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openssl/crypto/bn/bn_lib.c
David Benjamin 972c87dfc7 Make BN_num_bits_word constant-time. 
(This patch was written by Andy Polyakov. I only wrote the commit
message. Mistakes in the analysis are my fault.)

BN_num_bits, by way of BN_num_bits_word, currently leaks the
most-significant word of its argument via branching and memory access
pattern.

BN_num_bits is called on RSA prime factors in various places. These have
public bit lengths, but all bits beyond the high bit are secret. This
fully resolves those cases.

There are a few places where BN_num_bits is called on an input where the
bit length is also secret. This does *not* fully resolve those cases as
we still only look at the top word. Today, that is guaranteed to be
non-zero, but only because of the long-standing bn_correct_top timing
leak. Once that is fixed, a constant-time BN_num_bits on such inputs
must count bits on each word.

Instead, those cases should not call BN_num_bits at all. In particular,
BN_mod_exp_mont_consttime uses the exponent bit width to pick windows,
but it should be using the maximum bit width. The next patch will fix
this.

Thanks to Dinghao Wu, Danfeng Zhang, Shuai Wang, Pei Wang, and Xiao Liu
for reporting this issue.

Reviewed-by: Paul Dale <paul.dale@oracle.com>
Reviewed-by: Rich Salz <rsalz@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/5154)
2018-02-01 21:44:18 +01:00

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/*
* Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
*
* Licensed under the OpenSSL license (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
*/
#include <assert.h>
#include <limits.h>
#include "internal/cryptlib.h"
#include "bn_lcl.h"
#include <openssl/opensslconf.h>
/* This stuff appears to be completely unused, so is deprecated */
#if OPENSSL_API_COMPAT < 0x00908000L
/*-
* For a 32 bit machine
* 2 - 4 == 128
* 3 - 8 == 256
* 4 - 16 == 512
* 5 - 32 == 1024
* 6 - 64 == 2048
* 7 - 128 == 4096
* 8 - 256 == 8192
*/
static int bn_limit_bits = 0;
static int bn_limit_num = 8; /* (1<<bn_limit_bits) */
static int bn_limit_bits_low = 0;
static int bn_limit_num_low = 8; /* (1<<bn_limit_bits_low) */
static int bn_limit_bits_high = 0;
static int bn_limit_num_high = 8; /* (1<<bn_limit_bits_high) */
static int bn_limit_bits_mont = 0;
static int bn_limit_num_mont = 8; /* (1<<bn_limit_bits_mont) */
void BN_set_params(int mult, int high, int low, int mont)
{
if (mult >= 0) {
if (mult > (int)(sizeof(int) * 8) - 1)
mult = sizeof(int) * 8 - 1;
bn_limit_bits = mult;
bn_limit_num = 1 << mult;
}
if (high >= 0) {
if (high > (int)(sizeof(int) * 8) - 1)
high = sizeof(int) * 8 - 1;
bn_limit_bits_high = high;
bn_limit_num_high = 1 << high;
}
if (low >= 0) {
if (low > (int)(sizeof(int) * 8) - 1)
low = sizeof(int) * 8 - 1;
bn_limit_bits_low = low;
bn_limit_num_low = 1 << low;
}
if (mont >= 0) {
if (mont > (int)(sizeof(int) * 8) - 1)
mont = sizeof(int) * 8 - 1;
bn_limit_bits_mont = mont;
bn_limit_num_mont = 1 << mont;
}
}
int BN_get_params(int which)
{
if (which == 0)
return bn_limit_bits;
else if (which == 1)
return bn_limit_bits_high;
else if (which == 2)
return bn_limit_bits_low;
else if (which == 3)
return bn_limit_bits_mont;
else
return 0;
}
#endif
const BIGNUM *BN_value_one(void)
{
static const BN_ULONG data_one = 1L;
static const BIGNUM const_one =
{ (BN_ULONG *)&data_one, 1, 1, 0, BN_FLG_STATIC_DATA };
return &const_one;
}
int BN_num_bits_word(BN_ULONG l)
{
BN_ULONG x, mask;
int bits = (l != 0);
#if BN_BITS2 > 32
x = l >> 32;
mask = (0 - x) & BN_MASK2;
mask = (0 - (mask >> (BN_BITS2 - 1)));
bits += 32 & mask;
l ^= (x ^ l) & mask;
#endif
x = l >> 16;
mask = (0 - x) & BN_MASK2;
mask = (0 - (mask >> (BN_BITS2 - 1)));
bits += 16 & mask;
l ^= (x ^ l) & mask;
x = l >> 8;
mask = (0 - x) & BN_MASK2;
mask = (0 - (mask >> (BN_BITS2 - 1)));
bits += 8 & mask;
l ^= (x ^ l) & mask;
x = l >> 4;
mask = (0 - x) & BN_MASK2;
mask = (0 - (mask >> (BN_BITS2 - 1)));
bits += 4 & mask;
l ^= (x ^ l) & mask;
x = l >> 2;
mask = (0 - x) & BN_MASK2;
mask = (0 - (mask >> (BN_BITS2 - 1)));
bits += 2 & mask;
l ^= (x ^ l) & mask;
x = l >> 1;
mask = (0 - x) & BN_MASK2;
mask = (0 - (mask >> (BN_BITS2 - 1)));
bits += 1 & mask;
return bits;
}
int BN_num_bits(const BIGNUM *a)
{
int i = a->top - 1;
bn_check_top(a);
if (BN_is_zero(a))
return 0;
return ((i * BN_BITS2) + BN_num_bits_word(a->d[i]));
}
static void bn_free_d(BIGNUM *a)
{
if (BN_get_flags(a, BN_FLG_SECURE))
OPENSSL_secure_free(a->d);
else
OPENSSL_free(a->d);
}
void BN_clear_free(BIGNUM *a)
{
if (a == NULL)
return;
if (a->d != NULL && !BN_get_flags(a, BN_FLG_STATIC_DATA)) {
OPENSSL_cleanse(a->d, a->dmax * sizeof(a->d[0]));
bn_free_d(a);
}
if (BN_get_flags(a, BN_FLG_MALLOCED)) {
OPENSSL_cleanse(a, sizeof(*a));
OPENSSL_free(a);
}
}
void BN_free(BIGNUM *a)
{
if (a == NULL)
return;
if (!BN_get_flags(a, BN_FLG_STATIC_DATA))
bn_free_d(a);
if (a->flags & BN_FLG_MALLOCED)
OPENSSL_free(a);
}
void bn_init(BIGNUM *a)
{
static BIGNUM nilbn;
*a = nilbn;
bn_check_top(a);
}
BIGNUM *BN_new(void)
{
BIGNUM *ret;
if ((ret = OPENSSL_zalloc(sizeof(*ret))) == NULL) {
BNerr(BN_F_BN_NEW, ERR_R_MALLOC_FAILURE);
return NULL;
}
ret->flags = BN_FLG_MALLOCED;
bn_check_top(ret);
return ret;
}
BIGNUM *BN_secure_new(void)
{
BIGNUM *ret = BN_new();
if (ret != NULL)
ret->flags |= BN_FLG_SECURE;
return ret;
}
/* This is used by bn_expand2() */
/* The caller MUST check that words > b->dmax before calling this */
static BN_ULONG *bn_expand_internal(const BIGNUM *b, int words)
{
BN_ULONG *a = NULL;
bn_check_top(b);
if (words > (INT_MAX / (4 * BN_BITS2))) {
BNerr(BN_F_BN_EXPAND_INTERNAL, BN_R_BIGNUM_TOO_LONG);
return NULL;
}
if (BN_get_flags(b, BN_FLG_STATIC_DATA)) {
BNerr(BN_F_BN_EXPAND_INTERNAL, BN_R_EXPAND_ON_STATIC_BIGNUM_DATA);
return NULL;
}
if (BN_get_flags(b, BN_FLG_SECURE))
a = OPENSSL_secure_zalloc(words * sizeof(*a));
else
a = OPENSSL_zalloc(words * sizeof(*a));
if (a == NULL) {
BNerr(BN_F_BN_EXPAND_INTERNAL, ERR_R_MALLOC_FAILURE);
return NULL;
}
assert(b->top <= words);
if (b->top > 0)
memcpy(a, b->d, sizeof(*a) * b->top);
return a;
}
/*
* This is an internal function that should not be used in applications. It
* ensures that 'b' has enough room for a 'words' word number and initialises
* any unused part of b->d with leading zeros. It is mostly used by the
* various BIGNUM routines. If there is an error, NULL is returned. If not,
* 'b' is returned.
*/
BIGNUM *bn_expand2(BIGNUM *b, int words)
{
bn_check_top(b);
if (words > b->dmax) {
BN_ULONG *a = bn_expand_internal(b, words);
if (!a)
return NULL;
if (b->d) {
OPENSSL_cleanse(b->d, b->dmax * sizeof(b->d[0]));
bn_free_d(b);
}
b->d = a;
b->dmax = words;
}
bn_check_top(b);
return b;
}
BIGNUM *BN_dup(const BIGNUM *a)
{
BIGNUM *t;
if (a == NULL)
return NULL;
bn_check_top(a);
t = BN_get_flags(a, BN_FLG_SECURE) ? BN_secure_new() : BN_new();
if (t == NULL)
return NULL;
if (!BN_copy(t, a)) {
BN_free(t);
return NULL;
}
bn_check_top(t);
return t;
}
BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b)
{
bn_check_top(b);
if (a == b)
return a;
if (bn_wexpand(a, b->top) == NULL)
return NULL;
if (b->top > 0)
memcpy(a->d, b->d, sizeof(b->d[0]) * b->top);
a->top = b->top;
a->neg = b->neg;
bn_check_top(a);
return a;
}
void BN_swap(BIGNUM *a, BIGNUM *b)
{
int flags_old_a, flags_old_b;
BN_ULONG *tmp_d;
int tmp_top, tmp_dmax, tmp_neg;
bn_check_top(a);
bn_check_top(b);
flags_old_a = a->flags;
flags_old_b = b->flags;
tmp_d = a->d;
tmp_top = a->top;
tmp_dmax = a->dmax;
tmp_neg = a->neg;
a->d = b->d;
a->top = b->top;
a->dmax = b->dmax;
a->neg = b->neg;
b->d = tmp_d;
b->top = tmp_top;
b->dmax = tmp_dmax;
b->neg = tmp_neg;
a->flags =
(flags_old_a & BN_FLG_MALLOCED) | (flags_old_b & BN_FLG_STATIC_DATA);
b->flags =
(flags_old_b & BN_FLG_MALLOCED) | (flags_old_a & BN_FLG_STATIC_DATA);
bn_check_top(a);
bn_check_top(b);
}
void BN_clear(BIGNUM *a)
{
bn_check_top(a);
if (a->d != NULL)
OPENSSL_cleanse(a->d, sizeof(*a->d) * a->dmax);
a->top = 0;
a->neg = 0;
}
BN_ULONG BN_get_word(const BIGNUM *a)
{
if (a->top > 1)
return BN_MASK2;
else if (a->top == 1)
return a->d[0];
/* a->top == 0 */
return 0;
}
int BN_set_word(BIGNUM *a, BN_ULONG w)
{
bn_check_top(a);
if (bn_expand(a, (int)sizeof(BN_ULONG) * 8) == NULL)
return 0;
a->neg = 0;
a->d[0] = w;
a->top = (w ? 1 : 0);
bn_check_top(a);
return 1;
}
BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret)
{
unsigned int i, m;
unsigned int n;
BN_ULONG l;
BIGNUM *bn = NULL;
if (ret == NULL)
ret = bn = BN_new();
if (ret == NULL)
return NULL;
bn_check_top(ret);
/* Skip leading zero's. */
for ( ; len > 0 && *s == 0; s++, len--)
continue;
n = len;
if (n == 0) {
ret->top = 0;
return ret;
}
i = ((n - 1) / BN_BYTES) + 1;
m = ((n - 1) % (BN_BYTES));
if (bn_wexpand(ret, (int)i) == NULL) {
BN_free(bn);
return NULL;
}
ret->top = i;
ret->neg = 0;
l = 0;
while (n--) {
l = (l << 8L) | *(s++);
if (m-- == 0) {
ret->d[--i] = l;
l = 0;
m = BN_BYTES - 1;
}
}
/*
* need to call this due to clear byte at top if avoiding having the top
* bit set (-ve number)
*/
bn_correct_top(ret);
return ret;
}
/* ignore negative */
static int bn2binpad(const BIGNUM *a, unsigned char *to, int tolen)
{
int i;
BN_ULONG l;
bn_check_top(a);
i = BN_num_bytes(a);
if (tolen == -1)
tolen = i;
else if (tolen < i)
return -1;
/* Add leading zeroes if necessary */
if (tolen > i) {
memset(to, 0, tolen - i);
to += tolen - i;
}
while (i--) {
l = a->d[i / BN_BYTES];
*(to++) = (unsigned char)(l >> (8 * (i % BN_BYTES))) & 0xff;
}
return tolen;
}
int BN_bn2binpad(const BIGNUM *a, unsigned char *to, int tolen)
{
if (tolen < 0)
return -1;
return bn2binpad(a, to, tolen);
}
int BN_bn2bin(const BIGNUM *a, unsigned char *to)
{
return bn2binpad(a, to, -1);
}
BIGNUM *BN_lebin2bn(const unsigned char *s, int len, BIGNUM *ret)
{
unsigned int i, m;
unsigned int n;
BN_ULONG l;
BIGNUM *bn = NULL;
if (ret == NULL)
ret = bn = BN_new();
if (ret == NULL)
return NULL;
bn_check_top(ret);
s += len;
/* Skip trailing zeroes. */
for ( ; len > 0 && s[-1] == 0; s--, len--)
continue;
n = len;
if (n == 0) {
ret->top = 0;
return ret;
}
i = ((n - 1) / BN_BYTES) + 1;
m = ((n - 1) % (BN_BYTES));
if (bn_wexpand(ret, (int)i) == NULL) {
BN_free(bn);
return NULL;
}
ret->top = i;
ret->neg = 0;
l = 0;
while (n--) {
s--;
l = (l << 8L) | *s;
if (m-- == 0) {
ret->d[--i] = l;
l = 0;
m = BN_BYTES - 1;
}
}
/*
* need to call this due to clear byte at top if avoiding having the top
* bit set (-ve number)
*/
bn_correct_top(ret);
return ret;
}
int BN_bn2lebinpad(const BIGNUM *a, unsigned char *to, int tolen)
{
int i;
BN_ULONG l;
bn_check_top(a);
i = BN_num_bytes(a);
if (tolen < i)
return -1;
/* Add trailing zeroes if necessary */
if (tolen > i)
memset(to + i, 0, tolen - i);
to += i;
while (i--) {
l = a->d[i / BN_BYTES];
to--;
*to = (unsigned char)(l >> (8 * (i % BN_BYTES))) & 0xff;
}
return tolen;
}
int BN_ucmp(const BIGNUM *a, const BIGNUM *b)
{
int i;
BN_ULONG t1, t2, *ap, *bp;
bn_check_top(a);
bn_check_top(b);
i = a->top - b->top;
if (i != 0)
return i;
ap = a->d;
bp = b->d;
for (i = a->top - 1; i >= 0; i--) {
t1 = ap[i];
t2 = bp[i];
if (t1 != t2)
return ((t1 > t2) ? 1 : -1);
}
return 0;
}
int BN_cmp(const BIGNUM *a, const BIGNUM *b)
{
int i;
int gt, lt;
BN_ULONG t1, t2;
if ((a == NULL) || (b == NULL)) {
if (a != NULL)
return -1;
else if (b != NULL)
return 1;
else
return 0;
}
bn_check_top(a);
bn_check_top(b);
if (a->neg != b->neg) {
if (a->neg)
return -1;
else
return 1;
}
if (a->neg == 0) {
gt = 1;
lt = -1;
} else {
gt = -1;
lt = 1;
}
if (a->top > b->top)
return gt;
if (a->top < b->top)
return lt;
for (i = a->top - 1; i >= 0; i--) {
t1 = a->d[i];
t2 = b->d[i];
if (t1 > t2)
return gt;
if (t1 < t2)
return lt;
}
return 0;
}
int BN_set_bit(BIGNUM *a, int n)
{
int i, j, k;
if (n < 0)
return 0;
i = n / BN_BITS2;
j = n % BN_BITS2;
if (a->top <= i) {
if (bn_wexpand(a, i + 1) == NULL)
return 0;
for (k = a->top; k < i + 1; k++)
a->d[k] = 0;
a->top = i + 1;
}
a->d[i] |= (((BN_ULONG)1) << j);
bn_check_top(a);
return 1;
}
int BN_clear_bit(BIGNUM *a, int n)
{
int i, j;
bn_check_top(a);
if (n < 0)
return 0;
i = n / BN_BITS2;
j = n % BN_BITS2;
if (a->top <= i)
return 0;
a->d[i] &= (~(((BN_ULONG)1) << j));
bn_correct_top(a);
return 1;
}
int BN_is_bit_set(const BIGNUM *a, int n)
{
int i, j;
bn_check_top(a);
if (n < 0)
return 0;
i = n / BN_BITS2;
j = n % BN_BITS2;
if (a->top <= i)
return 0;
return (int)(((a->d[i]) >> j) & ((BN_ULONG)1));
}
int BN_mask_bits(BIGNUM *a, int n)
{
int b, w;
bn_check_top(a);
if (n < 0)
return 0;
w = n / BN_BITS2;
b = n % BN_BITS2;
if (w >= a->top)
return 0;
if (b == 0)
a->top = w;
else {
a->top = w + 1;
a->d[w] &= ~(BN_MASK2 << b);
}
bn_correct_top(a);
return 1;
}
void BN_set_negative(BIGNUM *a, int b)
{
if (b && !BN_is_zero(a))
a->neg = 1;
else
a->neg = 0;
}
int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n)
{
int i;
BN_ULONG aa, bb;
aa = a[n - 1];
bb = b[n - 1];
if (aa != bb)
return ((aa > bb) ? 1 : -1);
for (i = n - 2; i >= 0; i--) {
aa = a[i];
bb = b[i];
if (aa != bb)
return ((aa > bb) ? 1 : -1);
}
return 0;
}
/*
* Here follows a specialised variants of bn_cmp_words(). It has the
* capability of performing the operation on arrays of different sizes. The
* sizes of those arrays is expressed through cl, which is the common length
* ( basically, min(len(a),len(b)) ), and dl, which is the delta between the
* two lengths, calculated as len(a)-len(b). All lengths are the number of
* BN_ULONGs...
*/
int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl)
{
int n, i;
n = cl - 1;
if (dl < 0) {
for (i = dl; i < 0; i++) {
if (b[n - i] != 0)
return -1; /* a < b */
}
}
if (dl > 0) {
for (i = dl; i > 0; i--) {
if (a[n + i] != 0)
return 1; /* a > b */
}
}
return bn_cmp_words(a, b, cl);
}
/*
* Constant-time conditional swap of a and b.
* a and b are swapped if condition is not 0. The code assumes that at most one bit of condition is set.
* nwords is the number of words to swap. The code assumes that at least nwords are allocated in both a and b,
* and that no more than nwords are used by either a or b.
* a and b cannot be the same number
*/
void BN_consttime_swap(BN_ULONG condition, BIGNUM *a, BIGNUM *b, int nwords)
{
BN_ULONG t;
int i;
bn_wcheck_size(a, nwords);
bn_wcheck_size(b, nwords);
assert(a != b);
assert((condition & (condition - 1)) == 0);
assert(sizeof(BN_ULONG) >= sizeof(int));
condition = ((condition - 1) >> (BN_BITS2 - 1)) - 1;
t = (a->top ^ b->top) & condition;
a->top ^= t;
b->top ^= t;
#define BN_CONSTTIME_SWAP(ind) \
do { \
t = (a->d[ind] ^ b->d[ind]) & condition; \
a->d[ind] ^= t; \
b->d[ind] ^= t; \
} while (0)
switch (nwords) {
default:
for (i = 10; i < nwords; i++)
BN_CONSTTIME_SWAP(i);
/* Fallthrough */
case 10:
BN_CONSTTIME_SWAP(9); /* Fallthrough */
case 9:
BN_CONSTTIME_SWAP(8); /* Fallthrough */
case 8:
BN_CONSTTIME_SWAP(7); /* Fallthrough */
case 7:
BN_CONSTTIME_SWAP(6); /* Fallthrough */
case 6:
BN_CONSTTIME_SWAP(5); /* Fallthrough */
case 5:
BN_CONSTTIME_SWAP(4); /* Fallthrough */
case 4:
BN_CONSTTIME_SWAP(3); /* Fallthrough */
case 3:
BN_CONSTTIME_SWAP(2); /* Fallthrough */
case 2:
BN_CONSTTIME_SWAP(1); /* Fallthrough */
case 1:
BN_CONSTTIME_SWAP(0);
}
#undef BN_CONSTTIME_SWAP
}
/* Bits of security, see SP800-57 */
int BN_security_bits(int L, int N)
{
int secbits, bits;
if (L >= 15360)
secbits = 256;
else if (L >= 7680)
secbits = 192;
else if (L >= 3072)
secbits = 128;
else if (L >= 2048)
secbits = 112;
else if (L >= 1024)
secbits = 80;
else
return 0;
if (N == -1)
return secbits;
bits = N / 2;
if (bits < 80)
return 0;
return bits >= secbits ? secbits : bits;
}
void BN_zero_ex(BIGNUM *a)
{
a->top = 0;
a->neg = 0;
}
int BN_abs_is_word(const BIGNUM *a, const BN_ULONG w)
{
return ((a->top == 1) && (a->d[0] == w)) || ((w == 0) && (a->top == 0));
}
int BN_is_zero(const BIGNUM *a)
{
return a->top == 0;
}
int BN_is_one(const BIGNUM *a)
{
return BN_abs_is_word(a, 1) && !a->neg;
}
int BN_is_word(const BIGNUM *a, const BN_ULONG w)
{
return BN_abs_is_word(a, w) && (!w || !a->neg);
}
int BN_is_odd(const BIGNUM *a)
{
return (a->top > 0) && (a->d[0] & 1);
}
int BN_is_negative(const BIGNUM *a)
{
return (a->neg != 0);
}
int BN_to_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
BN_CTX *ctx)
{
return BN_mod_mul_montgomery(r, a, &(mont->RR), mont, ctx);
}
void BN_with_flags(BIGNUM *dest, const BIGNUM *b, int flags)
{
dest->d = b->d;
dest->top = b->top;
dest->dmax = b->dmax;
dest->neg = b->neg;
dest->flags = ((dest->flags & BN_FLG_MALLOCED)
| (b->flags & ~BN_FLG_MALLOCED)
| BN_FLG_STATIC_DATA | flags);
}
BN_GENCB *BN_GENCB_new(void)
{
BN_GENCB *ret;
if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL) {
BNerr(BN_F_BN_GENCB_NEW, ERR_R_MALLOC_FAILURE);
return NULL;
}
return ret;
}
void BN_GENCB_free(BN_GENCB *cb)
{
if (cb == NULL)
return;
OPENSSL_free(cb);
}
void BN_set_flags(BIGNUM *b, int n)
{
b->flags |= n;
}
int BN_get_flags(const BIGNUM *b, int n)
{
return b->flags & n;
}
/* Populate a BN_GENCB structure with an "old"-style callback */
void BN_GENCB_set_old(BN_GENCB *gencb, void (*callback) (int, int, void *),
void *cb_arg)
{
BN_GENCB *tmp_gencb = gencb;
tmp_gencb->ver = 1;
tmp_gencb->arg = cb_arg;
tmp_gencb->cb.cb_1 = callback;
}
/* Populate a BN_GENCB structure with a "new"-style callback */
void BN_GENCB_set(BN_GENCB *gencb, int (*callback) (int, int, BN_GENCB *),
void *cb_arg)
{
BN_GENCB *tmp_gencb = gencb;
tmp_gencb->ver = 2;
tmp_gencb->arg = cb_arg;
tmp_gencb->cb.cb_2 = callback;
}
void *BN_GENCB_get_arg(BN_GENCB *cb)
{
return cb->arg;
}
BIGNUM *bn_wexpand(BIGNUM *a, int words)
{
return (words <= a->dmax) ? a : bn_expand2(a, words);
}
void bn_correct_top(BIGNUM *a)
{
BN_ULONG *ftl;
int tmp_top = a->top;
if (tmp_top > 0) {
for (ftl = &(a->d[tmp_top]); tmp_top > 0; tmp_top--) {
ftl--;
if (*ftl != 0)
break;
}
a->top = tmp_top;
}
if (a->top == 0)
a->neg = 0;
bn_pollute(a);
}
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