 2*a */
void GFp_nistz384_point_double(P384_POINT *r, const P384_POINT *a) {
BN_ULONG S[P384_LIMBS];
BN_ULONG M[P384_LIMBS];
BN_ULONG Zsqr[P384_LIMBS];
BN_ULONG tmp0[P384_LIMBS];
const BN_ULONG *in_x = a->X;
const BN_ULONG *in_y = a->Y;
const BN_ULONG *in_z = a->Z;
BN_ULONG *res_x = r->X;
BN_ULONG *res_y = r->Y;
BN_ULONG *res_z = r->Z;
elem_mul_by_2(S, in_y);
elem_sqr_mont(Zsqr, in_z);
elem_sqr_mont(S, S);
elem_mul_mont(res_z, in_z, in_y);
elem_mul_by_2(res_z, res_z);
elem_add(M, in_x, Zsqr);
elem_sub(Zsqr, in_x, Zsqr);
elem_sqr_mont(res_y, S);
elem_div_by_2(res_y, res_y);
elem_mul_mont(M, M, Zsqr);
elem_mul_by_3(M, M);
elem_mul_mont(S, S, in_x);
elem_mul_by_2(tmp0, S);
elem_sqr_mont(res_x, M);
elem_sub(res_x, res_x, tmp0);
elem_sub(S, S, res_x);
elem_mul_mont(S, S, M);
elem_sub(res_y, S, res_y);
}
/* Point addition: r = a+b */
void GFp_nistz384_point_add(P384_POINT *r, const P384_POINT *a,
const P384_POINT *b) {
BN_ULONG U2[P384_LIMBS], S2[P384_LIMBS];
BN_ULONG U1[P384_LIMBS], S1[P384_LIMBS];
BN_ULONG Z1sqr[P384_LIMBS];
BN_ULONG Z2sqr[P384_LIMBS];
BN_ULONG H[P384_LIMBS], R[P384_LIMBS];
BN_ULONG Hsqr[P384_LIMBS];
BN_ULONG Rsqr[P384_LIMBS];
BN_ULONG Hcub[P384_LIMBS];
BN_ULONG res_x[P384_LIMBS];
BN_ULONG res_y[P384_LIMBS];
BN_ULONG res_z[P384_LIMBS];
const BN_ULONG *in1_x = a->X;
const BN_ULONG *in1_y = a->Y;
const BN_ULONG *in1_z = a->Z;
const BN_ULONG *in2_x = b->X;
const BN_ULONG *in2_y = b->Y;
const BN_ULONG *in2_z = b->Z;
BN_ULONG in1infty = is_zero(a->Z);
BN_ULONG in2infty = is_zero(b->Z);
elem_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
elem_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
elem_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
elem_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
elem_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
elem_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
elem_sub(R, S2, S1); /* R = S2 - S1 */
elem_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
elem_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
elem_sub(H, U2, U1); /* H = U2 - U1 */
/* This should not happen during sign/ecdh,
* so no constant time violation */
if (is_equal(U1, U2) && !in1infty && !in2infty) {
if (is_equal(S1, S2)) {
GFp_nistz384_point_double(r, a);
} else {
memset(r, 0, sizeof(*r));
}
return;
}
elem_sqr_mont(Rsqr, R); /* R^2 */
elem_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
elem_sqr_mont(Hsqr, H); /* H^2 */
elem_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
elem_mul_mont(Hcub, Hsqr, H); /* H^3 */
elem_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
elem_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
elem_sub(res_x, Rsqr, Hsqr);
elem_sub(res_x, res_x, Hcub);
elem_sub(res_y, U2, res_x);
elem_mul_mont(S2, S1, Hcub);
elem_mul_mont(res_y, R, res_y);
elem_sub(res_y, res_y, S2);
copy_conditional(res_x, in2_x, in1infty);
copy_conditional(res_y, in2_y, in1infty);
copy_conditional(res_z, in2_z, in1infty);
copy_conditional(res_x, in1_x, in2infty);
copy_conditional(res_y, in1_y, in2infty);
copy_conditional(res_z, in1_z, in2infty);
limbs_copy(r->X, res_x, P384_LIMBS);
limbs_copy(r->Y, res_y, P384_LIMBS);
limbs_copy(r->Z, res_z, P384_LIMBS);
}
static void add_precomputed_w5(P384_POINT *r, unsigned wvalue,
const P384_POINT table[16]) {
BN_ULONG recoded_is_negative;
unsigned int recoded;
booth_recode(&recoded_is_negative, &recoded, wvalue, 5);
alignas(64) P384_POINT h;
gfp_p384_point_select_w5(&h, table, recoded);
alignas(64) BN_ULONG tmp[P384_LIMBS];
GFp_p384_elem_neg(tmp, h.Y);
copy_conditional(h.Y, tmp, recoded_is_negative);
GFp_nistz384_point_add(r, r, &h);
}
/* r = p * p_scalar */
void GFp_nistz384_point_mul(P384_POINT *r, const BN_ULONG p_scalar[P384_LIMBS],
const BN_ULONG p_x[P384_LIMBS],
const BN_ULONG p_y[P384_LIMBS]) {
static const unsigned kWindowSize = 5;
static const unsigned kMask = (1 << (5 /* kWindowSize */ + 1)) - 1;
uint8_t p_str[(P384_LIMBS * sizeof(Limb)) + 1];
gfp_little_endian_bytes_from_scalar(p_str, sizeof(p_str) / sizeof(p_str[0]),
p_scalar, P384_LIMBS);
/* A |P384_POINT| is (3 * 48) = 144 bytes, and the 64-byte alignment should
* add no more than 63 bytes of overhead. Thus, |table| should require
* ~2367 ((144 * 16) + 63) bytes of stack space. */
alignas(64) P384_POINT table[16];
/* table[0] is implicitly (0,0,0) (the point at infinity), therefore it is
* not stored. All other values are actually stored with an offset of -1 in
* table. */
P384_POINT *row = table;
limbs_copy(row[1 - 1].X, p_x, P384_LIMBS);
limbs_copy(row[1 - 1].Y, p_y, P384_LIMBS);
limbs_copy(row[1 - 1].Z, ONE, P384_LIMBS);
GFp_nistz384_point_double(&row[2 - 1], &row[1 - 1]);
GFp_nistz384_point_add(&row[3 - 1], &row[2 - 1], &row[1 - 1]);
GFp_nistz384_point_double(&row[4 - 1], &row[2 - 1]);
GFp_nistz384_point_double(&row[6 - 1], &row[3 - 1]);
GFp_nistz384_point_double(&row[8 - 1], &row[4 - 1]);
GFp_nistz384_point_double(&row[12 - 1], &row[6 - 1]);
GFp_nistz384_point_add(&row[5 - 1], &row[4 - 1], &row[1 - 1]);
GFp_nistz384_point_add(&row[7 - 1], &row[6 - 1], &row[1 - 1]);
GFp_nistz384_point_add(&row[9 - 1], &row[8 - 1], &row[1 - 1]);
GFp_nistz384_point_add(&row[13 - 1], &row[12 - 1], &row[1 - 1]);
GFp_nistz384_point_double(&row[14 - 1], &row[7 - 1]);
GFp_nistz384_point_double(&row[10 - 1], &row[5 - 1]);
GFp_nistz384_point_add(&row[15 - 1], &row[14 - 1], &row[1 - 1]);
GFp_nistz384_point_add(&row[11 - 1], &row[10 - 1], &row[1 - 1]);
GFp_nistz384_point_double(&row[16 - 1], &row[8 - 1]);
static const unsigned START_INDEX = 384 - 4;
unsigned index = START_INDEX;
BN_ULONG recoded_is_negative;
unsigned recoded;
unsigned wvalue = p_str[(index - 1) / 8];
wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
booth_recode(&recoded_is_negative, &recoded, wvalue, 5);
assert(!recoded_is_negative);
gfp_p384_point_select_w5(r, table, recoded);
while (index >= kWindowSize) {
if (index != START_INDEX) {
unsigned off = (index - 1) / 8;
wvalue = p_str[off] | p_str[off + 1] << 8;
wvalue = (wvalue >> ((index - 1) % 8)) & kMask;
add_precomputed_w5(r, wvalue, table);
}
index -= kWindowSize;
GFp_nistz384_point_double(r, r);
GFp_nistz384_point_double(r, r);
GFp_nistz384_point_double(r, r);
GFp_nistz384_point_double(r, r);
GFp_nistz384_point_double(r, r);
}
/* Final window */
wvalue = p_str[0];
wvalue = (wvalue << 1) & kMask;
add_precomputed_w5(r, wvalue, table);
}
#if defined(__GNUC__)
#pragma GCC diagnostic pop
#endif