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openssl1.0/crypto/ec/ecp_nistz256.c

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Imported Upstream version 1.0.2s
2019-08-09 10:00:55 +02:00
/******************************************************************************
* *
* Copyright 2014 Intel Corporation *
* *
* Licensed under the Apache License, Version 2.0 (the "License"); *
* you may not use this file except in compliance with the License. *
* You may obtain a copy of the License at *
* *
* http://www.apache.org/licenses/LICENSE-2.0 *
* *
* Unless required by applicable law or agreed to in writing, software *
* distributed under the License is distributed on an "AS IS" BASIS, *
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
* See the License for the specific language governing permissions and *
* limitations under the License. *
* *
******************************************************************************
* *
* Developers and authors: *
* Shay Gueron (1, 2), and Vlad Krasnov (1) *
* (1) Intel Corporation, Israel Development Center *
* (2) University of Haifa *
* Reference: *
* S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with *
* 256 Bit Primes" *
* *
******************************************************************************/
#include <string.h>
#include <openssl/bn.h>
#include <openssl/err.h>
#include <openssl/ec.h>
#include "cryptlib.h"
#include "ec_lcl.h"
#if BN_BITS2 != 64
# define TOBN(hi,lo) lo,hi
#else
# define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo)
#endif
#if defined(__GNUC__)
# define ALIGN32 __attribute((aligned(32)))
#elif defined(_MSC_VER)
# define ALIGN32 __declspec(align(32))
#else
# define ALIGN32
#endif
#define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N)
#define P256_LIMBS (256/BN_BITS2)
typedef unsigned short u16;
typedef struct {
BN_ULONG X[P256_LIMBS];
BN_ULONG Y[P256_LIMBS];
BN_ULONG Z[P256_LIMBS];
} P256_POINT;
typedef struct {
BN_ULONG X[P256_LIMBS];
BN_ULONG Y[P256_LIMBS];
} P256_POINT_AFFINE;
typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
/* structure for precomputed multiples of the generator */
typedef struct ec_pre_comp_st {
const EC_GROUP *group; /* Parent EC_GROUP object */
size_t w; /* Window size */
/*
* Constant time access to the X and Y coordinates of the pre-computed,
* generator multiplies, in the Montgomery domain. Pre-calculated
* multiplies are stored in affine form.
*/
PRECOMP256_ROW *precomp;
void *precomp_storage;
int references;
} EC_PRE_COMP;
/* Functions implemented in assembly */
/*
* Most of below mentioned functions *preserve* the property of inputs
* being fully reduced, i.e. being in [0, modulus) range. Simply put if
* inputs are fully reduced, then output is too. Note that reverse is
* not true, in sense that given partially reduced inputs output can be
* either, not unlikely reduced. And "most" in first sentence refers to
* the fact that given the calculations flow one can tolerate that
* addition, 1st function below, produces partially reduced result *if*
* multiplications by 2 and 3, which customarily use addition, fully
* reduce it. This effectively gives two options: a) addition produces
* fully reduced result [as long as inputs are, just like remaining
* functions]; b) addition is allowed to produce partially reduced
* result, but multiplications by 2 and 3 perform additional reduction
* step. Choice between the two can be platform-specific, but it was a)
* in all cases so far...
*/
/* Modular add: res = a+b mod P */
void ecp_nistz256_add(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS],
const BN_ULONG b[P256_LIMBS]);
/* Modular mul by 2: res = 2*a mod P */
void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS]);
/* Modular mul by 3: res = 3*a mod P */
void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS]);
/* Modular div by 2: res = a/2 mod P */
void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS]);
/* Modular sub: res = a-b mod P */
void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS],
const BN_ULONG b[P256_LIMBS]);
/* Modular neg: res = -a mod P */
void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
/* Montgomery mul: res = a*b*2^-256 mod P */
void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS],
const BN_ULONG b[P256_LIMBS]);
/* Montgomery sqr: res = a*a*2^-256 mod P */
void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS]);
/* Convert a number from Montgomery domain, by multiplying with 1 */
void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
const BN_ULONG in[P256_LIMBS]);
/* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
const BN_ULONG in[P256_LIMBS]);
/* Functions that perform constant time access to the precomputed tables */
void ecp_nistz256_select_w5(P256_POINT * val,
const P256_POINT * in_t, int index);
void ecp_nistz256_select_w7(P256_POINT_AFFINE * val,
const P256_POINT_AFFINE * in_t, int index);
/* One converted into the Montgomery domain */
static const BN_ULONG ONE[P256_LIMBS] = {
TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)
};
static void *ecp_nistz256_pre_comp_dup(void *);
static void ecp_nistz256_pre_comp_free(void *);
static void ecp_nistz256_pre_comp_clear_free(void *);
static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group);
/* Precomputed tables for the default generator */
#include "ecp_nistz256_table.c"
/* Recode window to a signed digit, see ecp_nistputil.c for details */
static unsigned int _booth_recode_w5(unsigned int in)
{
unsigned int s, d;
s = ~((in >> 5) - 1);
d = (1 << 6) - in - 1;
d = (d & s) | (in & ~s);
d = (d >> 1) + (d & 1);
return (d << 1) + (s & 1);
}
static unsigned int _booth_recode_w7(unsigned int in)
{
unsigned int s, d;
s = ~((in >> 7) - 1);
d = (1 << 8) - in - 1;
d = (d & s) | (in & ~s);
d = (d >> 1) + (d & 1);
return (d << 1) + (s & 1);
}
static void copy_conditional(BN_ULONG dst[P256_LIMBS],
const BN_ULONG src[P256_LIMBS], BN_ULONG move)
{
BN_ULONG mask1 = -move;
BN_ULONG mask2 = ~mask1;
dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
if (P256_LIMBS == 8) {
dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
}
}
static BN_ULONG is_zero(BN_ULONG in)
{
in |= (0 - in);
in = ~in;
in &= BN_MASK2;
in >>= BN_BITS2 - 1;
return in;
}
static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],
const BN_ULONG b[P256_LIMBS])
{
BN_ULONG res;
res = a[0] ^ b[0];
res |= a[1] ^ b[1];
res |= a[2] ^ b[2];
res |= a[3] ^ b[3];
if (P256_LIMBS == 8) {
res |= a[4] ^ b[4];
res |= a[5] ^ b[5];
res |= a[6] ^ b[6];
res |= a[7] ^ b[7];
}
return is_zero(res);
}
static BN_ULONG is_one(const BIGNUM *z)
{
BN_ULONG res = 0;
BN_ULONG *a = z->d;
if (z->top == (P256_LIMBS - P256_LIMBS / 8)) {
res = a[0] ^ ONE[0];
res |= a[1] ^ ONE[1];
res |= a[2] ^ ONE[2];
res |= a[3] ^ ONE[3];
if (P256_LIMBS == 8) {
res |= a[4] ^ ONE[4];
res |= a[5] ^ ONE[5];
res |= a[6] ^ ONE[6];
/*
* no check for a[7] (being zero) on 32-bit platforms,
* because value of "one" takes only 7 limbs.
*/
}
res = is_zero(res);
}
return res;
}
static int ecp_nistz256_set_words(BIGNUM *a, BN_ULONG words[P256_LIMBS])
{
if (bn_wexpand(a, P256_LIMBS) == NULL) {
ECerr(EC_F_ECP_NISTZ256_SET_WORDS, ERR_R_MALLOC_FAILURE);
return 0;
}
memcpy(a->d, words, sizeof(BN_ULONG) * P256_LIMBS);
a->top = P256_LIMBS;
bn_correct_top(a);
return 1;
}
#ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
void ecp_nistz256_point_add(P256_POINT *r,
const P256_POINT *a, const P256_POINT *b);
void ecp_nistz256_point_add_affine(P256_POINT *r,
const P256_POINT *a,
const P256_POINT_AFFINE *b);
#else
/* Point double: r = 2*a */
static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a)
{
BN_ULONG S[P256_LIMBS];
BN_ULONG M[P256_LIMBS];
BN_ULONG Zsqr[P256_LIMBS];
BN_ULONG tmp0[P256_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;
ecp_nistz256_mul_by_2(S, in_y);
ecp_nistz256_sqr_mont(Zsqr, in_z);
ecp_nistz256_sqr_mont(S, S);
ecp_nistz256_mul_mont(res_z, in_z, in_y);
ecp_nistz256_mul_by_2(res_z, res_z);
ecp_nistz256_add(M, in_x, Zsqr);
ecp_nistz256_sub(Zsqr, in_x, Zsqr);
ecp_nistz256_sqr_mont(res_y, S);
ecp_nistz256_div_by_2(res_y, res_y);
ecp_nistz256_mul_mont(M, M, Zsqr);
ecp_nistz256_mul_by_3(M, M);
ecp_nistz256_mul_mont(S, S, in_x);
ecp_nistz256_mul_by_2(tmp0, S);
ecp_nistz256_sqr_mont(res_x, M);
ecp_nistz256_sub(res_x, res_x, tmp0);
ecp_nistz256_sub(S, S, res_x);
ecp_nistz256_mul_mont(S, S, M);
ecp_nistz256_sub(res_y, S, res_y);
}
/* Point addition: r = a+b */
static void ecp_nistz256_point_add(P256_POINT *r,
const P256_POINT *a, const P256_POINT *b)
{
BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];
BN_ULONG Z1sqr[P256_LIMBS];
BN_ULONG Z2sqr[P256_LIMBS];
BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
BN_ULONG Hsqr[P256_LIMBS];
BN_ULONG Rsqr[P256_LIMBS];
BN_ULONG Hcub[P256_LIMBS];
BN_ULONG res_x[P256_LIMBS];
BN_ULONG res_y[P256_LIMBS];
BN_ULONG res_z[P256_LIMBS];
BN_ULONG in1infty, in2infty;
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;
/*
* Infinity in encoded as (,,0)
*/
in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
if (P256_LIMBS == 8)
in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[3]);
if (P256_LIMBS == 8)
in2infty |= (in2_z[4] | in2_z[5] | in2_z[6] | in2_z[7]);
in1infty = is_zero(in1infty);
in2infty = is_zero(in2infty);
ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */
ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
ecp_nistz256_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)) {
ecp_nistz256_point_double(r, a);
return;
} else {
memset(r, 0, sizeof(*r));
return;
}
}
ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
ecp_nistz256_sub(res_x, Rsqr, Hsqr);
ecp_nistz256_sub(res_x, res_x, Hcub);
ecp_nistz256_sub(res_y, U2, res_x);
ecp_nistz256_mul_mont(S2, S1, Hcub);
ecp_nistz256_mul_mont(res_y, R, res_y);
ecp_nistz256_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);
memcpy(r->X, res_x, sizeof(res_x));
memcpy(r->Y, res_y, sizeof(res_y));
memcpy(r->Z, res_z, sizeof(res_z));
}
/* Point addition when b is known to be affine: r = a+b */
static void ecp_nistz256_point_add_affine(P256_POINT *r,
const P256_POINT *a,
const P256_POINT_AFFINE *b)
{
BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
BN_ULONG Z1sqr[P256_LIMBS];
BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
BN_ULONG Hsqr[P256_LIMBS];
BN_ULONG Rsqr[P256_LIMBS];
BN_ULONG Hcub[P256_LIMBS];
BN_ULONG res_x[P256_LIMBS];
BN_ULONG res_y[P256_LIMBS];
BN_ULONG res_z[P256_LIMBS];
BN_ULONG in1infty, in2infty;
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;
/*
* Infinity in encoded as (,,0)
*/
in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
if (P256_LIMBS == 8)
in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
/*
* In affine representation we encode infinity as (0,0), which is
* not on the curve, so it is OK
*/
in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
if (P256_LIMBS == 8)
in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
in1infty = is_zero(in1infty);
in2infty = is_zero(in2infty);
ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
ecp_nistz256_sub(res_x, Rsqr, Hsqr);
ecp_nistz256_sub(res_x, res_x, Hcub);
ecp_nistz256_sub(H, U2, res_x);
ecp_nistz256_mul_mont(S2, in1_y, Hcub);
ecp_nistz256_mul_mont(H, H, R);
ecp_nistz256_sub(res_y, H, S2);
copy_conditional(res_x, in2_x, in1infty);
copy_conditional(res_x, in1_x, in2infty);
copy_conditional(res_y, in2_y, in1infty);
copy_conditional(res_y, in1_y, in2infty);
copy_conditional(res_z, ONE, in1infty);
copy_conditional(res_z, in1_z, in2infty);
memcpy(r->X, res_x, sizeof(res_x));
memcpy(r->Y, res_y, sizeof(res_y));
memcpy(r->Z, res_z, sizeof(res_z));
}
#endif
/* r = in^-1 mod p */
static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
const BN_ULONG in[P256_LIMBS])
{
/*
* The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
* ffffffff ffffffff We use FLT and used poly-2 as exponent
*/
BN_ULONG p2[P256_LIMBS];
BN_ULONG p4[P256_LIMBS];
BN_ULONG p8[P256_LIMBS];
BN_ULONG p16[P256_LIMBS];
BN_ULONG p32[P256_LIMBS];
BN_ULONG res[P256_LIMBS];
int i;
ecp_nistz256_sqr_mont(res, in);
ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
ecp_nistz256_sqr_mont(res, p2);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
ecp_nistz256_sqr_mont(res, p4);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
ecp_nistz256_sqr_mont(res, p8);
for (i = 0; i < 7; i++)
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
ecp_nistz256_sqr_mont(res, p16);
for (i = 0; i < 15; i++)
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
ecp_nistz256_sqr_mont(res, p32);
for (i = 0; i < 31; i++)
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(res, res, in);
for (i = 0; i < 32 * 4; i++)
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(res, res, p32);
for (i = 0; i < 32; i++)
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(res, res, p32);
for (i = 0; i < 16; i++)
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(res, res, p16);
for (i = 0; i < 8; i++)
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(res, res, p8);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(res, res, p4);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(res, res, p2);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_sqr_mont(res, res);
ecp_nistz256_mul_mont(res, res, in);
memcpy(r, res, sizeof(res));
}
/*
* ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
* returns one if it fits. Otherwise it returns zero.
*/
static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
const BIGNUM *in)
{
if (in->top > P256_LIMBS)
return 0;
memset(out, 0, sizeof(BN_ULONG) * P256_LIMBS);
memcpy(out, in->d, sizeof(BN_ULONG) * in->top);
return 1;
}
/* r = sum(scalar[i]*point[i]) */
static int ecp_nistz256_windowed_mul(const EC_GROUP *group,
P256_POINT *r,
const BIGNUM **scalar,
const EC_POINT **point,
int num, BN_CTX *ctx)
{
int i, j, ret = 0;
unsigned int index;
unsigned char (*p_str)[33] = NULL;
const unsigned int window_size = 5;
const unsigned int mask = (1 << (window_size + 1)) - 1;
unsigned int wvalue;
BN_ULONG tmp[P256_LIMBS];
ALIGN32 P256_POINT h;
const BIGNUM **scalars = NULL;
P256_POINT (*table)[16] = NULL;
void *table_storage = NULL;
if ((table_storage =
OPENSSL_malloc(num * 16 * sizeof(P256_POINT) + 64)) == NULL
|| (p_str =
OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
|| (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) {
ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE);
goto err;
} else {
table = (void *)ALIGNPTR(table_storage, 64);
}
for (i = 0; i < num; i++) {
P256_POINT *row = table[i];
/* This is an unusual input, we don't guarantee constant-timeness. */
if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
BIGNUM *mod;
if ((mod = BN_CTX_get(ctx)) == NULL)
goto err;
if (!BN_nnmod(mod, scalar[i], &group->order, ctx)) {
ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB);
goto err;
}
scalars[i] = mod;
} else
scalars[i] = scalar[i];
for (j = 0; j < scalars[i]->top * BN_BYTES; j += BN_BYTES) {
BN_ULONG d = scalars[i]->d[j / BN_BYTES];
p_str[i][j + 0] = d & 0xff;
p_str[i][j + 1] = (d >> 8) & 0xff;
p_str[i][j + 2] = (d >> 16) & 0xff;
p_str[i][j + 3] = (d >>= 24) & 0xff;
if (BN_BYTES == 8) {
d >>= 8;
p_str[i][j + 4] = d & 0xff;
p_str[i][j + 5] = (d >> 8) & 0xff;
p_str[i][j + 6] = (d >> 16) & 0xff;
p_str[i][j + 7] = (d >> 24) & 0xff;
}
}
for (; j < 33; j++)
p_str[i][j] = 0;
/* 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.
*/
if (!ecp_nistz256_bignum_to_field_elem(row[1 - 1].X, &point[i]->X)
|| !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Y, &point[i]->Y)
|| !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Z, &point[i]->Z)) {
ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, EC_R_COORDINATES_OUT_OF_RANGE);
goto err;
}
ecp_nistz256_point_double(&row[ 2 - 1], &row[ 1 - 1]);
ecp_nistz256_point_add (&row[ 3 - 1], &row[ 2 - 1], &row[1 - 1]);
ecp_nistz256_point_double(&row[ 4 - 1], &row[ 2 - 1]);
ecp_nistz256_point_double(&row[ 6 - 1], &row[ 3 - 1]);
ecp_nistz256_point_double(&row[ 8 - 1], &row[ 4 - 1]);
ecp_nistz256_point_double(&row[12 - 1], &row[ 6 - 1]);
ecp_nistz256_point_add (&row[ 5 - 1], &row[ 4 - 1], &row[1 - 1]);
ecp_nistz256_point_add (&row[ 7 - 1], &row[ 6 - 1], &row[1 - 1]);
ecp_nistz256_point_add (&row[ 9 - 1], &row[ 8 - 1], &row[1 - 1]);
ecp_nistz256_point_add (&row[13 - 1], &row[12 - 1], &row[1 - 1]);
ecp_nistz256_point_double(&row[14 - 1], &row[ 7 - 1]);
ecp_nistz256_point_double(&row[10 - 1], &row[ 5 - 1]);
ecp_nistz256_point_add (&row[15 - 1], &row[14 - 1], &row[1 - 1]);
ecp_nistz256_point_add (&row[11 - 1], &row[10 - 1], &row[1 - 1]);
ecp_nistz256_point_add (&row[16 - 1], &row[15 - 1], &row[1 - 1]);
}
index = 255;
wvalue = p_str[0][(index - 1) / 8];
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
ecp_nistz256_select_w5(r, table[0], _booth_recode_w5(wvalue) >> 1);
while (index >= 5) {
for (i = (index == 255 ? 1 : 0); i < num; i++) {
unsigned int off = (index - 1) / 8;
wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
wvalue = _booth_recode_w5(wvalue);
ecp_nistz256_select_w5(&h, table[i], wvalue >> 1);
ecp_nistz256_neg(tmp, h.Y);
copy_conditional(h.Y, tmp, (wvalue & 1));
ecp_nistz256_point_add(r, r, &h);
}
index -= window_size;
ecp_nistz256_point_double(r, r);
ecp_nistz256_point_double(r, r);
ecp_nistz256_point_double(r, r);
ecp_nistz256_point_double(r, r);
ecp_nistz256_point_double(r, r);
}
/* Final window */
for (i = 0; i < num; i++) {
wvalue = p_str[i][0];
wvalue = (wvalue << 1) & mask;
wvalue = _booth_recode_w5(wvalue);
ecp_nistz256_select_w5(&h, table[i], wvalue >> 1);
ecp_nistz256_neg(tmp, h.Y);
copy_conditional(h.Y, tmp, wvalue & 1);
ecp_nistz256_point_add(r, r, &h);
}
ret = 1;
err:
if (table_storage)
OPENSSL_free(table_storage);
if (p_str)
OPENSSL_free(p_str);
if (scalars)
OPENSSL_free(scalars);
return ret;
}
/* Coordinates of G, for which we have precomputed tables */
const static BN_ULONG def_xG[P256_LIMBS] = {
TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
};
const static BN_ULONG def_yG[P256_LIMBS] = {
TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
};
/*
* ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
* generator.
*/
static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
{
return (generator->X.top == P256_LIMBS) &&
(generator->Y.top == P256_LIMBS) &&
is_equal(generator->X.d, def_xG) &&
is_equal(generator->Y.d, def_yG) && is_one(&generator->Z);
}
static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
{
/*
* We precompute a table for a Booth encoded exponent (wNAF) based
* computation. Each table holds 64 values for safe access, with an
* implicit value of infinity at index zero. We use window of size 7, and
* therefore require ceil(256/7) = 37 tables.
*/
BIGNUM *order;
EC_POINT *P = NULL, *T = NULL;
const EC_POINT *generator;
EC_PRE_COMP *pre_comp;
BN_CTX *new_ctx = NULL;
int i, j, k, ret = 0;
size_t w;
PRECOMP256_ROW *preComputedTable = NULL;
unsigned char *precomp_storage = NULL;
/* if there is an old EC_PRE_COMP object, throw it away */
EC_EX_DATA_free_data(&group->extra_data, ecp_nistz256_pre_comp_dup,
ecp_nistz256_pre_comp_free,
ecp_nistz256_pre_comp_clear_free);
generator = EC_GROUP_get0_generator(group);
if (generator == NULL) {
ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR);
return 0;
}
if (ecp_nistz256_is_affine_G(generator)) {
/*
* No need to calculate tables for the standard generator because we
* have them statically.
*/
return 1;
}
if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
return 0;
if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL)
goto err;
}
BN_CTX_start(ctx);
order = BN_CTX_get(ctx);
if (order == NULL)
goto err;
if (!EC_GROUP_get_order(group, order, ctx))
goto err;
if (BN_is_zero(order)) {
ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER);
goto err;
}
w = 7;
if ((precomp_storage =
OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) {
ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE);
goto err;
} else {
preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
}
P = EC_POINT_new(group);
T = EC_POINT_new(group);
if (P == NULL || T == NULL)
goto err;
/*
* The zero entry is implicitly infinity, and we skip it, storing other
* values with -1 offset.
*/
if (!EC_POINT_copy(T, generator))
goto err;
for (k = 0; k < 64; k++) {
if (!EC_POINT_copy(P, T))
goto err;
for (j = 0; j < 37; j++) {
/*
* It would be faster to use EC_POINTs_make_affine and
* make multiple points affine at the same time.
*/
if (!EC_POINT_make_affine(group, P, ctx))
goto err;
if (!ecp_nistz256_bignum_to_field_elem(preComputedTable[j][k].X,
&P->X) ||
!ecp_nistz256_bignum_to_field_elem(preComputedTable[j][k].Y,
&P->Y)) {
ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE,
EC_R_COORDINATES_OUT_OF_RANGE);
goto err;
}
for (i = 0; i < 7; i++) {
if (!EC_POINT_dbl(group, P, P, ctx))
goto err;
}
}
if (!EC_POINT_add(group, T, T, generator, ctx))
goto err;
}
pre_comp->group = group;
pre_comp->w = w;
pre_comp->precomp = preComputedTable;
pre_comp->precomp_storage = precomp_storage;
precomp_storage = NULL;
if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
ecp_nistz256_pre_comp_dup,
ecp_nistz256_pre_comp_free,
ecp_nistz256_pre_comp_clear_free)) {
goto err;
}
pre_comp = NULL;
ret = 1;
err:
if (ctx != NULL)
BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
if (pre_comp)
ecp_nistz256_pre_comp_free(pre_comp);
if (precomp_storage)
OPENSSL_free(precomp_storage);
if (P)
EC_POINT_free(P);
if (T)
EC_POINT_free(T);
return ret;
}
/*
* Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great
* code processing 4 points in parallel, corresponding serial operation
* is several times slower, because it uses 29x29=58-bit multiplication
* as opposite to 64x64=128-bit in integer-only scalar case. As result
* it doesn't provide *significant* performance improvement. Note that
* just defining ECP_NISTZ256_AVX2 is not sufficient to make it work,
* you'd need to compile even asm/ecp_nistz256-avx.pl module.
*/
#if defined(ECP_NISTZ256_AVX2)
# if !(defined(__x86_64) || defined(__x86_64__)) || \
defined(_M_AMD64) || defined(_MX64)) || \
!(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
# undef ECP_NISTZ256_AVX2
# else
/* Constant time access, loading four values, from four consecutive tables */
void ecp_nistz256_avx2_select_w7(P256_POINT_AFFINE * val,
const P256_POINT_AFFINE * in_t, int index);
void ecp_nistz256_avx2_multi_select_w7(void *result, const void *in, int index0,
int index1, int index2, int index3);
void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in);
void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4);
void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4,
const void *Bx4);
void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4,
const void *Bx4);
void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4);
void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4);
void ecp_nistz256_avx2_set1(void *RESULTx4);
int ecp_nistz_avx2_eligible(void);
static void booth_recode_w7(unsigned char *sign,
unsigned char *digit, unsigned char in)
{
unsigned char s, d;
s = ~((in >> 7) - 1);
d = (1 << 8) - in - 1;
d = (d & s) | (in & ~s);
d = (d >> 1) + (d & 1);
*sign = s & 1;
*digit = d;
}
/*
* ecp_nistz256_avx2_mul_g performs multiplication by G, using only the
* precomputed table. It does 4 affine point additions in parallel,
* significantly speeding up point multiplication for a fixed value.
*/
static void ecp_nistz256_avx2_mul_g(P256_POINT *r,
unsigned char p_str[33],
const P256_POINT_AFFINE(*preComputedTable)[64])
{
const unsigned int window_size = 7;
const unsigned int mask = (1 << (window_size + 1)) - 1;
unsigned int wvalue;
/* Using 4 windows at a time */
unsigned char sign0, digit0;
unsigned char sign1, digit1;
unsigned char sign2, digit2;
unsigned char sign3, digit3;
unsigned int index = 0;
BN_ULONG tmp[P256_LIMBS];
int i;
ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 };
ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 };
ALIGN32 P256_POINT_AFFINE point_arr[P256_LIMBS];
ALIGN32 P256_POINT res_point_arr[P256_LIMBS];
/* Initial four windows */
wvalue = *((u16 *) & p_str[0]);
wvalue = (wvalue << 1) & mask;
index += window_size;
booth_recode_w7(&sign0, &digit0, wvalue);
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
index += window_size;
booth_recode_w7(&sign1, &digit1, wvalue);
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
index += window_size;
booth_recode_w7(&sign2, &digit2, wvalue);
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
index += window_size;
booth_recode_w7(&sign3, &digit3, wvalue);
ecp_nistz256_avx2_multi_select_w7(point_arr, preComputedTable[0],
digit0, digit1, digit2, digit3);
ecp_nistz256_neg(tmp, point_arr[0].Y);
copy_conditional(point_arr[0].Y, tmp, sign0);
ecp_nistz256_neg(tmp, point_arr[1].Y);
copy_conditional(point_arr[1].Y, tmp, sign1);
ecp_nistz256_neg(tmp, point_arr[2].Y);
copy_conditional(point_arr[2].Y, tmp, sign2);
ecp_nistz256_neg(tmp, point_arr[3].Y);
copy_conditional(point_arr[3].Y, tmp, sign3);
ecp_nistz256_avx2_transpose_convert(aX4, point_arr);
ecp_nistz256_avx2_to_mont(aX4, aX4);
ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]);
ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]);
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
index += window_size;
booth_recode_w7(&sign0, &digit0, wvalue);
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
index += window_size;
booth_recode_w7(&sign1, &digit1, wvalue);
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
index += window_size;
booth_recode_w7(&sign2, &digit2, wvalue);
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
index += window_size;
booth_recode_w7(&sign3, &digit3, wvalue);
ecp_nistz256_avx2_multi_select_w7(point_arr, preComputedTable[4 * 1],
digit0, digit1, digit2, digit3);
ecp_nistz256_neg(tmp, point_arr[0].Y);
copy_conditional(point_arr[0].Y, tmp, sign0);
ecp_nistz256_neg(tmp, point_arr[1].Y);
copy_conditional(point_arr[1].Y, tmp, sign1);
ecp_nistz256_neg(tmp, point_arr[2].Y);
copy_conditional(point_arr[2].Y, tmp, sign2);
ecp_nistz256_neg(tmp, point_arr[3].Y);
copy_conditional(point_arr[3].Y, tmp, sign3);
ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
ecp_nistz256_avx2_to_mont(bX4, bX4);
ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
/* Optimized when both inputs are affine */
ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4);
for (i = 2; i < 9; i++) {
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
index += window_size;
booth_recode_w7(&sign0, &digit0, wvalue);
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
index += window_size;
booth_recode_w7(&sign1, &digit1, wvalue);
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
index += window_size;
booth_recode_w7(&sign2, &digit2, wvalue);
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
index += window_size;
booth_recode_w7(&sign3, &digit3, wvalue);
ecp_nistz256_avx2_multi_select_w7(point_arr,
preComputedTable[4 * i],
digit0, digit1, digit2, digit3);
ecp_nistz256_neg(tmp, point_arr[0].Y);
copy_conditional(point_arr[0].Y, tmp, sign0);
ecp_nistz256_neg(tmp, point_arr[1].Y);
copy_conditional(point_arr[1].Y, tmp, sign1);
ecp_nistz256_neg(tmp, point_arr[2].Y);
copy_conditional(point_arr[2].Y, tmp, sign2);
ecp_nistz256_neg(tmp, point_arr[3].Y);
copy_conditional(point_arr[3].Y, tmp, sign3);
ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
ecp_nistz256_avx2_to_mont(bX4, bX4);
ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4);
}
ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]);
ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]);
ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]);
ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4);
/* Last window is performed serially */
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
booth_recode_w7(&sign0, &digit0, wvalue);
ecp_nistz256_avx2_select_w7((P256_POINT_AFFINE *) r,
preComputedTable[36], digit0);
ecp_nistz256_neg(tmp, r->Y);
copy_conditional(r->Y, tmp, sign0);
memcpy(r->Z, ONE, sizeof(ONE));
/* Sum the four windows */
ecp_nistz256_point_add(r, r, &res_point_arr[0]);
ecp_nistz256_point_add(r, r, &res_point_arr[1]);
ecp_nistz256_point_add(r, r, &res_point_arr[2]);
ecp_nistz256_point_add(r, r, &res_point_arr[3]);
}
# endif
#endif
static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
const P256_POINT_AFFINE *in,
BN_CTX *ctx)
{
BIGNUM x, y, z;
int ret = 0;
/*
* |const| qualifier omission is compensated by BN_FLG_STATIC_DATA
* flag, which effectively means "read-only data".
*/
x.d = (BN_ULONG *)in->X;
x.dmax = x.top = P256_LIMBS;
x.neg = 0;
x.flags = BN_FLG_STATIC_DATA;
y.d = (BN_ULONG *)in->Y;
y.dmax = y.top = P256_LIMBS;
y.neg = 0;
y.flags = BN_FLG_STATIC_DATA;
z.d = (BN_ULONG *)ONE;
z.dmax = z.top = P256_LIMBS;
z.neg = 0;
z.flags = BN_FLG_STATIC_DATA;
if ((ret = (BN_copy(&out->X, &x) != NULL))
&& (ret = (BN_copy(&out->Y, &y) != NULL))
&& (ret = (BN_copy(&out->Z, &z) != NULL)))
out->Z_is_one = 1;
return ret;
}
/* r = scalar*G + sum(scalars[i]*points[i]) */
static int ecp_nistz256_points_mul(const EC_GROUP *group,
EC_POINT *r,
const BIGNUM *scalar,
size_t num,
const EC_POINT *points[],
const BIGNUM *scalars[], BN_CTX *ctx)
{
int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
size_t j;
unsigned char p_str[33] = { 0 };
const PRECOMP256_ROW *preComputedTable = NULL;
const EC_PRE_COMP *pre_comp = NULL;
const EC_POINT *generator = NULL;
unsigned int index = 0;
BN_CTX *new_ctx = NULL;
const BIGNUM **new_scalars = NULL;
const EC_POINT **new_points = NULL;
const unsigned int window_size = 7;
const unsigned int mask = (1 << (window_size + 1)) - 1;
unsigned int wvalue;
ALIGN32 union {
P256_POINT p;
P256_POINT_AFFINE a;
} t, p;
BIGNUM *tmp_scalar;
if (group->meth != r->meth) {
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
return 0;
}
if ((scalar == NULL) && (num == 0))
return EC_POINT_set_to_infinity(group, r);
for (j = 0; j < num; j++) {
if (group->meth != points[j]->meth) {
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
return 0;
}
}
if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL)
goto err;
}
BN_CTX_start(ctx);
if (scalar) {
generator = EC_GROUP_get0_generator(group);
if (generator == NULL) {
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
goto err;
}
/* look if we can use precomputed multiples of generator */
pre_comp =
EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
ecp_nistz256_pre_comp_free,
ecp_nistz256_pre_comp_clear_free);
if (pre_comp) {
/*
* If there is a precomputed table for the generator, check that
* it was generated with the same generator.
*/
EC_POINT *pre_comp_generator = EC_POINT_new(group);
if (pre_comp_generator == NULL)
goto err;
if (!ecp_nistz256_set_from_affine
(pre_comp_generator, group, pre_comp->precomp[0], ctx)) {
EC_POINT_free(pre_comp_generator);
goto err;
}
if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
EC_POINT_free(pre_comp_generator);
}
if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
/*
* If there is no precomputed data, but the generator
* is the default, a hardcoded table of precomputed
* data is used. This is because applications, such as
* Apache, do not use EC_KEY_precompute_mult.
*/
preComputedTable = (const PRECOMP256_ROW *)ecp_nistz256_precomputed;
}
if (preComputedTable) {
if ((BN_num_bits(scalar) > 256)
|| BN_is_negative(scalar)) {
if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
goto err;
if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) {
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
goto err;
}
scalar = tmp_scalar;
}
for (i = 0; i < scalar->top * BN_BYTES; i += BN_BYTES) {
BN_ULONG d = scalar->d[i / BN_BYTES];
p_str[i + 0] = d & 0xff;
p_str[i + 1] = (d >> 8) & 0xff;
p_str[i + 2] = (d >> 16) & 0xff;
p_str[i + 3] = (d >>= 24) & 0xff;
if (BN_BYTES == 8) {
d >>= 8;
p_str[i + 4] = d & 0xff;
p_str[i + 5] = (d >> 8) & 0xff;
p_str[i + 6] = (d >> 16) & 0xff;
p_str[i + 7] = (d >> 24) & 0xff;
}
}
for (; i < 33; i++)
p_str[i] = 0;
#if defined(ECP_NISTZ256_AVX2)
if (ecp_nistz_avx2_eligible()) {
ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable);
} else
#endif
{
BN_ULONG infty;
/* First window */
wvalue = (p_str[0] << 1) & mask;
index += window_size;
wvalue = _booth_recode_w7(wvalue);
ecp_nistz256_select_w7(&p.a, preComputedTable[0], wvalue >> 1);
ecp_nistz256_neg(p.p.Z, p.p.Y);
copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
/*
* Since affine infinity is encoded as (0,0) and
* Jacobian ias (,,0), we need to harmonize them
* by assigning "one" or zero to Z.
*/
infty = (p.p.X[0] | p.p.X[1] | p.p.X[2] | p.p.X[3] |
p.p.Y[0] | p.p.Y[1] | p.p.Y[2] | p.p.Y[3]);
if (P256_LIMBS == 8)
infty |= (p.p.X[4] | p.p.X[5] | p.p.X[6] | p.p.X[7] |
p.p.Y[4] | p.p.Y[5] | p.p.Y[6] | p.p.Y[7]);
infty = 0 - is_zero(infty);
infty = ~infty;
p.p.Z[0] = ONE[0] & infty;
p.p.Z[1] = ONE[1] & infty;
p.p.Z[2] = ONE[2] & infty;
p.p.Z[3] = ONE[3] & infty;
if (P256_LIMBS == 8) {
p.p.Z[4] = ONE[4] & infty;
p.p.Z[5] = ONE[5] & infty;
p.p.Z[6] = ONE[6] & infty;
p.p.Z[7] = ONE[7] & infty;
}
for (i = 1; i < 37; i++) {
unsigned int off = (index - 1) / 8;
wvalue = p_str[off] | p_str[off + 1] << 8;
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
index += window_size;
wvalue = _booth_recode_w7(wvalue);
ecp_nistz256_select_w7(&t.a,
preComputedTable[i], wvalue >> 1);
ecp_nistz256_neg(t.p.Z, t.a.Y);
copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
}
}
} else {
p_is_infinity = 1;
no_precomp_for_generator = 1;
}
} else
p_is_infinity = 1;
if (no_precomp_for_generator) {
/*
* Without a precomputed table for the generator, it has to be
* handled like a normal point.
*/
new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
if (!new_scalars) {
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
goto err;
}
new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
if (!new_points) {
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
goto err;
}
memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
new_scalars[num] = scalar;
memcpy(new_points, points, num * sizeof(EC_POINT *));
new_points[num] = generator;
scalars = new_scalars;
points = new_points;
num++;
}
if (num) {
P256_POINT *out = &t.p;
if (p_is_infinity)
out = &p.p;
if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx))
goto err;
if (!p_is_infinity)
ecp_nistz256_point_add(&p.p, &p.p, out);
}
/* Not constant-time, but we're only operating on the public output. */
if (!ecp_nistz256_set_words(&r->X, p.p.X) ||
!ecp_nistz256_set_words(&r->Y, p.p.Y) ||
!ecp_nistz256_set_words(&r->Z, p.p.Z)) {
goto err;
}
r->Z_is_one = is_one(&r->Z) & 1;
ret = 1;
err:
if (ctx)
BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
if (new_points)
OPENSSL_free(new_points);
if (new_scalars)
OPENSSL_free(new_scalars);
return ret;
}
static int ecp_nistz256_get_affine(const EC_GROUP *group,
const EC_POINT *point,
BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
{
BN_ULONG z_inv2[P256_LIMBS];
BN_ULONG z_inv3[P256_LIMBS];
BN_ULONG x_aff[P256_LIMBS];
BN_ULONG y_aff[P256_LIMBS];
BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS];
if (EC_POINT_is_at_infinity(group, point)) {
ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
return 0;
}
if (!ecp_nistz256_bignum_to_field_elem(point_x, &point->X) ||
!ecp_nistz256_bignum_to_field_elem(point_y, &point->Y) ||
!ecp_nistz256_bignum_to_field_elem(point_z, &point->Z)) {
ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
return 0;
}
ecp_nistz256_mod_inverse(z_inv3, point_z);
ecp_nistz256_sqr_mont(z_inv2, z_inv3);
ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
if (x != NULL) {
ecp_nistz256_from_mont(x_ret, x_aff);
if (!ecp_nistz256_set_words(x, x_ret))
return 0;
}
if (y != NULL) {
ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
ecp_nistz256_from_mont(y_ret, y_aff);
if (!ecp_nistz256_set_words(y, y_ret))
return 0;
}
return 1;
}
static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
{
EC_PRE_COMP *ret = NULL;
if (!group)
return NULL;
ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
if (!ret) {
ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
return ret;
}
ret->group = group;
ret->w = 6; /* default */
ret->precomp = NULL;
ret->precomp_storage = NULL;
ret->references = 1;
return ret;
}
static void *ecp_nistz256_pre_comp_dup(void *src_)
{
EC_PRE_COMP *src = src_;
/* no need to actually copy, these objects never change! */
CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
return src_;
}
static void ecp_nistz256_pre_comp_free(void *pre_)
{
int i;
EC_PRE_COMP *pre = pre_;
if (!pre)
return;
i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
if (i > 0)
return;
if (pre->precomp_storage)
OPENSSL_free(pre->precomp_storage);
OPENSSL_free(pre);
}
static void ecp_nistz256_pre_comp_clear_free(void *pre_)
{
int i;
EC_PRE_COMP *pre = pre_;
if (!pre)
return;
i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
if (i > 0)
return;
if (pre->precomp_storage) {
OPENSSL_cleanse(pre->precomp,
32 * sizeof(unsigned char) * (1 << pre->w) * 2 * 37);
OPENSSL_free(pre->precomp_storage);
}
OPENSSL_cleanse(pre, sizeof(*pre));
OPENSSL_free(pre);
}
static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
{
/* There is a hard-coded table for the default generator. */
const EC_POINT *generator = EC_GROUP_get0_generator(group);
if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
/* There is a hard-coded table for the default generator. */
return 1;
}
return EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
ecp_nistz256_pre_comp_free,
ecp_nistz256_pre_comp_clear_free) != NULL;
}
const EC_METHOD *EC_GFp_nistz256_method(void)
{
static const EC_METHOD ret = {
EC_FLAGS_DEFAULT_OCT,
NID_X9_62_prime_field,
ec_GFp_mont_group_init,
ec_GFp_mont_group_finish,
ec_GFp_mont_group_clear_finish,
ec_GFp_mont_group_copy,
ec_GFp_mont_group_set_curve,
ec_GFp_simple_group_get_curve,
ec_GFp_simple_group_get_degree,
ec_GFp_simple_group_check_discriminant,
ec_GFp_simple_point_init,
ec_GFp_simple_point_finish,
ec_GFp_simple_point_clear_finish,
ec_GFp_simple_point_copy,
ec_GFp_simple_point_set_to_infinity,
ec_GFp_simple_set_Jprojective_coordinates_GFp,
ec_GFp_simple_get_Jprojective_coordinates_GFp,
ec_GFp_simple_point_set_affine_coordinates,
ecp_nistz256_get_affine,
0, 0, 0,
ec_GFp_simple_add,
ec_GFp_simple_dbl,
ec_GFp_simple_invert,
ec_GFp_simple_is_at_infinity,
ec_GFp_simple_is_on_curve,
ec_GFp_simple_cmp,
ec_GFp_simple_make_affine,
ec_GFp_simple_points_make_affine,
ecp_nistz256_points_mul, /* mul */
ecp_nistz256_mult_precompute, /* precompute_mult */
ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
ec_GFp_mont_field_mul,
ec_GFp_mont_field_sqr,
0, /* field_div */
ec_GFp_mont_field_encode,
ec_GFp_mont_field_decode,
ec_GFp_mont_field_set_to_one
};
return &ret;
}
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