ecp_nistp384.c
/*
* Copyright 2023 The OpenSSL Project Authors. All Rights Reserved.
*
* Licensed under the Apache License 2.0 (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
*/
/* Copyright 2023 IBM Corp.
*
* 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.
*/
/*
* Designed for 56-bit limbs by Rohan McLure <rohan.mclure@linux.ibm.com>.
* The layout is based on that of ecp_nistp{224,521}.c, allowing even for asm
* acceleration of felem_{square,mul} as supported in these files.
*/
#include <openssl/e_os2.h>
#include <string.h>
#include <openssl/err.h>
#include "ec_local.h"
#include "internal/numbers.h"
#ifndef INT128_MAX
# error "Your compiler doesn't appear to support 128-bit integer types"
#endif
typedef uint8_t u8;
typedef uint64_t u64;
/*
* The underlying field. P384 operates over GF(2^384-2^128-2^96+2^32-1). We
* can serialize an element of this field into 48 bytes. We call this an
* felem_bytearray.
*/
typedef u8 felem_bytearray[48];
/*
* These are the parameters of P384, taken from FIPS 186-3, section D.1.2.4.
* These values are big-endian.
*/
static const felem_bytearray nistp384_curve_params[5] = {
{0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF},
{0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a = -3 */
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFC},
{0xB3, 0x31, 0x2F, 0xA7, 0xE2, 0x3E, 0xE7, 0xE4, 0x98, 0x8E, 0x05, 0x6B, /* b */
0xE3, 0xF8, 0x2D, 0x19, 0x18, 0x1D, 0x9C, 0x6E, 0xFE, 0x81, 0x41, 0x12,
0x03, 0x14, 0x08, 0x8F, 0x50, 0x13, 0x87, 0x5A, 0xC6, 0x56, 0x39, 0x8D,
0x8A, 0x2E, 0xD1, 0x9D, 0x2A, 0x85, 0xC8, 0xED, 0xD3, 0xEC, 0x2A, 0xEF},
{0xAA, 0x87, 0xCA, 0x22, 0xBE, 0x8B, 0x05, 0x37, 0x8E, 0xB1, 0xC7, 0x1E, /* x */
0xF3, 0x20, 0xAD, 0x74, 0x6E, 0x1D, 0x3B, 0x62, 0x8B, 0xA7, 0x9B, 0x98,
0x59, 0xF7, 0x41, 0xE0, 0x82, 0x54, 0x2A, 0x38, 0x55, 0x02, 0xF2, 0x5D,
0xBF, 0x55, 0x29, 0x6C, 0x3A, 0x54, 0x5E, 0x38, 0x72, 0x76, 0x0A, 0xB7},
{0x36, 0x17, 0xDE, 0x4A, 0x96, 0x26, 0x2C, 0x6F, 0x5D, 0x9E, 0x98, 0xBF, /* y */
0x92, 0x92, 0xDC, 0x29, 0xF8, 0xF4, 0x1D, 0xBD, 0x28, 0x9A, 0x14, 0x7C,
0xE9, 0xDA, 0x31, 0x13, 0xB5, 0xF0, 0xB8, 0xC0, 0x0A, 0x60, 0xB1, 0xCE,
0x1D, 0x7E, 0x81, 0x9D, 0x7A, 0x43, 0x1D, 0x7C, 0x90, 0xEA, 0x0E, 0x5F},
};
/*-
* The representation of field elements.
* ------------------------------------
*
* We represent field elements with seven values. These values are either 64 or
* 128 bits and the field element represented is:
* v[0]*2^0 + v[1]*2^56 + v[2]*2^112 + ... + v[6]*2^336 (mod p)
* Each of the seven values is called a 'limb'. Since the limbs are spaced only
* 56 bits apart, but are greater than 56 bits in length, the most significant
* bits of each limb overlap with the least significant bits of the next
*
* This representation is considered to be 'redundant' in the sense that
* intermediate values can each contain more than a 56-bit value in each limb.
* Reduction causes all but the final limb to be reduced to contain a value less
* than 2^56, with the final value represented allowed to be larger than 2^384,
* inasmuch as we can be sure that arithmetic overflow remains impossible. The
* reduced value must of course be congruent to the unreduced value.
*
* A field element with 64-bit limbs is an 'felem'. One with 128-bit limbs is a
* 'widefelem', featuring enough bits to store the result of a multiplication
* and even some further arithmetic without need for immediate reduction.
*/
#define NLIMBS 7
typedef uint64_t limb;
typedef uint128_t widelimb;
typedef limb limb_aX __attribute((__aligned__(1)));
typedef limb felem[NLIMBS];
typedef widelimb widefelem[2*NLIMBS-1];
static const limb bottom56bits = 0xffffffffffffff;
/* Helper functions (de)serialising reduced field elements in little endian */
static void bin48_to_felem(felem out, const u8 in[48])
{
memset(out, 0, 56);
out[0] = (*((limb *) & in[0])) & bottom56bits;
out[1] = (*((limb_aX *) & in[7])) & bottom56bits;
out[2] = (*((limb_aX *) & in[14])) & bottom56bits;
out[3] = (*((limb_aX *) & in[21])) & bottom56bits;
out[4] = (*((limb_aX *) & in[28])) & bottom56bits;
out[5] = (*((limb_aX *) & in[35])) & bottom56bits;
memmove(&out[6], &in[42], 6);
}
static void felem_to_bin48(u8 out[48], const felem in)
{
memset(out, 0, 48);
(*((limb *) & out[0])) |= (in[0] & bottom56bits);
(*((limb_aX *) & out[7])) |= (in[1] & bottom56bits);
(*((limb_aX *) & out[14])) |= (in[2] & bottom56bits);
(*((limb_aX *) & out[21])) |= (in[3] & bottom56bits);
(*((limb_aX *) & out[28])) |= (in[4] & bottom56bits);
(*((limb_aX *) & out[35])) |= (in[5] & bottom56bits);
memmove(&out[42], &in[6], 6);
}
/* BN_to_felem converts an OpenSSL BIGNUM into an felem */
static int BN_to_felem(felem out, const BIGNUM *bn)
{
felem_bytearray b_out;
int num_bytes;
if (BN_is_negative(bn)) {
ERR_raise(ERR_LIB_EC, EC_R_BIGNUM_OUT_OF_RANGE);
return 0;
}
num_bytes = BN_bn2lebinpad(bn, b_out, sizeof(b_out));
if (num_bytes < 0) {
ERR_raise(ERR_LIB_EC, EC_R_BIGNUM_OUT_OF_RANGE);
return 0;
}
bin48_to_felem(out, b_out);
return 1;
}
/* felem_to_BN converts an felem into an OpenSSL BIGNUM */
static BIGNUM *felem_to_BN(BIGNUM *out, const felem in)
{
felem_bytearray b_out;
felem_to_bin48(b_out, in);
return BN_lebin2bn(b_out, sizeof(b_out), out);
}
/*-
* Field operations
* ----------------
*/
static void felem_one(felem out)
{
out[0] = 1;
memset(&out[1], 0, sizeof(limb) * (NLIMBS-1));
}
static void felem_assign(felem out, const felem in)
{
memcpy(out, in, sizeof(felem));
}
/* felem_sum64 sets out = out + in. */
static void felem_sum64(felem out, const felem in)
{
unsigned int i;
for (i = 0; i < NLIMBS; i++)
out[i] += in[i];
}
/* felem_scalar sets out = in * scalar */
static void felem_scalar(felem out, const felem in, limb scalar)
{
unsigned int i;
for (i = 0; i < NLIMBS; i++)
out[i] = in[i] * scalar;
}
/* felem_scalar64 sets out = out * scalar */
static void felem_scalar64(felem out, limb scalar)
{
unsigned int i;
for (i = 0; i < NLIMBS; i++)
out[i] *= scalar;
}
/* felem_scalar128 sets out = out * scalar */
static void felem_scalar128(widefelem out, limb scalar)
{
unsigned int i;
for (i = 0; i < 2*NLIMBS-1; i++)
out[i] *= scalar;
}
/*-
* felem_neg sets |out| to |-in|
* On entry:
* in[i] < 2^60 - 2^29
* On exit:
* out[i] < 2^60
*/
static void felem_neg(felem out, const felem in)
{
/*
* In order to prevent underflow, we add a multiple of p before subtracting.
* Use telescopic sums to represent 2^12 * p redundantly with each limb
* of the form 2^60 + ...
*/
static const limb two60m52m4 = (((limb) 1) << 60)
- (((limb) 1) << 52)
- (((limb) 1) << 4);
static const limb two60p44m12 = (((limb) 1) << 60)
+ (((limb) 1) << 44)
- (((limb) 1) << 12);
static const limb two60m28m4 = (((limb) 1) << 60)
- (((limb) 1) << 28)
- (((limb) 1) << 4);
static const limb two60m4 = (((limb) 1) << 60)
- (((limb) 1) << 4);
out[0] = two60p44m12 - in[0];
out[1] = two60m52m4 - in[1];
out[2] = two60m28m4 - in[2];
out[3] = two60m4 - in[3];
out[4] = two60m4 - in[4];
out[5] = two60m4 - in[5];
out[6] = two60m4 - in[6];
}
/*-
* felem_diff64 subtracts |in| from |out|
* On entry:
* in[i] < 2^60 - 2^52 - 2^4
* On exit:
* out[i] < out_orig[i] + 2^60 + 2^44
*/
static void felem_diff64(felem out, const felem in)
{
/*
* In order to prevent underflow, we add a multiple of p before subtracting.
* Use telescopic sums to represent 2^12 * p redundantly with each limb
* of the form 2^60 + ...
*/
static const limb two60m52m4 = (((limb) 1) << 60)
- (((limb) 1) << 52)
- (((limb) 1) << 4);
static const limb two60p44m12 = (((limb) 1) << 60)
+ (((limb) 1) << 44)
- (((limb) 1) << 12);
static const limb two60m28m4 = (((limb) 1) << 60)
- (((limb) 1) << 28)
- (((limb) 1) << 4);
static const limb two60m4 = (((limb) 1) << 60)
- (((limb) 1) << 4);
out[0] += two60p44m12 - in[0];
out[1] += two60m52m4 - in[1];
out[2] += two60m28m4 - in[2];
out[3] += two60m4 - in[3];
out[4] += two60m4 - in[4];
out[5] += two60m4 - in[5];
out[6] += two60m4 - in[6];
}
/*
* in[i] < 2^63
* out[i] < out_orig[i] + 2^64 + 2^48
*/
static void felem_diff_128_64(widefelem out, const felem in)
{
/*
* In order to prevent underflow, we add a multiple of p before subtracting.
* Use telescopic sums to represent 2^16 * p redundantly with each limb
* of the form 2^64 + ...
*/
static const widelimb two64m56m8 = (((widelimb) 1) << 64)
- (((widelimb) 1) << 56)
- (((widelimb) 1) << 8);
static const widelimb two64m32m8 = (((widelimb) 1) << 64)
- (((widelimb) 1) << 32)
- (((widelimb) 1) << 8);
static const widelimb two64m8 = (((widelimb) 1) << 64)
- (((widelimb) 1) << 8);
static const widelimb two64p48m16 = (((widelimb) 1) << 64)
+ (((widelimb) 1) << 48)
- (((widelimb) 1) << 16);
unsigned int i;
out[0] += two64p48m16;
out[1] += two64m56m8;
out[2] += two64m32m8;
out[3] += two64m8;
out[4] += two64m8;
out[5] += two64m8;
out[6] += two64m8;
for (i = 0; i < NLIMBS; i++)
out[i] -= in[i];
}
/*
* in[i] < 2^127 - 2^119 - 2^71
* out[i] < out_orig[i] + 2^127 + 2^111
*/
static void felem_diff128(widefelem out, const widefelem in)
{
/*
* In order to prevent underflow, we add a multiple of p before subtracting.
* Use telescopic sums to represent 2^415 * p redundantly with each limb
* of the form 2^127 + ...
*/
static const widelimb two127 = ((widelimb) 1) << 127;
static const widelimb two127m71 = (((widelimb) 1) << 127)
- (((widelimb) 1) << 71);
static const widelimb two127p111m79m71 = (((widelimb) 1) << 127)
+ (((widelimb) 1) << 111)
- (((widelimb) 1) << 79)
- (((widelimb) 1) << 71);
static const widelimb two127m119m71 = (((widelimb) 1) << 127)
- (((widelimb) 1) << 119)
- (((widelimb) 1) << 71);
static const widelimb two127m95m71 = (((widelimb) 1) << 127)
- (((widelimb) 1) << 95)
- (((widelimb) 1) << 71);
unsigned int i;
out[0] += two127;
out[1] += two127m71;
out[2] += two127m71;
out[3] += two127m71;
out[4] += two127m71;
out[5] += two127m71;
out[6] += two127p111m79m71;
out[7] += two127m119m71;
out[8] += two127m95m71;
out[9] += two127m71;
out[10] += two127m71;
out[11] += two127m71;
out[12] += two127m71;
for (i = 0; i < 2*NLIMBS-1; i++)
out[i] -= in[i];
}
static void felem_square_ref(widefelem out, const felem in)
{
felem inx2;
felem_scalar(inx2, in, 2);
out[0] = ((uint128_t) in[0]) * in[0];
out[1] = ((uint128_t) in[0]) * inx2[1];
out[2] = ((uint128_t) in[0]) * inx2[2]
+ ((uint128_t) in[1]) * in[1];
out[3] = ((uint128_t) in[0]) * inx2[3]
+ ((uint128_t) in[1]) * inx2[2];
out[4] = ((uint128_t) in[0]) * inx2[4]
+ ((uint128_t) in[1]) * inx2[3]
+ ((uint128_t) in[2]) * in[2];
out[5] = ((uint128_t) in[0]) * inx2[5]
+ ((uint128_t) in[1]) * inx2[4]
+ ((uint128_t) in[2]) * inx2[3];
out[6] = ((uint128_t) in[0]) * inx2[6]
+ ((uint128_t) in[1]) * inx2[5]
+ ((uint128_t) in[2]) * inx2[4]
+ ((uint128_t) in[3]) * in[3];
out[7] = ((uint128_t) in[1]) * inx2[6]
+ ((uint128_t) in[2]) * inx2[5]
+ ((uint128_t) in[3]) * inx2[4];
out[8] = ((uint128_t) in[2]) * inx2[6]
+ ((uint128_t) in[3]) * inx2[5]
+ ((uint128_t) in[4]) * in[4];
out[9] = ((uint128_t) in[3]) * inx2[6]
+ ((uint128_t) in[4]) * inx2[5];
out[10] = ((uint128_t) in[4]) * inx2[6]
+ ((uint128_t) in[5]) * in[5];
out[11] = ((uint128_t) in[5]) * inx2[6];
out[12] = ((uint128_t) in[6]) * in[6];
}
static void felem_mul_ref(widefelem out, const felem in1, const felem in2)
{
out[0] = ((uint128_t) in1[0]) * in2[0];
out[1] = ((uint128_t) in1[0]) * in2[1]
+ ((uint128_t) in1[1]) * in2[0];
out[2] = ((uint128_t) in1[0]) * in2[2]
+ ((uint128_t) in1[1]) * in2[1]
+ ((uint128_t) in1[2]) * in2[0];
out[3] = ((uint128_t) in1[0]) * in2[3]
+ ((uint128_t) in1[1]) * in2[2]
+ ((uint128_t) in1[2]) * in2[1]
+ ((uint128_t) in1[3]) * in2[0];
out[4] = ((uint128_t) in1[0]) * in2[4]
+ ((uint128_t) in1[1]) * in2[3]
+ ((uint128_t) in1[2]) * in2[2]
+ ((uint128_t) in1[3]) * in2[1]
+ ((uint128_t) in1[4]) * in2[0];
out[5] = ((uint128_t) in1[0]) * in2[5]
+ ((uint128_t) in1[1]) * in2[4]
+ ((uint128_t) in1[2]) * in2[3]
+ ((uint128_t) in1[3]) * in2[2]
+ ((uint128_t) in1[4]) * in2[1]
+ ((uint128_t) in1[5]) * in2[0];
out[6] = ((uint128_t) in1[0]) * in2[6]
+ ((uint128_t) in1[1]) * in2[5]
+ ((uint128_t) in1[2]) * in2[4]
+ ((uint128_t) in1[3]) * in2[3]
+ ((uint128_t) in1[4]) * in2[2]
+ ((uint128_t) in1[5]) * in2[1]
+ ((uint128_t) in1[6]) * in2[0];
out[7] = ((uint128_t) in1[1]) * in2[6]
+ ((uint128_t) in1[2]) * in2[5]
+ ((uint128_t) in1[3]) * in2[4]
+ ((uint128_t) in1[4]) * in2[3]
+ ((uint128_t) in1[5]) * in2[2]
+ ((uint128_t) in1[6]) * in2[1];
out[8] = ((uint128_t) in1[2]) * in2[6]
+ ((uint128_t) in1[3]) * in2[5]
+ ((uint128_t) in1[4]) * in2[4]
+ ((uint128_t) in1[5]) * in2[3]
+ ((uint128_t) in1[6]) * in2[2];
out[9] = ((uint128_t) in1[3]) * in2[6]
+ ((uint128_t) in1[4]) * in2[5]
+ ((uint128_t) in1[5]) * in2[4]
+ ((uint128_t) in1[6]) * in2[3];
out[10] = ((uint128_t) in1[4]) * in2[6]
+ ((uint128_t) in1[5]) * in2[5]
+ ((uint128_t) in1[6]) * in2[4];
out[11] = ((uint128_t) in1[5]) * in2[6]
+ ((uint128_t) in1[6]) * in2[5];
out[12] = ((uint128_t) in1[6]) * in2[6];
}
/*-
* Reduce thirteen 128-bit coefficients to seven 64-bit coefficients.
* in[i] < 2^128 - 2^125
* out[i] < 2^56 for i < 6,
* out[6] <= 2^48
*
* The technique in use here stems from the format of the prime modulus:
* P384 = 2^384 - delta
*
* Thus we can reduce numbers of the form (X + 2^384 * Y) by substituting
* them with (X + delta Y), with delta = 2^128 + 2^96 + (-2^32 + 1). These
* coefficients are still quite large, and so we repeatedly apply this
* technique on high-order bits in order to guarantee the desired bounds on
* the size of our output.
*
* The three phases of elimination are as follows:
* [1]: Y = 2^120 (in[12] | in[11] | in[10] | in[9])
* [2]: Y = 2^8 (acc[8] | acc[7])
* [3]: Y = 2^48 (acc[6] >> 48)
* (Where a | b | c | d = (2^56)^3 a + (2^56)^2 b + (2^56) c + d)
*/
static void felem_reduce(felem out, const widefelem in)
{
/*
* In order to prevent underflow, we add a multiple of p before subtracting.
* Use telescopic sums to represent 2^76 * p redundantly with each limb
* of the form 2^124 + ...
*/
static const widelimb two124m68 = (((widelimb) 1) << 124)
- (((widelimb) 1) << 68);
static const widelimb two124m116m68 = (((widelimb) 1) << 124)
- (((widelimb) 1) << 116)
- (((widelimb) 1) << 68);
static const widelimb two124p108m76 = (((widelimb) 1) << 124)
+ (((widelimb) 1) << 108)
- (((widelimb) 1) << 76);
static const widelimb two124m92m68 = (((widelimb) 1) << 124)
- (((widelimb) 1) << 92)
- (((widelimb) 1) << 68);
widelimb temp, acc[9];
unsigned int i;
memcpy(acc, in, sizeof(widelimb) * 9);
acc[0] += two124p108m76;
acc[1] += two124m116m68;
acc[2] += two124m92m68;
acc[3] += two124m68;
acc[4] += two124m68;
acc[5] += two124m68;
acc[6] += two124m68;
/* [1]: Eliminate in[9], ..., in[12] */
acc[8] += in[12] >> 32;
acc[7] += (in[12] & 0xffffffff) << 24;
acc[7] += in[12] >> 8;
acc[6] += (in[12] & 0xff) << 48;
acc[6] -= in[12] >> 16;
acc[5] -= (in[12] & 0xffff) << 40;
acc[6] += in[12] >> 48;
acc[5] += (in[12] & 0xffffffffffff) << 8;
acc[7] += in[11] >> 32;
acc[6] += (in[11] & 0xffffffff) << 24;
acc[6] += in[11] >> 8;
acc[5] += (in[11] & 0xff) << 48;
acc[5] -= in[11] >> 16;
acc[4] -= (in[11] & 0xffff) << 40;
acc[5] += in[11] >> 48;
acc[4] += (in[11] & 0xffffffffffff) << 8;
acc[6] += in[10] >> 32;
acc[5] += (in[10] & 0xffffffff) << 24;
acc[5] += in[10] >> 8;
acc[4] += (in[10] & 0xff) << 48;
acc[4] -= in[10] >> 16;
acc[3] -= (in[10] & 0xffff) << 40;
acc[4] += in[10] >> 48;
acc[3] += (in[10] & 0xffffffffffff) << 8;
acc[5] += in[9] >> 32;
acc[4] += (in[9] & 0xffffffff) << 24;
acc[4] += in[9] >> 8;
acc[3] += (in[9] & 0xff) << 48;
acc[3] -= in[9] >> 16;
acc[2] -= (in[9] & 0xffff) << 40;
acc[3] += in[9] >> 48;
acc[2] += (in[9] & 0xffffffffffff) << 8;
/*
* [2]: Eliminate acc[7], acc[8], that is the 7 and eighth limbs, as
* well as the contributions made from eliminating higher limbs.
* acc[7] < in[7] + 2^120 + 2^56 < in[7] + 2^121
* acc[8] < in[8] + 2^96
*/
acc[4] += acc[8] >> 32;
acc[3] += (acc[8] & 0xffffffff) << 24;
acc[3] += acc[8] >> 8;
acc[2] += (acc[8] & 0xff) << 48;
acc[2] -= acc[8] >> 16;
acc[1] -= (acc[8] & 0xffff) << 40;
acc[2] += acc[8] >> 48;
acc[1] += (acc[8] & 0xffffffffffff) << 8;
acc[3] += acc[7] >> 32;
acc[2] += (acc[7] & 0xffffffff) << 24;
acc[2] += acc[7] >> 8;
acc[1] += (acc[7] & 0xff) << 48;
acc[1] -= acc[7] >> 16;
acc[0] -= (acc[7] & 0xffff) << 40;
acc[1] += acc[7] >> 48;
acc[0] += (acc[7] & 0xffffffffffff) << 8;
/*-
* acc[k] < in[k] + 2^124 + 2^121
* < in[k] + 2^125
* < 2^128, for k <= 6
*/
/*
* Carry 4 -> 5 -> 6
* This has the effect of ensuring that these more significant limbs
* will be small in value after eliminating high bits from acc[6].
*/
acc[5] += acc[4] >> 56;
acc[4] &= 0x00ffffffffffffff;
acc[6] += acc[5] >> 56;
acc[5] &= 0x00ffffffffffffff;
/*-
* acc[6] < in[6] + 2^124 + 2^121 + 2^72 + 2^16
* < in[6] + 2^125
* < 2^128
*/
/* [3]: Eliminate high bits of acc[6] */
temp = acc[6] >> 48;
acc[6] &= 0x0000ffffffffffff;
/* temp < 2^80 */
acc[3] += temp >> 40;
acc[2] += (temp & 0xffffffffff) << 16;
acc[2] += temp >> 16;
acc[1] += (temp & 0xffff) << 40;
acc[1] -= temp >> 24;
acc[0] -= (temp & 0xffffff) << 32;
acc[0] += temp;
/*-
* acc[k] < acc_old[k] + 2^64 + 2^56
* < in[k] + 2^124 + 2^121 + 2^72 + 2^64 + 2^56 + 2^16 , k < 4
*/
/* Carry 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 */
acc[1] += acc[0] >> 56; /* acc[1] < acc_old[1] + 2^72 */
acc[0] &= 0x00ffffffffffffff;
acc[2] += acc[1] >> 56; /* acc[2] < acc_old[2] + 2^72 + 2^16 */
acc[1] &= 0x00ffffffffffffff;
acc[3] += acc[2] >> 56; /* acc[3] < acc_old[3] + 2^72 + 2^16 */
acc[2] &= 0x00ffffffffffffff;
/*-
* acc[k] < acc_old[k] + 2^72 + 2^16
* < in[k] + 2^124 + 2^121 + 2^73 + 2^64 + 2^56 + 2^17
* < in[k] + 2^125
* < 2^128 , k < 4
*/
acc[4] += acc[3] >> 56; /*-
* acc[4] < acc_old[4] + 2^72 + 2^16
* < 2^72 + 2^56 + 2^16
*/
acc[3] &= 0x00ffffffffffffff;
acc[5] += acc[4] >> 56; /*-
* acc[5] < acc_old[5] + 2^16 + 1
* < 2^56 + 2^16 + 1
*/
acc[4] &= 0x00ffffffffffffff;
acc[6] += acc[5] >> 56; /* acc[6] < 2^48 + 1 <= 2^48 */
acc[5] &= 0x00ffffffffffffff;
for (i = 0; i < NLIMBS; i++)
out[i] = acc[i];
}
#if defined(ECP_NISTP384_ASM)
static void felem_square_wrapper(widefelem out, const felem in);
static void felem_mul_wrapper(widefelem out, const felem in1, const felem in2);
static void (*felem_square_p)(widefelem out, const felem in) =
felem_square_wrapper;
static void (*felem_mul_p)(widefelem out, const felem in1, const felem in2) =
felem_mul_wrapper;
void p384_felem_square(widefelem out, const felem in);
void p384_felem_mul(widefelem out, const felem in1, const felem in2);
# if defined(_ARCH_PPC64)
# include "crypto/ppc_arch.h"
# endif
static void felem_select(void)
{
# if defined(_ARCH_PPC64)
if ((OPENSSL_ppccap_P & PPC_MADD300) && (OPENSSL_ppccap_P & PPC_ALTIVEC)) {
felem_square_p = p384_felem_square;
felem_mul_p = p384_felem_mul;
return;
}
# endif
/* Default */
felem_square_p = felem_square_ref;
felem_mul_p = felem_mul_ref;
}
static void felem_square_wrapper(widefelem out, const felem in)
{
felem_select();
felem_square_p(out, in);
}
static void felem_mul_wrapper(widefelem out, const felem in1, const felem in2)
{
felem_select();
felem_mul_p(out, in1, in2);
}
# define felem_square felem_square_p
# define felem_mul felem_mul_p
#else
# define felem_square felem_square_ref
# define felem_mul felem_mul_ref
#endif
static ossl_inline void felem_square_reduce(felem out, const felem in)
{
widefelem tmp;
felem_square(tmp, in);
felem_reduce(out, tmp);
}
static ossl_inline void felem_mul_reduce(felem out, const felem in1, const felem in2)
{
widefelem tmp;
felem_mul(tmp, in1, in2);
felem_reduce(out, tmp);
}
/*-
* felem_inv calculates |out| = |in|^{-1}
*
* Based on Fermat's Little Theorem:
* a^p = a (mod p)
* a^{p-1} = 1 (mod p)
* a^{p-2} = a^{-1} (mod p)
*/
static void felem_inv(felem out, const felem in)
{
felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6;
unsigned int i = 0;
felem_square_reduce(ftmp, in); /* 2^1 */
felem_mul_reduce(ftmp, ftmp, in); /* 2^1 + 2^0 */
felem_assign(ftmp2, ftmp);
felem_square_reduce(ftmp, ftmp); /* 2^2 + 2^1 */
felem_mul_reduce(ftmp, ftmp, in); /* 2^2 + 2^1 * 2^0 */
felem_assign(ftmp3, ftmp);
for (i = 0; i < 3; i++)
felem_square_reduce(ftmp, ftmp); /* 2^5 + 2^4 + 2^3 */
felem_mul_reduce(ftmp, ftmp3, ftmp); /* 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0 */
felem_assign(ftmp4, ftmp);
for (i = 0; i < 6; i++)
felem_square_reduce(ftmp, ftmp); /* 2^11 + ... + 2^6 */
felem_mul_reduce(ftmp, ftmp4, ftmp); /* 2^11 + ... + 2^0 */
for (i = 0; i < 3; i++)
felem_square_reduce(ftmp, ftmp); /* 2^14 + ... + 2^3 */
felem_mul_reduce(ftmp, ftmp3, ftmp); /* 2^14 + ... + 2^0 */
felem_assign(ftmp5, ftmp);
for (i = 0; i < 15; i++)
felem_square_reduce(ftmp, ftmp); /* 2^29 + ... + 2^15 */
felem_mul_reduce(ftmp, ftmp5, ftmp); /* 2^29 + ... + 2^0 */
felem_assign(ftmp6, ftmp);
for (i = 0; i < 30; i++)
felem_square_reduce(ftmp, ftmp); /* 2^59 + ... + 2^30 */
felem_mul_reduce(ftmp, ftmp6, ftmp); /* 2^59 + ... + 2^0 */
felem_assign(ftmp4, ftmp);
for (i = 0; i < 60; i++)
felem_square_reduce(ftmp, ftmp); /* 2^119 + ... + 2^60 */
felem_mul_reduce(ftmp, ftmp4, ftmp); /* 2^119 + ... + 2^0 */
felem_assign(ftmp4, ftmp);
for (i = 0; i < 120; i++)
felem_square_reduce(ftmp, ftmp); /* 2^239 + ... + 2^120 */
felem_mul_reduce(ftmp, ftmp4, ftmp); /* 2^239 + ... + 2^0 */
for (i = 0; i < 15; i++)
felem_square_reduce(ftmp, ftmp); /* 2^254 + ... + 2^15 */
felem_mul_reduce(ftmp, ftmp5, ftmp); /* 2^254 + ... + 2^0 */
for (i = 0; i < 31; i++)
felem_square_reduce(ftmp, ftmp); /* 2^285 + ... + 2^31 */
felem_mul_reduce(ftmp, ftmp6, ftmp); /* 2^285 + ... + 2^31 + 2^29 + ... + 2^0 */
for (i = 0; i < 2; i++)
felem_square_reduce(ftmp, ftmp); /* 2^287 + ... + 2^33 + 2^31 + ... + 2^2 */
felem_mul_reduce(ftmp, ftmp2, ftmp); /* 2^287 + ... + 2^33 + 2^31 + ... + 2^0 */
for (i = 0; i < 94; i++)
felem_square_reduce(ftmp, ftmp); /* 2^381 + ... + 2^127 + 2^125 + ... + 2^94 */
felem_mul_reduce(ftmp, ftmp6, ftmp); /* 2^381 + ... + 2^127 + 2^125 + ... + 2^94 + 2^29 + ... + 2^0 */
for (i = 0; i < 2; i++)
felem_square_reduce(ftmp, ftmp); /* 2^383 + ... + 2^129 + 2^127 + ... + 2^96 + 2^31 + ... + 2^2 */
felem_mul_reduce(ftmp, in, ftmp); /* 2^383 + ... + 2^129 + 2^127 + ... + 2^96 + 2^31 + ... + 2^2 + 2^0 */
memcpy(out, ftmp, sizeof(felem));
}
/*
* Zero-check: returns a limb with all bits set if |in| == 0 (mod p)
* and 0 otherwise. We know that field elements are reduced to
* 0 < in < 2p, so we only need to check two cases:
* 0 and 2^384 - 2^128 - 2^96 + 2^32 - 1
* in[k] < 2^56, k < 6
* in[6] <= 2^48
*/
static limb felem_is_zero(const felem in)
{
limb zero, p384;
zero = in[0] | in[1] | in[2] | in[3] | in[4] | in[5] | in[6];
zero = ((int64_t) (zero) - 1) >> 63;
p384 = (in[0] ^ 0x000000ffffffff) | (in[1] ^ 0xffff0000000000)
| (in[2] ^ 0xfffffffffeffff) | (in[3] ^ 0xffffffffffffff)
| (in[4] ^ 0xffffffffffffff) | (in[5] ^ 0xffffffffffffff)
| (in[6] ^ 0xffffffffffff);
p384 = ((int64_t) (p384) - 1) >> 63;
return (zero | p384);
}
static int felem_is_zero_int(const void *in)
{
return (int)(felem_is_zero(in) & ((limb) 1));
}
/*-
* felem_contract converts |in| to its unique, minimal representation.
* Assume we've removed all redundant bits.
* On entry:
* in[k] < 2^56, k < 6
* in[6] <= 2^48
*/
static void felem_contract(felem out, const felem in)
{
static const int64_t two56 = ((limb) 1) << 56;
/*
* We know for a fact that 0 <= |in| < 2*p, for p = 2^384 - 2^128 - 2^96 + 2^32 - 1
* Perform two successive, idempotent subtractions to reduce if |in| >= p.
*/
int64_t tmp[NLIMBS], cond[5], a;
unsigned int i;
memcpy(tmp, in, sizeof(felem));
/* Case 1: a = 1 iff |in| >= 2^384 */
a = (in[6] >> 48);
tmp[0] += a;
tmp[0] -= a << 32;
tmp[1] += a << 40;
tmp[2] += a << 16;
tmp[6] &= 0x0000ffffffffffff;
/*
* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be
* non-zero, so we only need one step
*/
a = tmp[0] >> 63;
tmp[0] += a & two56;
tmp[1] -= a & 1;
/* Carry 1 -> 2 -> 3 -> 4 -> 5 -> 6 */
tmp[2] += tmp[1] >> 56;
tmp[1] &= 0x00ffffffffffffff;
tmp[3] += tmp[2] >> 56;
tmp[2] &= 0x00ffffffffffffff;
tmp[4] += tmp[3] >> 56;
tmp[3] &= 0x00ffffffffffffff;
tmp[5] += tmp[4] >> 56;
tmp[4] &= 0x00ffffffffffffff;
tmp[6] += tmp[5] >> 56; /* tmp[6] < 2^48 */
tmp[5] &= 0x00ffffffffffffff;
/*
* Case 2: a = all ones if p <= |in| < 2^384, 0 otherwise
*/
/* 0 iff (2^129..2^383) are all one */
cond[0] = ((tmp[6] | 0xff000000000000) & tmp[5] & tmp[4] & tmp[3] & (tmp[2] | 0x0000000001ffff)) + 1;
/* 0 iff 2^128 bit is one */
cond[1] = (tmp[2] | ~0x00000000010000) + 1;
/* 0 iff (2^96..2^127) bits are all one */
cond[2] = ((tmp[2] | 0xffffffffff0000) & (tmp[1] | 0x0000ffffffffff)) + 1;
/* 0 iff (2^32..2^95) bits are all zero */
cond[3] = (tmp[1] & ~0xffff0000000000) | (tmp[0] & ~((int64_t) 0x000000ffffffff));
/* 0 iff (2^0..2^31) bits are all one */
cond[4] = (tmp[0] | 0xffffff00000000) + 1;
/*
* In effect, invert our conditions, so that 0 values become all 1's,
* any non-zero value in the low-order 56 bits becomes all 0's
*/
for (i = 0; i < 5; i++)
cond[i] = ((cond[i] & 0x00ffffffffffffff) - 1) >> 63;
/*
* The condition for determining whether in is greater than our
* prime is given by the following condition.
*/
/* First subtract 2^384 - 2^129 cheaply */
a = cond[0] & (cond[1] | (cond[2] & (~cond[3] | cond[4])));
tmp[6] &= ~a;
tmp[5] &= ~a;
tmp[4] &= ~a;
tmp[3] &= ~a;
tmp[2] &= ~a | 0x0000000001ffff;
/*
* Subtract 2^128 - 2^96 by
* means of disjoint cases.
*/
/* subtract 2^128 if that bit is present, and add 2^96 */
a = cond[0] & cond[1];
tmp[2] &= ~a | 0xfffffffffeffff;
tmp[1] += a & ((int64_t) 1 << 40);
/* otherwise, clear bits 2^127 .. 2^96 */
a = cond[0] & ~cond[1] & (cond[2] & (~cond[3] | cond[4]));
tmp[2] &= ~a | 0xffffffffff0000;
tmp[1] &= ~a | 0x0000ffffffffff;
/* finally, subtract the last 2^32 - 1 */
a = cond[0] & (cond[1] | (cond[2] & (~cond[3] | cond[4])));
tmp[0] += a & (-((int64_t) 1 << 32) + 1);
/*
* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be
* non-zero, so we only need one step
*/
a = tmp[0] >> 63;
tmp[0] += a & two56;
tmp[1] -= a & 1;
/* Carry 1 -> 2 -> 3 -> 4 -> 5 -> 6 */
tmp[2] += tmp[1] >> 56;
tmp[1] &= 0x00ffffffffffffff;
tmp[3] += tmp[2] >> 56;
tmp[2] &= 0x00ffffffffffffff;
tmp[4] += tmp[3] >> 56;
tmp[3] &= 0x00ffffffffffffff;
tmp[5] += tmp[4] >> 56;
tmp[4] &= 0x00ffffffffffffff;
tmp[6] += tmp[5] >> 56;
tmp[5] &= 0x00ffffffffffffff;
memcpy(out, tmp, sizeof(felem));
}
/*-
* Group operations
* ----------------
*
* Building on top of the field operations we have the operations on the
* elliptic curve group itself. Points on the curve are represented in Jacobian
* coordinates
*/
/*-
* point_double calculates 2*(x_in, y_in, z_in)
*
* The method is taken from:
* http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
*
* Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed.
* while x_out == y_in is not (maybe this works, but it's not tested).
*/
static void
point_double(felem x_out, felem y_out, felem z_out,
const felem x_in, const felem y_in, const felem z_in)
{
widefelem tmp, tmp2;
felem delta, gamma, beta, alpha, ftmp, ftmp2;
felem_assign(ftmp, x_in);
felem_assign(ftmp2, x_in);
/* delta = z^2 */
felem_square_reduce(delta, z_in); /* delta[i] < 2^56 */
/* gamma = y^2 */
felem_square_reduce(gamma, y_in); /* gamma[i] < 2^56 */
/* beta = x*gamma */
felem_mul_reduce(beta, x_in, gamma); /* beta[i] < 2^56 */
/* alpha = 3*(x-delta)*(x+delta) */
felem_diff64(ftmp, delta); /* ftmp[i] < 2^60 + 2^58 + 2^44 */
felem_sum64(ftmp2, delta); /* ftmp2[i] < 2^59 */
felem_scalar64(ftmp2, 3); /* ftmp2[i] < 2^61 */
felem_mul_reduce(alpha, ftmp, ftmp2); /* alpha[i] < 2^56 */
/* x' = alpha^2 - 8*beta */
felem_square(tmp, alpha); /* tmp[i] < 2^115 */
felem_assign(ftmp, beta); /* ftmp[i] < 2^56 */
felem_scalar64(ftmp, 8); /* ftmp[i] < 2^59 */
felem_diff_128_64(tmp, ftmp); /* tmp[i] < 2^115 + 2^64 + 2^48 */
felem_reduce(x_out, tmp); /* x_out[i] < 2^56 */
/* z' = (y + z)^2 - gamma - delta */
felem_sum64(delta, gamma); /* delta[i] < 2^57 */
felem_assign(ftmp, y_in); /* ftmp[i] < 2^56 */
felem_sum64(ftmp, z_in); /* ftmp[i] < 2^56 */
felem_square(tmp, ftmp); /* tmp[i] < 2^115 */
felem_diff_128_64(tmp, delta); /* tmp[i] < 2^115 + 2^64 + 2^48 */
felem_reduce(z_out, tmp); /* z_out[i] < 2^56 */
/* y' = alpha*(4*beta - x') - 8*gamma^2 */
felem_scalar64(beta, 4); /* beta[i] < 2^58 */
felem_diff64(beta, x_out); /* beta[i] < 2^60 + 2^58 + 2^44 */
felem_mul(tmp, alpha, beta); /* tmp[i] < 2^119 */
felem_square(tmp2, gamma); /* tmp2[i] < 2^115 */
felem_scalar128(tmp2, 8); /* tmp2[i] < 2^118 */
felem_diff128(tmp, tmp2); /* tmp[i] < 2^127 + 2^119 + 2^111 */
felem_reduce(y_out, tmp); /* tmp[i] < 2^56 */
}
/* copy_conditional copies in to out iff mask is all ones. */
static void copy_conditional(felem out, const felem in, limb mask)
{
unsigned int i;
for (i = 0; i < NLIMBS; i++)
out[i] ^= mask & (in[i] ^ out[i]);
}
/*-
* point_add calculates (x1, y1, z1) + (x2, y2, z2)
*
* The method is taken from
* http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl,
* adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity).
*
* This function includes a branch for checking whether the two input points
* are equal (while not equal to the point at infinity). See comment below
* on constant-time.
*/
static void point_add(felem x3, felem y3, felem z3,
const felem x1, const felem y1, const felem z1,
const int mixed, const felem x2, const felem y2,
const felem z2)
{
felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out;
widefelem tmp, tmp2;
limb x_equal, y_equal, z1_is_zero, z2_is_zero;
limb points_equal;
z1_is_zero = felem_is_zero(z1);
z2_is_zero = felem_is_zero(z2);
/* ftmp = z1z1 = z1**2 */
felem_square_reduce(ftmp, z1); /* ftmp[i] < 2^56 */
if (!mixed) {
/* ftmp2 = z2z2 = z2**2 */
felem_square_reduce(ftmp2, z2); /* ftmp2[i] < 2^56 */
/* u1 = ftmp3 = x1*z2z2 */
felem_mul_reduce(ftmp3, x1, ftmp2); /* ftmp3[i] < 2^56 */
/* ftmp5 = z1 + z2 */
felem_assign(ftmp5, z1); /* ftmp5[i] < 2^56 */
felem_sum64(ftmp5, z2); /* ftmp5[i] < 2^57 */
/* ftmp5 = (z1 + z2)**2 - z1z1 - z2z2 = 2*z1z2 */
felem_square(tmp, ftmp5); /* tmp[i] < 2^117 */
felem_diff_128_64(tmp, ftmp); /* tmp[i] < 2^117 + 2^64 + 2^48 */
felem_diff_128_64(tmp, ftmp2); /* tmp[i] < 2^117 + 2^65 + 2^49 */
felem_reduce(ftmp5, tmp); /* ftmp5[i] < 2^56 */
/* ftmp2 = z2 * z2z2 */
felem_mul_reduce(ftmp2, ftmp2, z2); /* ftmp2[i] < 2^56 */
/* s1 = ftmp6 = y1 * z2**3 */
felem_mul_reduce(ftmp6, y1, ftmp2); /* ftmp6[i] < 2^56 */
} else {
/*
* We'll assume z2 = 1 (special case z2 = 0 is handled later)
*/
/* u1 = ftmp3 = x1*z2z2 */
felem_assign(ftmp3, x1); /* ftmp3[i] < 2^56 */
/* ftmp5 = 2*z1z2 */
felem_scalar(ftmp5, z1, 2); /* ftmp5[i] < 2^57 */
/* s1 = ftmp6 = y1 * z2**3 */
felem_assign(ftmp6, y1); /* ftmp6[i] < 2^56 */
}
/* ftmp3[i] < 2^56, ftmp5[i] < 2^57, ftmp6[i] < 2^56 */
/* u2 = x2*z1z1 */
felem_mul(tmp, x2, ftmp); /* tmp[i] < 2^115 */
/* h = ftmp4 = u2 - u1 */
felem_diff_128_64(tmp, ftmp3); /* tmp[i] < 2^115 + 2^64 + 2^48 */
felem_reduce(ftmp4, tmp); /* ftmp[4] < 2^56 */
x_equal = felem_is_zero(ftmp4);
/* z_out = ftmp5 * h */
felem_mul_reduce(z_out, ftmp5, ftmp4); /* z_out[i] < 2^56 */
/* ftmp = z1 * z1z1 */
felem_mul_reduce(ftmp, ftmp, z1); /* ftmp[i] < 2^56 */
/* s2 = tmp = y2 * z1**3 */
felem_mul(tmp, y2, ftmp); /* tmp[i] < 2^115 */
/* r = ftmp5 = (s2 - s1)*2 */
felem_diff_128_64(tmp, ftmp6); /* tmp[i] < 2^115 + 2^64 + 2^48 */
felem_reduce(ftmp5, tmp); /* ftmp5[i] < 2^56 */
y_equal = felem_is_zero(ftmp5);
felem_scalar64(ftmp5, 2); /* ftmp5[i] < 2^57 */
/*
* The formulae are incorrect if the points are equal, in affine coordinates
* (X_1, Y_1) == (X_2, Y_2), so we check for this and do doubling if this
* happens.
*
* We use bitwise operations to avoid potential side-channels introduced by
* the short-circuiting behaviour of boolean operators.
*
* The special case of either point being the point at infinity (z1 and/or
* z2 are zero), is handled separately later on in this function, so we
* avoid jumping to point_double here in those special cases.
*
* Notice the comment below on the implications of this branching for timing
* leaks and why it is considered practically irrelevant.
*/
points_equal = (x_equal & y_equal & (~z1_is_zero) & (~z2_is_zero));
if (points_equal) {
/*
* This is obviously not constant-time but it will almost-never happen
* for ECDH / ECDSA.
*/
point_double(x3, y3, z3, x1, y1, z1);
return;
}
/* I = ftmp = (2h)**2 */
felem_assign(ftmp, ftmp4); /* ftmp[i] < 2^56 */
felem_scalar64(ftmp, 2); /* ftmp[i] < 2^57 */
felem_square_reduce(ftmp, ftmp); /* ftmp[i] < 2^56 */
/* J = ftmp2 = h * I */
felem_mul_reduce(ftmp2, ftmp4, ftmp); /* ftmp2[i] < 2^56 */
/* V = ftmp4 = U1 * I */
felem_mul_reduce(ftmp4, ftmp3, ftmp); /* ftmp4[i] < 2^56 */
/* x_out = r**2 - J - 2V */
felem_square(tmp, ftmp5); /* tmp[i] < 2^117 */
felem_diff_128_64(tmp, ftmp2); /* tmp[i] < 2^117 + 2^64 + 2^48 */
felem_assign(ftmp3, ftmp4); /* ftmp3[i] < 2^56 */
felem_scalar64(ftmp4, 2); /* ftmp4[i] < 2^57 */
felem_diff_128_64(tmp, ftmp4); /* tmp[i] < 2^117 + 2^65 + 2^49 */
felem_reduce(x_out, tmp); /* x_out[i] < 2^56 */
/* y_out = r(V-x_out) - 2 * s1 * J */
felem_diff64(ftmp3, x_out); /* ftmp3[i] < 2^60 + 2^56 + 2^44 */
felem_mul(tmp, ftmp5, ftmp3); /* tmp[i] < 2^116 */
felem_mul(tmp2, ftmp6, ftmp2); /* tmp2[i] < 2^115 */
felem_scalar128(tmp2, 2); /* tmp2[i] < 2^116 */
felem_diff128(tmp, tmp2); /* tmp[i] < 2^127 + 2^116 + 2^111 */
felem_reduce(y_out, tmp); /* y_out[i] < 2^56 */
copy_conditional(x_out, x2, z1_is_zero);
copy_conditional(x_out, x1, z2_is_zero);
copy_conditional(y_out, y2, z1_is_zero);
copy_conditional(y_out, y1, z2_is_zero);
copy_conditional(z_out, z2, z1_is_zero);
copy_conditional(z_out, z1, z2_is_zero);
felem_assign(x3, x_out);
felem_assign(y3, y_out);
felem_assign(z3, z_out);
}
/*-
* Base point pre computation
* --------------------------
*
* Two different sorts of precomputed tables are used in the following code.
* Each contain various points on the curve, where each point is three field
* elements (x, y, z).
*
* For the base point table, z is usually 1 (0 for the point at infinity).
* This table has 16 elements:
* index | bits | point
* ------+---------+------------------------------
* 0 | 0 0 0 0 | 0G
* 1 | 0 0 0 1 | 1G
* 2 | 0 0 1 0 | 2^95G
* 3 | 0 0 1 1 | (2^95 + 1)G
* 4 | 0 1 0 0 | 2^190G
* 5 | 0 1 0 1 | (2^190 + 1)G
* 6 | 0 1 1 0 | (2^190 + 2^95)G
* 7 | 0 1 1 1 | (2^190 + 2^95 + 1)G
* 8 | 1 0 0 0 | 2^285G
* 9 | 1 0 0 1 | (2^285 + 1)G
* 10 | 1 0 1 0 | (2^285 + 2^95)G
* 11 | 1 0 1 1 | (2^285 + 2^95 + 1)G
* 12 | 1 1 0 0 | (2^285 + 2^190)G
* 13 | 1 1 0 1 | (2^285 + 2^190 + 1)G
* 14 | 1 1 1 0 | (2^285 + 2^190 + 2^95)G
* 15 | 1 1 1 1 | (2^285 + 2^190 + 2^95 + 1)G
*
* The reason for this is so that we can clock bits into four different
* locations when doing simple scalar multiplies against the base point.
*
* Tables for other points have table[i] = iG for i in 0 .. 16.
*/
/* gmul is the table of precomputed base points */
static const felem gmul[16][3] = {
{{0, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0},
{0, 0, 0, 0, 0, 0, 0}},
{{0x00545e3872760ab7, 0x00f25dbf55296c3a, 0x00e082542a385502, 0x008ba79b9859f741,
0x0020ad746e1d3b62, 0x0005378eb1c71ef3, 0x0000aa87ca22be8b},
{0x00431d7c90ea0e5f, 0x00b1ce1d7e819d7a, 0x0013b5f0b8c00a60, 0x00289a147ce9da31,
0x0092dc29f8f41dbd, 0x002c6f5d9e98bf92, 0x00003617de4a9626},
{1, 0, 0, 0, 0, 0, 0}},
{{0x00024711cc902a90, 0x00acb2e579ab4fe1, 0x00af818a4b4d57b1, 0x00a17c7bec49c3de,
0x004280482d726a8b, 0x00128dd0f0a90f3b, 0x00004387c1c3fa3c},
{0x002ce76543cf5c3a, 0x00de6cee5ef58f0a, 0x00403e42fa561ca6, 0x00bc54d6f9cb9731,
0x007155f925fb4ff1, 0x004a9ce731b7b9bc, 0x00002609076bd7b2},
{1, 0, 0, 0, 0, 0, 0}},
{{0x00e74c9182f0251d, 0x0039bf54bb111974, 0x00b9d2f2eec511d2, 0x0036b1594eb3a6a4,
0x00ac3bb82d9d564b, 0x00f9313f4615a100, 0x00006716a9a91b10},
{0x0046698116e2f15c, 0x00f34347067d3d33, 0x008de4ccfdebd002, 0x00e838c6b8e8c97b,
0x006faf0798def346, 0x007349794a57563c, 0x00002629e7e6ad84},
{1, 0, 0, 0, 0, 0, 0}},
{{0x0075300e34fd163b, 0x0092e9db4e8d0ad3, 0x00254be9f625f760, 0x00512c518c72ae68,
0x009bfcf162bede5a, 0x00bf9341566ce311, 0x0000cd6175bd41cf},
{0x007dfe52af4ac70f, 0x0002159d2d5c4880, 0x00b504d16f0af8d0, 0x0014585e11f5e64c,
0x0089c6388e030967, 0x00ffb270cbfa5f71, 0x00009a15d92c3947},
{1, 0, 0, 0, 0, 0, 0}},
{{0x0033fc1278dc4fe5, 0x00d53088c2caa043, 0x0085558827e2db66, 0x00c192bef387b736,
0x00df6405a2225f2c, 0x0075205aa90fd91a, 0x0000137e3f12349d},
{0x00ce5b115efcb07e, 0x00abc3308410deeb, 0x005dc6fc1de39904, 0x00907c1c496f36b4,
0x0008e6ad3926cbe1, 0x00110747b787928c, 0x0000021b9162eb7e},
{1, 0, 0, 0, 0, 0, 0}},
{{0x008180042cfa26e1, 0x007b826a96254967, 0x0082473694d6b194, 0x007bd6880a45b589,
0x00c0a5097072d1a3, 0x0019186555e18b4e, 0x000020278190e5ca},
{0x00b4bef17de61ac0, 0x009535e3c38ed348, 0x002d4aa8e468ceab, 0x00ef40b431036ad3,
0x00defd52f4542857, 0x0086edbf98234266, 0x00002025b3a7814d},
{1, 0, 0, 0, 0, 0, 0}},
{{0x00b238aa97b886be, 0x00ef3192d6dd3a32, 0x0079f9e01fd62df8, 0x00742e890daba6c5,
0x008e5289144408ce, 0x0073bbcc8e0171a5, 0x0000c4fd329d3b52},
{0x00c6f64a15ee23e7, 0x00dcfb7b171cad8b, 0x00039f6cbd805867, 0x00de024e428d4562,
0x00be6a594d7c64c5, 0x0078467b70dbcd64, 0x0000251f2ed7079b},
{1, 0, 0, 0, 0, 0, 0}},
{{0x000e5cc25fc4b872, 0x005ebf10d31ef4e1, 0x0061e0ebd11e8256, 0x0076e026096f5a27,
0x0013e6fc44662e9a, 0x0042b00289d3597e, 0x000024f089170d88},
{0x001604d7e0effbe6, 0x0048d77cba64ec2c, 0x008166b16da19e36, 0x006b0d1a0f28c088,
0x000259fcd47754fd, 0x00cc643e4d725f9a, 0x00007b10f3c79c14},
{1, 0, 0, 0, 0, 0, 0}},
{{0x00430155e3b908af, 0x00b801e4fec25226, 0x00b0d4bcfe806d26, 0x009fc4014eb13d37,
0x0066c94e44ec07e8, 0x00d16adc03874ba2, 0x000030c917a0d2a7},
{0x00edac9e21eb891c, 0x00ef0fb768102eff, 0x00c088cef272a5f3, 0x00cbf782134e2964,
0x0001044a7ba9a0e3, 0x00e363f5b194cf3c, 0x00009ce85249e372},
{1, 0, 0, 0, 0, 0, 0}},
{{0x001dd492dda5a7eb, 0x008fd577be539fd1, 0x002ff4b25a5fc3f1, 0x0074a8a1b64df72f,
0x002ba3d8c204a76c, 0x009d5cff95c8235a, 0x0000e014b9406e0f},
{0x008c2e4dbfc98aba, 0x00f30bb89f1a1436, 0x00b46f7aea3e259c, 0x009224454ac02f54,
0x00906401f5645fa2, 0x003a1d1940eabc77, 0x00007c9351d680e6},
{1, 0, 0, 0, 0, 0, 0}},
{{0x005a35d872ef967c, 0x0049f1b7884e1987, 0x0059d46d7e31f552, 0x00ceb4869d2d0fb6,
0x00e8e89eee56802a, 0x0049d806a774aaf2, 0x0000147e2af0ae24},
{0x005fd1bd852c6e5e, 0x00b674b7b3de6885, 0x003b9ea5eb9b6c08, 0x005c9f03babf3ef7,
0x00605337fecab3c7, 0x009a3f85b11bbcc8, 0x0000455470f330ec},
{1, 0, 0, 0, 0, 0, 0}},
{{0x002197ff4d55498d, 0x00383e8916c2d8af, 0x00eb203f34d1c6d2, 0x0080367cbd11b542,
0x00769b3be864e4f5, 0x0081a8458521c7bb, 0x0000c531b34d3539},
{0x00e2a3d775fa2e13, 0x00534fc379573844, 0x00ff237d2a8db54a, 0x00d301b2335a8882,
0x000f75ea96103a80, 0x0018fecb3cdd96fa, 0x0000304bf61e94eb},
{1, 0, 0, 0, 0, 0, 0}},
{{0x00b2afc332a73dbd, 0x0029a0d5bb007bc5, 0x002d628eb210f577, 0x009f59a36dd05f50,
0x006d339de4eca613, 0x00c75a71addc86bc, 0x000060384c5ea93c},
{0x00aa9641c32a30b4, 0x00cc73ae8cce565d, 0x00ec911a4df07f61, 0x00aa4b762ea4b264,
0x0096d395bb393629, 0x004efacfb7632fe0, 0x00006f252f46fa3f},
{1, 0, 0, 0, 0, 0, 0}},
{{0x00567eec597c7af6, 0x0059ba6795204413, 0x00816d4e6f01196f, 0x004ae6b3eb57951d,
0x00420f5abdda2108, 0x003401d1f57ca9d9, 0x0000cf5837b0b67a},
{0x00eaa64b8aeeabf9, 0x00246ddf16bcb4de, 0x000e7e3c3aecd751, 0x0008449f04fed72e,
0x00307b67ccf09183, 0x0017108c3556b7b1, 0x0000229b2483b3bf},
{1, 0, 0, 0, 0, 0, 0}},
{{0x00e7c491a7bb78a1, 0x00eafddd1d3049ab, 0x00352c05e2bc7c98, 0x003d6880c165fa5c,
0x00b6ac61cc11c97d, 0x00beeb54fcf90ce5, 0x0000dc1f0b455edc},
{0x002db2e7aee34d60, 0x0073b5f415a2d8c0, 0x00dd84e4193e9a0c, 0x00d02d873467c572,
0x0018baaeda60aee5, 0x0013fb11d697c61e, 0x000083aafcc3a973},
{1, 0, 0, 0, 0, 0, 0}}
};
/*
* select_point selects the |idx|th point from a precomputation table and
* copies it to out.
*
* pre_comp below is of the size provided in |size|.
*/
static void select_point(const limb idx, unsigned int size,
const felem pre_comp[][3], felem out[3])
{
unsigned int i, j;
limb *outlimbs = &out[0][0];
memset(out, 0, sizeof(*out) * 3);
for (i = 0; i < size; i++) {
const limb *inlimbs = &pre_comp[i][0][0];
limb mask = i ^ idx;
mask |= mask >> 4;
mask |= mask >> 2;
mask |= mask >> 1;
mask &= 1;
mask--;
for (j = 0; j < NLIMBS * 3; j++)
outlimbs[j] |= inlimbs[j] & mask;
}
}
/* get_bit returns the |i|th bit in |in| */
static char get_bit(const felem_bytearray in, int i)
{
if (i < 0 || i >= 384)
return 0;
return (in[i >> 3] >> (i & 7)) & 1;
}
/*
* Interleaved point multiplication using precomputed point multiples: The
* small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], the scalars
* in scalars[]. If g_scalar is non-NULL, we also add this multiple of the
* generator, using certain (large) precomputed multiples in g_pre_comp.
* Output point (X, Y, Z) is stored in x_out, y_out, z_out
*/
static void batch_mul(felem x_out, felem y_out, felem z_out,
const felem_bytearray scalars[],
const unsigned int num_points, const u8 *g_scalar,
const int mixed, const felem pre_comp[][17][3],
const felem g_pre_comp[16][3])
{
int i, skip;
unsigned int num, gen_mul = (g_scalar != NULL);
felem nq[3], tmp[4];
limb bits;
u8 sign, digit;
/* set nq to the point at infinity */
memset(nq, 0, sizeof(nq));
/*
* Loop over all scalars msb-to-lsb, interleaving additions of multiples
* of the generator (last quarter of rounds) and additions of other
* points multiples (every 5th round).
*/
skip = 1; /* save two point operations in the first
* round */
for (i = (num_points ? 380 : 98); i >= 0; --i) {
/* double */
if (!skip)
point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
/* add multiples of the generator */
if (gen_mul && (i <= 98)) {
bits = get_bit(g_scalar, i + 285) << 3;
if (i < 95) {
bits |= get_bit(g_scalar, i + 190) << 2;
bits |= get_bit(g_scalar, i + 95) << 1;
bits |= get_bit(g_scalar, i);
}
/* select the point to add, in constant time */
select_point(bits, 16, g_pre_comp, tmp);
if (!skip) {
/* The 1 argument below is for "mixed" */
point_add(nq[0], nq[1], nq[2],
nq[0], nq[1], nq[2], 1,
tmp[0], tmp[1], tmp[2]);
} else {
memcpy(nq, tmp, 3 * sizeof(felem));
skip = 0;
}
}
/* do other additions every 5 doublings */
if (num_points && (i % 5 == 0)) {
/* loop over all scalars */
for (num = 0; num < num_points; ++num) {
bits = get_bit(scalars[num], i + 4) << 5;
bits |= get_bit(scalars[num], i + 3) << 4;
bits |= get_bit(scalars[num], i + 2) << 3;
bits |= get_bit(scalars[num], i + 1) << 2;
bits |= get_bit(scalars[num], i) << 1;
bits |= get_bit(scalars[num], i - 1);
ossl_ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits);
/*
* select the point to add or subtract, in constant time
*/
select_point(digit, 17, pre_comp[num], tmp);
felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative
* point */
copy_conditional(tmp[1], tmp[3], (-(limb) sign));
if (!skip) {
point_add(nq[0], nq[1], nq[2],
nq[0], nq[1], nq[2], mixed,
tmp[0], tmp[1], tmp[2]);
} else {
memcpy(nq, tmp, 3 * sizeof(felem));
skip = 0;
}
}
}
}
felem_assign(x_out, nq[0]);
felem_assign(y_out, nq[1]);
felem_assign(z_out, nq[2]);
}
/* Precomputation for the group generator. */
struct nistp384_pre_comp_st {
felem g_pre_comp[16][3];
CRYPTO_REF_COUNT references;
};
const EC_METHOD *ossl_ec_GFp_nistp384_method(void)
{
static const EC_METHOD ret = {
EC_FLAGS_DEFAULT_OCT,
NID_X9_62_prime_field,
ossl_ec_GFp_nistp384_group_init,
ossl_ec_GFp_simple_group_finish,
ossl_ec_GFp_simple_group_clear_finish,
ossl_ec_GFp_nist_group_copy,
ossl_ec_GFp_nistp384_group_set_curve,
ossl_ec_GFp_simple_group_get_curve,
ossl_ec_GFp_simple_group_get_degree,
ossl_ec_group_simple_order_bits,
ossl_ec_GFp_simple_group_check_discriminant,
ossl_ec_GFp_simple_point_init,
ossl_ec_GFp_simple_point_finish,
ossl_ec_GFp_simple_point_clear_finish,
ossl_ec_GFp_simple_point_copy,
ossl_ec_GFp_simple_point_set_to_infinity,
ossl_ec_GFp_simple_point_set_affine_coordinates,
ossl_ec_GFp_nistp384_point_get_affine_coordinates,
0, /* point_set_compressed_coordinates */
0, /* point2oct */
0, /* oct2point */
ossl_ec_GFp_simple_add,
ossl_ec_GFp_simple_dbl,
ossl_ec_GFp_simple_invert,
ossl_ec_GFp_simple_is_at_infinity,
ossl_ec_GFp_simple_is_on_curve,
ossl_ec_GFp_simple_cmp,
ossl_ec_GFp_simple_make_affine,
ossl_ec_GFp_simple_points_make_affine,
ossl_ec_GFp_nistp384_points_mul,
ossl_ec_GFp_nistp384_precompute_mult,
ossl_ec_GFp_nistp384_have_precompute_mult,
ossl_ec_GFp_nist_field_mul,
ossl_ec_GFp_nist_field_sqr,
0, /* field_div */
ossl_ec_GFp_simple_field_inv,
0, /* field_encode */
0, /* field_decode */
0, /* field_set_to_one */
ossl_ec_key_simple_priv2oct,
ossl_ec_key_simple_oct2priv,
0, /* set private */
ossl_ec_key_simple_generate_key,
ossl_ec_key_simple_check_key,
ossl_ec_key_simple_generate_public_key,
0, /* keycopy */
0, /* keyfinish */
ossl_ecdh_simple_compute_key,
ossl_ecdsa_simple_sign_setup,
ossl_ecdsa_simple_sign_sig,
ossl_ecdsa_simple_verify_sig,
0, /* field_inverse_mod_ord */
0, /* blind_coordinates */
0, /* ladder_pre */
0, /* ladder_step */
0 /* ladder_post */
};
return &ret;
}
/******************************************************************************/
/*
* FUNCTIONS TO MANAGE PRECOMPUTATION
*/
static NISTP384_PRE_COMP *nistp384_pre_comp_new(void)
{
NISTP384_PRE_COMP *ret = OPENSSL_zalloc(sizeof(*ret));
if (ret == NULL)
return ret;
if (!CRYPTO_NEW_REF(&ret->references, 1)) {
OPENSSL_free(ret);
return NULL;
}
return ret;
}
NISTP384_PRE_COMP *ossl_ec_nistp384_pre_comp_dup(NISTP384_PRE_COMP *p)
{
int i;
if (p != NULL)
CRYPTO_UP_REF(&p->references, &i);
return p;
}
void ossl_ec_nistp384_pre_comp_free(NISTP384_PRE_COMP *p)
{
int i;
if (p == NULL)
return;
CRYPTO_DOWN_REF(&p->references, &i);
REF_PRINT_COUNT("ossl_ec_nistp384", p);
if (i > 0)
return;
REF_ASSERT_ISNT(i < 0);
CRYPTO_FREE_REF(&p->references);
OPENSSL_free(p);
}
/******************************************************************************/
/*
* OPENSSL EC_METHOD FUNCTIONS
*/
int ossl_ec_GFp_nistp384_group_init(EC_GROUP *group)
{
int ret;
ret = ossl_ec_GFp_simple_group_init(group);
group->a_is_minus3 = 1;
return ret;
}
int ossl_ec_GFp_nistp384_group_set_curve(EC_GROUP *group, const BIGNUM *p,
const BIGNUM *a, const BIGNUM *b,
BN_CTX *ctx)
{
int ret = 0;
BIGNUM *curve_p, *curve_a, *curve_b;
#ifndef FIPS_MODULE
BN_CTX *new_ctx = NULL;
if (ctx == NULL)
ctx = new_ctx = BN_CTX_new();
#endif
if (ctx == NULL)
return 0;
BN_CTX_start(ctx);
curve_p = BN_CTX_get(ctx);
curve_a = BN_CTX_get(ctx);
curve_b = BN_CTX_get(ctx);
if (curve_b == NULL)
goto err;
BN_bin2bn(nistp384_curve_params[0], sizeof(felem_bytearray), curve_p);
BN_bin2bn(nistp384_curve_params[1], sizeof(felem_bytearray), curve_a);
BN_bin2bn(nistp384_curve_params[2], sizeof(felem_bytearray), curve_b);
if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) {
ERR_raise(ERR_LIB_EC, EC_R_WRONG_CURVE_PARAMETERS);
goto err;
}
group->field_mod_func = BN_nist_mod_384;
ret = ossl_ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
err:
BN_CTX_end(ctx);
#ifndef FIPS_MODULE
BN_CTX_free(new_ctx);
#endif
return ret;
}
/*
* Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') =
* (X/Z^2, Y/Z^3)
*/
int ossl_ec_GFp_nistp384_point_get_affine_coordinates(const EC_GROUP *group,
const EC_POINT *point,
BIGNUM *x, BIGNUM *y,
BN_CTX *ctx)
{
felem z1, z2, x_in, y_in, x_out, y_out;
widefelem tmp;
if (EC_POINT_is_at_infinity(group, point)) {
ERR_raise(ERR_LIB_EC, EC_R_POINT_AT_INFINITY);
return 0;
}
if ((!BN_to_felem(x_in, point->X)) || (!BN_to_felem(y_in, point->Y)) ||
(!BN_to_felem(z1, point->Z)))
return 0;
felem_inv(z2, z1);
felem_square(tmp, z2);
felem_reduce(z1, tmp);
felem_mul(tmp, x_in, z1);
felem_reduce(x_in, tmp);
felem_contract(x_out, x_in);
if (x != NULL) {
if (!felem_to_BN(x, x_out)) {
ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
return 0;
}
}
felem_mul(tmp, z1, z2);
felem_reduce(z1, tmp);
felem_mul(tmp, y_in, z1);
felem_reduce(y_in, tmp);
felem_contract(y_out, y_in);
if (y != NULL) {
if (!felem_to_BN(y, y_out)) {
ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
return 0;
}
}
return 1;
}
/* points below is of size |num|, and tmp_felems is of size |num+1/ */
static void make_points_affine(size_t num, felem points[][3],
felem tmp_felems[])
{
/*
* Runs in constant time, unless an input is the point at infinity (which
* normally shouldn't happen).
*/
ossl_ec_GFp_nistp_points_make_affine_internal(num,
points,
sizeof(felem),
tmp_felems,
(void (*)(void *))felem_one,
felem_is_zero_int,
(void (*)(void *, const void *))
felem_assign,
(void (*)(void *, const void *))
felem_square_reduce,
(void (*)(void *, const void *, const void*))
felem_mul_reduce,
(void (*)(void *, const void *))
felem_inv,
(void (*)(void *, const void *))
felem_contract);
}
/*
* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL
* values Result is stored in r (r can equal one of the inputs).
*/
int ossl_ec_GFp_nistp384_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 ret = 0;
int j;
int mixed = 0;
BIGNUM *x, *y, *z, *tmp_scalar;
felem_bytearray g_secret;
felem_bytearray *secrets = NULL;
felem (*pre_comp)[17][3] = NULL;
felem *tmp_felems = NULL;
unsigned int i;
int num_bytes;
int have_pre_comp = 0;
size_t num_points = num;
felem x_in, y_in, z_in, x_out, y_out, z_out;
NISTP384_PRE_COMP *pre = NULL;
felem(*g_pre_comp)[3] = NULL;
EC_POINT *generator = NULL;
const EC_POINT *p = NULL;
const BIGNUM *p_scalar = NULL;
BN_CTX_start(ctx);
x = BN_CTX_get(ctx);
y = BN_CTX_get(ctx);
z = BN_CTX_get(ctx);
tmp_scalar = BN_CTX_get(ctx);
if (tmp_scalar == NULL)
goto err;
if (scalar != NULL) {
pre = group->pre_comp.nistp384;
if (pre)
/* we have precomputation, try to use it */
g_pre_comp = &pre->g_pre_comp[0];
else
/* try to use the standard precomputation */
g_pre_comp = (felem(*)[3]) gmul;
generator = EC_POINT_new(group);
if (generator == NULL)
goto err;
/* get the generator from precomputation */
if (!felem_to_BN(x, g_pre_comp[1][0]) ||
!felem_to_BN(y, g_pre_comp[1][1]) ||
!felem_to_BN(z, g_pre_comp[1][2])) {
ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
goto err;
}
if (!ossl_ec_GFp_simple_set_Jprojective_coordinates_GFp(group,
generator,
x, y, z, ctx))
goto err;
if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
/* precomputation matches generator */
have_pre_comp = 1;
else
/*
* we don't have valid precomputation: treat the generator as a
* random point
*/
num_points++;
}
if (num_points > 0) {
if (num_points >= 2) {
/*
* unless we precompute multiples for just one point, converting
* those into affine form is time well spent
*/
mixed = 1;
}
secrets = OPENSSL_zalloc(sizeof(*secrets) * num_points);
pre_comp = OPENSSL_zalloc(sizeof(*pre_comp) * num_points);
if (mixed)
tmp_felems =
OPENSSL_malloc(sizeof(*tmp_felems) * (num_points * 17 + 1));
if ((secrets == NULL) || (pre_comp == NULL)
|| (mixed && (tmp_felems == NULL)))
goto err;
/*
* we treat NULL scalars as 0, and NULL points as points at infinity,
* i.e., they contribute nothing to the linear combination
*/
for (i = 0; i < num_points; ++i) {
if (i == num) {
/*
* we didn't have a valid precomputation, so we pick the
* generator
*/
p = EC_GROUP_get0_generator(group);
p_scalar = scalar;
} else {
/* the i^th point */
p = points[i];
p_scalar = scalars[i];
}
if (p_scalar != NULL && p != NULL) {
/* reduce scalar to 0 <= scalar < 2^384 */
if ((BN_num_bits(p_scalar) > 384)
|| (BN_is_negative(p_scalar))) {
/*
* this is an unusual input, and we don't guarantee
* constant-timeness
*/
if (!BN_nnmod(tmp_scalar, p_scalar, group->order, ctx)) {
ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
goto err;
}
num_bytes = BN_bn2lebinpad(tmp_scalar,
secrets[i], sizeof(secrets[i]));
} else {
num_bytes = BN_bn2lebinpad(p_scalar,
secrets[i], sizeof(secrets[i]));
}
if (num_bytes < 0) {
ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
goto err;
}
/* precompute multiples */
if ((!BN_to_felem(x_out, p->X)) ||
(!BN_to_felem(y_out, p->Y)) ||
(!BN_to_felem(z_out, p->Z)))
goto err;
memcpy(pre_comp[i][1][0], x_out, sizeof(felem));
memcpy(pre_comp[i][1][1], y_out, sizeof(felem));
memcpy(pre_comp[i][1][2], z_out, sizeof(felem));
for (j = 2; j <= 16; ++j) {
if (j & 1) {
point_add(pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], 0,
pre_comp[i][j - 1][0], pre_comp[i][j - 1][1], pre_comp[i][j - 1][2]);
} else {
point_double(pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
pre_comp[i][j / 2][0], pre_comp[i][j / 2][1], pre_comp[i][j / 2][2]);
}
}
}
}
if (mixed)
make_points_affine(num_points * 17, pre_comp[0], tmp_felems);
}
/* the scalar for the generator */
if (scalar != NULL && have_pre_comp) {
memset(g_secret, 0, sizeof(g_secret));
/* reduce scalar to 0 <= scalar < 2^384 */
if ((BN_num_bits(scalar) > 384) || (BN_is_negative(scalar))) {
/*
* this is an unusual input, and we don't guarantee
* constant-timeness
*/
if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
goto err;
}
num_bytes = BN_bn2lebinpad(tmp_scalar, g_secret, sizeof(g_secret));
} else {
num_bytes = BN_bn2lebinpad(scalar, g_secret, sizeof(g_secret));
}
/* do the multiplication with generator precomputation */
batch_mul(x_out, y_out, z_out,
(const felem_bytearray(*))secrets, num_points,
g_secret,
mixed, (const felem(*)[17][3])pre_comp,
(const felem(*)[3])g_pre_comp);
} else {
/* do the multiplication without generator precomputation */
batch_mul(x_out, y_out, z_out,
(const felem_bytearray(*))secrets, num_points,
NULL, mixed, (const felem(*)[17][3])pre_comp, NULL);
}
/* reduce the output to its unique minimal representation */
felem_contract(x_in, x_out);
felem_contract(y_in, y_out);
felem_contract(z_in, z_out);
if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) ||
(!felem_to_BN(z, z_in))) {
ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
goto err;
}
ret = ossl_ec_GFp_simple_set_Jprojective_coordinates_GFp(group, r, x, y, z,
ctx);
err:
BN_CTX_end(ctx);
EC_POINT_free(generator);
OPENSSL_free(secrets);
OPENSSL_free(pre_comp);
OPENSSL_free(tmp_felems);
return ret;
}
int ossl_ec_GFp_nistp384_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
{
int ret = 0;
NISTP384_PRE_COMP *pre = NULL;
int i, j;
BIGNUM *x, *y;
EC_POINT *generator = NULL;
felem tmp_felems[16];
#ifndef FIPS_MODULE
BN_CTX *new_ctx = NULL;
#endif
/* throw away old precomputation */
EC_pre_comp_free(group);
#ifndef FIPS_MODULE
if (ctx == NULL)
ctx = new_ctx = BN_CTX_new();
#endif
if (ctx == NULL)
return 0;
BN_CTX_start(ctx);
x = BN_CTX_get(ctx);
y = BN_CTX_get(ctx);
if (y == NULL)
goto err;
/* get the generator */
if (group->generator == NULL)
goto err;
generator = EC_POINT_new(group);
if (generator == NULL)
goto err;
BN_bin2bn(nistp384_curve_params[3], sizeof(felem_bytearray), x);
BN_bin2bn(nistp384_curve_params[4], sizeof(felem_bytearray), y);
if (!EC_POINT_set_affine_coordinates(group, generator, x, y, ctx))
goto err;
if ((pre = nistp384_pre_comp_new()) == NULL)
goto err;
/*
* if the generator is the standard one, use built-in precomputation
*/
if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) {
memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
goto done;
}
if ((!BN_to_felem(pre->g_pre_comp[1][0], group->generator->X)) ||
(!BN_to_felem(pre->g_pre_comp[1][1], group->generator->Y)) ||
(!BN_to_felem(pre->g_pre_comp[1][2], group->generator->Z)))
goto err;
/* compute 2^95*G, 2^190*G, 2^285*G */
for (i = 1; i <= 4; i <<= 1) {
point_double(pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2],
pre->g_pre_comp[i][0], pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]);
for (j = 0; j < 94; ++j) {
point_double(pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2],
pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2]);
}
}
/* g_pre_comp[0] is the point at infinity */
memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0]));
/* the remaining multiples */
/* 2^95*G + 2^190*G */
point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1], pre->g_pre_comp[6][2],
pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], pre->g_pre_comp[4][2], 0,
pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], pre->g_pre_comp[2][2]);
/* 2^95*G + 2^285*G */
point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1], pre->g_pre_comp[10][2],
pre->g_pre_comp[8][0], pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], 0,
pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], pre->g_pre_comp[2][2]);
/* 2^190*G + 2^285*G */
point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1], pre->g_pre_comp[12][2],
pre->g_pre_comp[8][0], pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], 0,
pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], pre->g_pre_comp[4][2]);
/* 2^95*G + 2^190*G + 2^285*G */
point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1], pre->g_pre_comp[14][2],
pre->g_pre_comp[12][0], pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], 0,
pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], pre->g_pre_comp[2][2]);
for (i = 1; i < 8; ++i) {
/* odd multiples: add G */
point_add(pre->g_pre_comp[2 * i + 1][0], pre->g_pre_comp[2 * i + 1][1], pre->g_pre_comp[2 * i + 1][2],
pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2], 0,
pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], pre->g_pre_comp[1][2]);
}
make_points_affine(15, &(pre->g_pre_comp[1]), tmp_felems);
done:
SETPRECOMP(group, nistp384, pre);
ret = 1;
pre = NULL;
err:
BN_CTX_end(ctx);
EC_POINT_free(generator);
#ifndef FIPS_MODULE
BN_CTX_free(new_ctx);
#endif
ossl_ec_nistp384_pre_comp_free(pre);
return ret;
}
int ossl_ec_GFp_nistp384_have_precompute_mult(const EC_GROUP *group)
{
return HAVEPRECOMP(group, nistp384);
}
