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ec_mult.c
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ec_mult.c
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/* crypto/ec/ec_mult.c */
/*
* Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
*/
/* ====================================================================
* Copyright (c) 1998-2019 The OpenSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. All advertising materials mentioning features or use of this
* software must display the following acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
*
* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
* endorse or promote products derived from this software without
* prior written permission. For written permission, please contact
* openssl-core@openssl.org.
*
* 5. Products derived from this software may not be called "OpenSSL"
* nor may "OpenSSL" appear in their names without prior written
* permission of the OpenSSL Project.
*
* 6. Redistributions of any form whatsoever must retain the following
* acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
*
* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
* ====================================================================
*
* This product includes cryptographic software written by Eric Young
* (eay@cryptsoft.com). This product includes software written by Tim
* Hudson (tjh@cryptsoft.com).
*
*/
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
* Portions of this software developed by SUN MICROSYSTEMS, INC.,
* and contributed to the OpenSSL project.
*/
#include <string.h>
#include <openssl/err.h>
#include "ec_lcl.h"
/*
* This file implements the wNAF-based interleaving multi-exponentiation method
* Formerly at:
* http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp
* You might now find it here:
* http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13
* http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf
* For multiplication with precomputation, we use wNAF splitting, formerly at:
* http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp
*/
/* structure for precomputed multiples of the generator */
typedef struct ec_pre_comp_st {
const EC_GROUP *group; /* parent EC_GROUP object */
size_t blocksize; /* block size for wNAF splitting */
size_t numblocks; /* max. number of blocks for which we have
* precomputation */
size_t w; /* window size */
EC_POINT **points; /* array with pre-calculated multiples of
* generator: 'num' pointers to EC_POINT
* objects followed by a NULL */
size_t num; /* numblocks * 2^(w-1) */
int references;
} EC_PRE_COMP;
/* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
static void *ec_pre_comp_dup(void *);
static void ec_pre_comp_free(void *);
static void ec_pre_comp_clear_free(void *);
static EC_PRE_COMP *ec_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_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
return ret;
}
ret->group = group;
ret->blocksize = 8; /* default */
ret->numblocks = 0;
ret->w = 4; /* default */
ret->points = NULL;
ret->num = 0;
ret->references = 1;
return ret;
}
static void *ec_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 ec_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->points) {
EC_POINT **p;
for (p = pre->points; *p != NULL; p++)
EC_POINT_free(*p);
OPENSSL_free(pre->points);
}
OPENSSL_free(pre);
}
static void ec_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->points) {
EC_POINT **p;
for (p = pre->points; *p != NULL; p++) {
EC_POINT_clear_free(*p);
OPENSSL_cleanse(p, sizeof(*p));
}
OPENSSL_free(pre->points);
}
OPENSSL_cleanse(pre, sizeof(*pre));
OPENSSL_free(pre);
}
/*-
* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
* This is an array r[] of values that are either zero or odd with an
* absolute value less than 2^w satisfying
* scalar = \sum_j r[j]*2^j
* where at most one of any w+1 consecutive digits is non-zero
* with the exception that the most significant digit may be only
* w-1 zeros away from that next non-zero digit.
*/
static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
{
int window_val;
int ok = 0;
signed char *r = NULL;
int sign = 1;
int bit, next_bit, mask;
size_t len = 0, j;
if (BN_is_zero(scalar)) {
r = OPENSSL_malloc(1);
if (!r) {
ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
goto err;
}
r[0] = 0;
*ret_len = 1;
return r;
}
if (w <= 0 || w > 7) { /* 'signed char' can represent integers with
* absolute values less than 2^7 */
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
bit = 1 << w; /* at most 128 */
next_bit = bit << 1; /* at most 256 */
mask = next_bit - 1; /* at most 255 */
if (BN_is_negative(scalar)) {
sign = -1;
}
if (scalar->d == NULL || scalar->top == 0) {
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
len = BN_num_bits(scalar);
r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer
* than binary representation (*ret_len will
* be set to the actual length, i.e. at most
* BN_num_bits(scalar) + 1) */
if (r == NULL) {
ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
goto err;
}
window_val = scalar->d[0] & mask;
j = 0;
while ((window_val != 0) || (j + w + 1 < len)) { /* if j+w+1 >= len,
* window_val will not
* increase */
int digit = 0;
/* 0 <= window_val <= 2^(w+1) */
if (window_val & 1) {
/* 0 < window_val < 2^(w+1) */
if (window_val & bit) {
digit = window_val - next_bit; /* -2^w < digit < 0 */
#if 1 /* modified wNAF */
if (j + w + 1 >= len) {
/*
* special case for generating modified wNAFs: no new
* bits will be added into window_val, so using a
* positive digit here will decrease the total length of
* the representation
*/
digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
}
#endif
} else {
digit = window_val; /* 0 < digit < 2^w */
}
if (digit <= -bit || digit >= bit || !(digit & 1)) {
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
window_val -= digit;
/*
* now window_val is 0 or 2^(w+1) in standard wNAF generation;
* for modified window NAFs, it may also be 2^w
*/
if (window_val != 0 && window_val != next_bit
&& window_val != bit) {
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
}
r[j++] = sign * digit;
window_val >>= 1;
window_val += bit * BN_is_bit_set(scalar, j + w);
if (window_val > next_bit) {
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
}
if (j > len + 1) {
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
len = j;
ok = 1;
err:
if (!ok) {
OPENSSL_free(r);
r = NULL;
}
if (ok)
*ret_len = len;
return r;
}
#define EC_POINT_BN_set_flags(P, flags) do { \
BN_set_flags(&(P)->X, (flags)); \
BN_set_flags(&(P)->Y, (flags)); \
BN_set_flags(&(P)->Z, (flags)); \
} while(0)
/*-
* This functions computes (in constant time) a point multiplication over the
* EC group.
*
* At a high level, it is Montgomery ladder with conditional swaps.
*
* It performs either a fixed scalar point multiplication
* (scalar * generator)
* when point is NULL, or a generic scalar point multiplication
* (scalar * point)
* when point is not NULL.
*
* scalar should be in the range [0,n) otherwise all constant time bets are off.
*
* NB: This says nothing about EC_POINT_add and EC_POINT_dbl,
* which of course are not constant time themselves.
*
* The product is stored in r.
*
* Returns 1 on success, 0 otherwise.
*/
static int ec_mul_consttime(const EC_GROUP *group, EC_POINT *r,
const BIGNUM *scalar, const EC_POINT *point,
BN_CTX *ctx)
{
int i, cardinality_bits, group_top, kbit, pbit, Z_is_one;
EC_POINT *s = NULL;
BIGNUM *k = NULL;
BIGNUM *lambda = NULL;
BIGNUM *cardinality = NULL;
BN_CTX *new_ctx = NULL;
int ret = 0;
if (ctx == NULL && (ctx = new_ctx = BN_CTX_new()) == NULL)
return 0;
BN_CTX_start(ctx);
s = EC_POINT_new(group);
if (s == NULL)
goto err;
if (point == NULL) {
if (!EC_POINT_copy(s, group->generator))
goto err;
} else {
if (!EC_POINT_copy(s, point))
goto err;
}
EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME);
cardinality = BN_CTX_get(ctx);
lambda = BN_CTX_get(ctx);
k = BN_CTX_get(ctx);
if (k == NULL || !BN_mul(cardinality, &group->order, &group->cofactor, ctx))
goto err;
/*
* Group cardinalities are often on a word boundary.
* So when we pad the scalar, some timing diff might
* pop if it needs to be expanded due to carries.
* So expand ahead of time.
*/
cardinality_bits = BN_num_bits(cardinality);
group_top = cardinality->top;
if ((bn_wexpand(k, group_top + 2) == NULL)
|| (bn_wexpand(lambda, group_top + 2) == NULL))
goto err;
if (!BN_copy(k, scalar))
goto err;
BN_set_flags(k, BN_FLG_CONSTTIME);
if ((BN_num_bits(k) > cardinality_bits) || (BN_is_negative(k))) {
/*-
* this is an unusual input, and we don't guarantee
* constant-timeness
*/
if (!BN_nnmod(k, k, cardinality, ctx))
goto err;
}
if (!BN_add(lambda, k, cardinality))
goto err;
BN_set_flags(lambda, BN_FLG_CONSTTIME);
if (!BN_add(k, lambda, cardinality))
goto err;
/*
* lambda := scalar + cardinality
* k := scalar + 2*cardinality
*/
kbit = BN_is_bit_set(lambda, cardinality_bits);
BN_consttime_swap(kbit, k, lambda, group_top + 2);
group_top = group->field.top;
if ((bn_wexpand(&s->X, group_top) == NULL)
|| (bn_wexpand(&s->Y, group_top) == NULL)
|| (bn_wexpand(&s->Z, group_top) == NULL)
|| (bn_wexpand(&r->X, group_top) == NULL)
|| (bn_wexpand(&r->Y, group_top) == NULL)
|| (bn_wexpand(&r->Z, group_top) == NULL))
goto err;
if (group->meth->field_type == NID_X9_62_prime_field) {
/*
* Apply blinding independently to r and s: use point r as temporary
* variable.
*
* Blinding requires using a projective representation, and later we
* implement the ladder step using EC_POINT_add() and EC_POINT_dbl():
* this requires EC_METHODs that support projective coordinates in their
* point addition and point doubling implementations.
*
* All the built-in EC_METHODs for prime curves at the moment satisfy
* this condition, while the EC_METHOD for binary curves does not.
*
* This is why we check for a prime field to apply blinding.
*/
/* first randomize r->Z to blind s. */
do {
if (!BN_rand_range(&r->Z, &group->field)) {
ECerr(EC_F_EC_MUL_CONSTTIME, ERR_R_BN_LIB);
goto err;
}
} while (BN_is_zero(&r->Z));
/* convert r->Z to the correct field representation. */
if (group->meth->field_encode != NULL
&& !group->meth->field_encode(group, &r->Z, &r->Z, ctx)) {
goto err;
}
/* scale s->X and s->Y by r->Z^2 and r->Z^3, respectively. */
if (!group->meth->field_sqr(group, &r->X, &r->Z, ctx)
|| !group->meth->field_mul(group, &r->Y, &r->X, &r->Z, ctx)) {
goto err;
}
if (!group->meth->field_mul(group, &s->X, &s->X, &r->X, ctx)
|| !group->meth->field_mul(group, &s->Y, &s->Y, &r->Y, ctx)
|| !group->meth->field_mul(group, &s->Z, &s->Z, &r->Z, ctx)) {
goto err;
}
/* mark the flag in s to full projective coordinates. */
s->Z_is_one = 0;
/* blinding: now rerandomize r->Z to make r a blinded copy of s. */
do {
if (!BN_rand_range(&r->Z, &group->field)) {
ECerr(EC_F_EC_MUL_CONSTTIME, ERR_R_BN_LIB);
goto err;
}
} while (BN_is_zero(&r->Z));
/* convert r->Z to the correct field representation. */
if (group->meth->field_encode != NULL
&& !group->meth->field_encode(group, &r->Z, &r->Z, ctx)) {
goto err;
}
/* scale r->X and r->Y by r->Z^2 and r->Z^3, respectively. */
if (!group->meth->field_sqr(group, &r->X, &r->Z, ctx)
|| !group->meth->field_mul(group, &r->Y, &r->X, &r->Z, ctx)) {
goto err;
}
if (!group->meth->field_mul(group, &r->X, &s->X, &r->X, ctx)
|| !group->meth->field_mul(group, &r->Y, &s->Y, &r->Y, ctx)
|| !group->meth->field_mul(group, &r->Z, &s->Z, &r->Z, ctx)) {
goto err;
}
/* mark the flag in s to full projective coordinates. */
r->Z_is_one = 0;
} else {
/* top bit is a 1, in a fixed pos; binary curves are not blinded here */
if (!EC_POINT_copy(r, s))
goto err;
}
EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);
if (!EC_POINT_dbl(group, s, s, ctx))
goto err;
pbit = 0;
#define EC_POINT_CSWAP(c, a, b, w, t) do { \
BN_consttime_swap(c, &(a)->X, &(b)->X, w); \
BN_consttime_swap(c, &(a)->Y, &(b)->Y, w); \
BN_consttime_swap(c, &(a)->Z, &(b)->Z, w); \
t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
(a)->Z_is_one ^= (t); \
(b)->Z_is_one ^= (t); \
} while(0)
/*-
* The ladder step, with branches, is
*
* k[i] == 0: S = add(R, S), R = dbl(R)
* k[i] == 1: R = add(S, R), S = dbl(S)
*
* Swapping R, S conditionally on k[i] leaves you with state
*
* k[i] == 0: T, U = R, S
* k[i] == 1: T, U = S, R
*
* Then perform the ECC ops.
*
* U = add(T, U)
* T = dbl(T)
*
* Which leaves you with state
*
* k[i] == 0: U = add(R, S), T = dbl(R)
* k[i] == 1: U = add(S, R), T = dbl(S)
*
* Swapping T, U conditionally on k[i] leaves you with state
*
* k[i] == 0: R, S = T, U
* k[i] == 1: R, S = U, T
*
* Which leaves you with state
*
* k[i] == 0: S = add(R, S), R = dbl(R)
* k[i] == 1: R = add(S, R), S = dbl(S)
*
* So we get the same logic, but instead of a branch it's a
* conditional swap, followed by ECC ops, then another conditional swap.
*
* Optimization: The end of iteration i and start of i-1 looks like
*
* ...
* CSWAP(k[i], R, S)
* ECC
* CSWAP(k[i], R, S)
* (next iteration)
* CSWAP(k[i-1], R, S)
* ECC
* CSWAP(k[i-1], R, S)
* ...
*
* So instead of two contiguous swaps, you can merge the condition
* bits and do a single swap.
*
* k[i] k[i-1] Outcome
* 0 0 No Swap
* 0 1 Swap
* 1 0 Swap
* 1 1 No Swap
*
* This is XOR. pbit tracks the previous bit of k.
*/
for (i = cardinality_bits - 1; i >= 0; i--) {
kbit = BN_is_bit_set(k, i) ^ pbit;
EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
if (!EC_POINT_add(group, s, r, s, ctx))
goto err;
if (!EC_POINT_dbl(group, r, r, ctx))
goto err;
/*
* pbit logic merges this cswap with that of the
* next iteration
*/
pbit ^= kbit;
}
/* one final cswap to move the right value into r */
EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
#undef EC_POINT_CSWAP
ret = 1;
err:
EC_POINT_clear_free(s);
BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
return ret;
}
#undef EC_POINT_BN_set_flags
/*
* TODO: table should be optimised for the wNAF-based implementation,
* sometimes smaller windows will give better performance (thus the
* boundaries should be increased)
*/
#define EC_window_bits_for_scalar_size(b) \
((size_t) \
((b) >= 2000 ? 6 : \
(b) >= 800 ? 5 : \
(b) >= 300 ? 4 : \
(b) >= 70 ? 3 : \
(b) >= 20 ? 2 : \
1))
/*-
* Compute
* \sum scalars[i]*points[i],
* also including
* scalar*generator
* in the addition if scalar != NULL
*/
int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
BN_CTX *ctx)
{
BN_CTX *new_ctx = NULL;
const EC_POINT *generator = NULL;
EC_POINT *tmp = NULL;
size_t totalnum;
size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
size_t pre_points_per_block = 0;
size_t i, j;
int k;
int r_is_inverted = 0;
int r_is_at_infinity = 1;
size_t *wsize = NULL; /* individual window sizes */
signed char **wNAF = NULL; /* individual wNAFs */
size_t *wNAF_len = NULL;
size_t max_len = 0;
size_t num_val;
EC_POINT **val = NULL; /* precomputation */
EC_POINT **v;
EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
* 'pre_comp->points' */
const EC_PRE_COMP *pre_comp = NULL;
int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be
* treated like other scalars, i.e.
* precomputation is not available */
int ret = 0;
if (group->meth != r->meth) {
ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
return 0;
}
if ((scalar == NULL) && (num == 0)) {
return EC_POINT_set_to_infinity(group, r);
}
if (!BN_is_zero(&group->order) && !BN_is_zero(&group->cofactor)) {
/*-
* Handle the common cases where the scalar is secret, enforcing a constant
* time scalar multiplication algorithm.
*/
if ((scalar != NULL) && (num == 0)) {
/*-
* In this case we want to compute scalar * GeneratorPoint: this
* codepath is reached most prominently by (ephemeral) key generation
* of EC cryptosystems (i.e. ECDSA keygen and sign setup, ECDH
* keygen/first half), where the scalar is always secret. This is why
* we ignore if BN_FLG_CONSTTIME is actually set and we always call the
* constant time version.
*/
return ec_mul_consttime(group, r, scalar, NULL, ctx);
}
if ((scalar == NULL) && (num == 1)) {
/*-
* In this case we want to compute scalar * GenericPoint: this codepath
* is reached most prominently by the second half of ECDH, where the
* secret scalar is multiplied by the peer's public point. To protect
* the secret scalar, we ignore if BN_FLG_CONSTTIME is actually set and
* we always call the constant time version.
*/
return ec_mul_consttime(group, r, scalars[0], points[0], ctx);
}
}
for (i = 0; i < num; i++) {
if (group->meth != points[i]->meth) {
ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
return 0;
}
}
if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL)
goto err;
}
if (scalar != NULL) {
generator = EC_GROUP_get0_generator(group);
if (generator == NULL) {
ECerr(EC_F_EC_WNAF_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, ec_pre_comp_dup,
ec_pre_comp_free, ec_pre_comp_clear_free);
if (pre_comp && pre_comp->numblocks
&& (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
0)) {
blocksize = pre_comp->blocksize;
/*
* determine maximum number of blocks that wNAF splitting may
* yield (NB: maximum wNAF length is bit length plus one)
*/
numblocks = (BN_num_bits(scalar) / blocksize) + 1;
/*
* we cannot use more blocks than we have precomputation for
*/
if (numblocks > pre_comp->numblocks)
numblocks = pre_comp->numblocks;
pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
/* check that pre_comp looks sane */
if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
goto err;
}
} else {
/* can't use precomputation */
pre_comp = NULL;
numblocks = 1;
num_scalar = 1; /* treat 'scalar' like 'num'-th element of
* 'scalars' */
}
}
totalnum = num + numblocks;
wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0]));
wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0]));
/* include space for pivot */
wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0]));
val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0]));
/* Ensure wNAF is initialised in case we end up going to err */
if (wNAF)
wNAF[0] = NULL; /* preliminary pivot */
if (!wsize || !wNAF_len || !wNAF || !val_sub) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
goto err;
}
/*
* num_val will be the total number of temporarily precomputed points
*/
num_val = 0;
for (i = 0; i < num + num_scalar; i++) {
size_t bits;
bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
wsize[i] = EC_window_bits_for_scalar_size(bits);
num_val += (size_t)1 << (wsize[i] - 1);
wNAF[i + 1] = NULL; /* make sure we always have a pivot */
wNAF[i] =
compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
&wNAF_len[i]);
if (wNAF[i] == NULL)
goto err;
if (wNAF_len[i] > max_len)
max_len = wNAF_len[i];
}
if (numblocks) {
/* we go here iff scalar != NULL */
if (pre_comp == NULL) {
if (num_scalar != 1) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
goto err;
}
/* we have already generated a wNAF for 'scalar' */
} else {
signed char *tmp_wNAF = NULL;
size_t tmp_len = 0;
if (num_scalar != 0) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
goto err;
}
/*
* use the window size for which we have precomputation
*/
wsize[num] = pre_comp->w;
tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
if (!tmp_wNAF)
goto err;
if (tmp_len <= max_len) {
/*
* One of the other wNAFs is at least as long as the wNAF
* belonging to the generator, so wNAF splitting will not buy
* us anything.
*/
numblocks = 1;
totalnum = num + 1; /* don't use wNAF splitting */
wNAF[num] = tmp_wNAF;
wNAF[num + 1] = NULL;
wNAF_len[num] = tmp_len;
if (tmp_len > max_len)
max_len = tmp_len;
/*
* pre_comp->points starts with the points that we need here:
*/
val_sub[num] = pre_comp->points;
} else {
/*
* don't include tmp_wNAF directly into wNAF array - use wNAF
* splitting and include the blocks
*/
signed char *pp;
EC_POINT **tmp_points;
if (tmp_len < numblocks * blocksize) {
/*
* possibly we can do with fewer blocks than estimated
*/
numblocks = (tmp_len + blocksize - 1) / blocksize;
if (numblocks > pre_comp->numblocks) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
goto err;
}
totalnum = num + numblocks;
}
/* split wNAF in 'numblocks' parts */
pp = tmp_wNAF;
tmp_points = pre_comp->points;
for (i = num; i < totalnum; i++) {
if (i < totalnum - 1) {
wNAF_len[i] = blocksize;
if (tmp_len < blocksize) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
goto err;
}
tmp_len -= blocksize;
} else
/*
* last block gets whatever is left (this could be
* more or less than 'blocksize'!)
*/
wNAF_len[i] = tmp_len;
wNAF[i + 1] = NULL;
wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
if (wNAF[i] == NULL) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
OPENSSL_free(tmp_wNAF);
goto err;
}
memcpy(wNAF[i], pp, wNAF_len[i]);
if (wNAF_len[i] > max_len)
max_len = wNAF_len[i];
if (*tmp_points == NULL) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
OPENSSL_free(tmp_wNAF);
goto err;
}
val_sub[i] = tmp_points;
tmp_points += pre_points_per_block;
pp += blocksize;
}
OPENSSL_free(tmp_wNAF);
}
}
}
/*
* All points we precompute now go into a single array 'val'.
* 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
* subarray of 'pre_comp->points' if we already have precomputation.
*/
val = OPENSSL_malloc((num_val + 1) * sizeof(val[0]));
if (val == NULL) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
goto err;
}
val[num_val] = NULL; /* pivot element */
/* allocate points for precomputation */
v = val;
for (i = 0; i < num + num_scalar; i++) {
val_sub[i] = v;
for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
*v = EC_POINT_new(group);
if (*v == NULL)
goto err;
v++;
}
}
if (!(v == val + num_val)) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
goto err;
}
if (!(tmp = EC_POINT_new(group)))
goto err;
/*-
* prepare precomputed values:
* val_sub[i][0] := points[i]
* val_sub[i][1] := 3 * points[i]
* val_sub[i][2] := 5 * points[i]
* ...
*/
for (i = 0; i < num + num_scalar; i++) {
if (i < num) {
if (!EC_POINT_copy(val_sub[i][0], points[i]))
goto err;
} else {
if (!EC_POINT_copy(val_sub[i][0], generator))
goto err;
}
if (wsize[i] > 1) {
if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
goto err;
for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
if (!EC_POINT_add
(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
goto err;
}
}
}
#if 1 /* optional; EC_window_bits_for_scalar_size
* assumes we do this step */
if (!EC_POINTs_make_affine(group, num_val, val, ctx))
goto err;
#endif
r_is_at_infinity = 1;
for (k = max_len - 1; k >= 0; k--) {
if (!r_is_at_infinity) {
if (!EC_POINT_dbl(group, r, r, ctx))
goto err;
}
for (i = 0; i < totalnum; i++) {
if (wNAF_len[i] > (size_t)k) {
int digit = wNAF[i][k];
int is_neg;
if (digit) {
is_neg = digit < 0;
if (is_neg)
digit = -digit;
if (is_neg != r_is_inverted) {
if (!r_is_at_infinity) {
if (!EC_POINT_invert(group, r, ctx))
goto err;
}
r_is_inverted = !r_is_inverted;
}
/* digit > 0 */
if (r_is_at_infinity) {
if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
goto err;
r_is_at_infinity = 0;
} else {
if (!EC_POINT_add
(group, r, r, val_sub[i][digit >> 1], ctx))
goto err;
}
}
}
}
}