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- /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
- * All rights reserved.
- *
- * This package is an SSL implementation written
- * by Eric Young (eay@cryptsoft.com).
- * The implementation was written so as to conform with Netscapes SSL.
- *
- * This library is free for commercial and non-commercial use as long as
- * the following conditions are aheared to. The following conditions
- * apply to all code found in this distribution, be it the RC4, RSA,
- * lhash, DES, etc., code; not just the SSL code. The SSL documentation
- * included with this distribution is covered by the same copyright terms
- * except that the holder is Tim Hudson (tjh@cryptsoft.com).
- *
- * Copyright remains Eric Young's, and as such any Copyright notices in
- * the code are not to be removed.
- * If this package is used in a product, Eric Young should be given attribution
- * as the author of the parts of the library used.
- * This can be in the form of a textual message at program startup or
- * in documentation (online or textual) provided with the package.
- *
- * 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 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 acknowledgement:
- * "This product includes cryptographic software written by
- * Eric Young (eay@cryptsoft.com)"
- * The word 'cryptographic' can be left out if the rouines from the library
- * being used are not cryptographic related :-).
- * 4. If you include any Windows specific code (or a derivative thereof) from
- * the apps directory (application code) you must include an acknowledgement:
- * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
- *
- * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
- * ANY EXPRESS 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 AUTHOR OR 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.
- *
- * The licence and distribution terms for any publically available version or
- * derivative of this code cannot be changed. i.e. this code cannot simply be
- * copied and put under another distribution licence
- * [including the GNU Public Licence.] */
-
- #include <openssl/bn.h>
-
- #include <assert.h>
- #include <limits.h>
- #include <openssl/err.h>
-
- #include "internal.h"
-
-
- #if !defined(BN_ULLONG)
- /* bn_div_words divides a double-width |h|,|l| by |d| and returns the result,
- * which must fit in a |BN_ULONG|. */
- static BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d) {
- BN_ULONG dh, dl, q, ret = 0, th, tl, t;
- int i, count = 2;
-
- if (d == 0) {
- return BN_MASK2;
- }
-
- i = BN_num_bits_word(d);
- assert((i == BN_BITS2) || (h <= (BN_ULONG)1 << i));
-
- i = BN_BITS2 - i;
- if (h >= d) {
- h -= d;
- }
-
- if (i) {
- d <<= i;
- h = (h << i) | (l >> (BN_BITS2 - i));
- l <<= i;
- }
- dh = (d & BN_MASK2h) >> BN_BITS4;
- dl = (d & BN_MASK2l);
- for (;;) {
- if ((h >> BN_BITS4) == dh) {
- q = BN_MASK2l;
- } else {
- q = h / dh;
- }
-
- th = q * dh;
- tl = dl * q;
- for (;;) {
- t = h - th;
- if ((t & BN_MASK2h) ||
- ((tl) <= ((t << BN_BITS4) | ((l & BN_MASK2h) >> BN_BITS4)))) {
- break;
- }
- q--;
- th -= dh;
- tl -= dl;
- }
- t = (tl >> BN_BITS4);
- tl = (tl << BN_BITS4) & BN_MASK2h;
- th += t;
-
- if (l < tl) {
- th++;
- }
- l -= tl;
- if (h < th) {
- h += d;
- q--;
- }
- h -= th;
-
- if (--count == 0) {
- break;
- }
-
- ret = q << BN_BITS4;
- h = ((h << BN_BITS4) | (l >> BN_BITS4)) & BN_MASK2;
- l = (l & BN_MASK2l) << BN_BITS4;
- }
-
- ret |= q;
- return ret;
- }
- #endif /* !defined(BN_ULLONG) */
-
- static inline void bn_div_rem_words(BN_ULONG *quotient_out, BN_ULONG *rem_out,
- BN_ULONG n0, BN_ULONG n1, BN_ULONG d0) {
- /* GCC and Clang generate function calls to |__udivdi3| and |__umoddi3| when
- * the |BN_ULLONG|-based C code is used.
- *
- * GCC bugs:
- * * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=14224
- * * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=43721
- * * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=54183
- * * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=58897
- * * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=65668
- *
- * Clang bugs:
- * * https://llvm.org/bugs/show_bug.cgi?id=6397
- * * https://llvm.org/bugs/show_bug.cgi?id=12418
- *
- * These issues aren't specific to x86 and x86_64, so it might be worthwhile
- * to add more assembly language implementations. */
- #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86) && defined(__GNUC__)
- __asm__ volatile (
- "divl %4"
- : "=a"(*quotient_out), "=d"(*rem_out)
- : "a"(n1), "d"(n0), "g"(d0)
- : "cc" );
- #elif !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && defined(__GNUC__)
- __asm__ volatile (
- "divq %4"
- : "=a"(*quotient_out), "=d"(*rem_out)
- : "a"(n1), "d"(n0), "g"(d0)
- : "cc" );
- #else
- #if defined(BN_ULLONG)
- BN_ULLONG n = (((BN_ULLONG)n0) << BN_BITS2) | n1;
- *quotient_out = (BN_ULONG)(n / d0);
- #else
- *quotient_out = bn_div_words(n0, n1, d0);
- #endif
- *rem_out = n1 - (*quotient_out * d0);
- #endif
- }
-
- /* BN_div computes dv := num / divisor, rounding towards
- * zero, and sets up rm such that dv*divisor + rm = num holds.
- * Thus:
- * dv->neg == num->neg ^ divisor->neg (unless the result is zero)
- * rm->neg == num->neg (unless the remainder is zero)
- * If 'dv' or 'rm' is NULL, the respective value is not returned. */
- int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
- BN_CTX *ctx) {
- int norm_shift, i, loop;
- BIGNUM *tmp, wnum, *snum, *sdiv, *res;
- BN_ULONG *resp, *wnump;
- BN_ULONG d0, d1;
- int num_n, div_n;
- int no_branch = 0;
-
- /* Invalid zero-padding would have particularly bad consequences
- * so don't just rely on bn_check_top() here */
- if ((num->top > 0 && num->d[num->top - 1] == 0) ||
- (divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
- OPENSSL_PUT_ERROR(BN, BN_R_NOT_INITIALIZED);
- return 0;
- }
-
- if ((num->flags & BN_FLG_CONSTTIME) != 0 ||
- (divisor->flags & BN_FLG_CONSTTIME) != 0) {
- no_branch = 1;
- }
-
- if (BN_is_zero(divisor)) {
- OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO);
- return 0;
- }
-
- if (!no_branch && BN_ucmp(num, divisor) < 0) {
- if (rm != NULL) {
- if (BN_copy(rm, num) == NULL) {
- return 0;
- }
- }
- if (dv != NULL) {
- BN_zero(dv);
- }
- return 1;
- }
-
- BN_CTX_start(ctx);
- tmp = BN_CTX_get(ctx);
- snum = BN_CTX_get(ctx);
- sdiv = BN_CTX_get(ctx);
- if (dv == NULL) {
- res = BN_CTX_get(ctx);
- } else {
- res = dv;
- }
- if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL) {
- goto err;
- }
-
- /* First we normalise the numbers */
- norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
- if (!(BN_lshift(sdiv, divisor, norm_shift))) {
- goto err;
- }
- sdiv->neg = 0;
- norm_shift += BN_BITS2;
- if (!(BN_lshift(snum, num, norm_shift))) {
- goto err;
- }
- snum->neg = 0;
-
- if (no_branch) {
- /* Since we don't know whether snum is larger than sdiv,
- * we pad snum with enough zeroes without changing its
- * value.
- */
- if (snum->top <= sdiv->top + 1) {
- if (bn_wexpand(snum, sdiv->top + 2) == NULL) {
- goto err;
- }
- for (i = snum->top; i < sdiv->top + 2; i++) {
- snum->d[i] = 0;
- }
- snum->top = sdiv->top + 2;
- } else {
- if (bn_wexpand(snum, snum->top + 1) == NULL) {
- goto err;
- }
- snum->d[snum->top] = 0;
- snum->top++;
- }
- }
-
- div_n = sdiv->top;
- num_n = snum->top;
- loop = num_n - div_n;
- /* Lets setup a 'window' into snum
- * This is the part that corresponds to the current
- * 'area' being divided */
- wnum.neg = 0;
- wnum.d = &(snum->d[loop]);
- wnum.top = div_n;
- /* only needed when BN_ucmp messes up the values between top and max */
- wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
-
- /* Get the top 2 words of sdiv */
- /* div_n=sdiv->top; */
- d0 = sdiv->d[div_n - 1];
- d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
-
- /* pointer to the 'top' of snum */
- wnump = &(snum->d[num_n - 1]);
-
- /* Setup to 'res' */
- res->neg = (num->neg ^ divisor->neg);
- if (!bn_wexpand(res, (loop + 1))) {
- goto err;
- }
- res->top = loop - no_branch;
- resp = &(res->d[loop - 1]);
-
- /* space for temp */
- if (!bn_wexpand(tmp, (div_n + 1))) {
- goto err;
- }
-
- if (!no_branch) {
- if (BN_ucmp(&wnum, sdiv) >= 0) {
- bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
- *resp = 1;
- } else {
- res->top--;
- }
- }
-
- /* if res->top == 0 then clear the neg value otherwise decrease
- * the resp pointer */
- if (res->top == 0) {
- res->neg = 0;
- } else {
- resp--;
- }
-
- for (i = 0; i < loop - 1; i++, wnump--, resp--) {
- BN_ULONG q, l0;
- /* the first part of the loop uses the top two words of snum and sdiv to
- * calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv */
- BN_ULONG n0, n1, rem = 0;
-
- n0 = wnump[0];
- n1 = wnump[-1];
- if (n0 == d0) {
- q = BN_MASK2;
- } else {
- /* n0 < d0 */
- bn_div_rem_words(&q, &rem, n0, n1, d0);
-
- #ifdef BN_ULLONG
- BN_ULLONG t2 = (BN_ULLONG)d1 * q;
- for (;;) {
- if (t2 <= ((((BN_ULLONG)rem) << BN_BITS2) | wnump[-2])) {
- break;
- }
- q--;
- rem += d0;
- if (rem < d0) {
- break; /* don't let rem overflow */
- }
- t2 -= d1;
- }
- #else /* !BN_ULLONG */
- BN_ULONG t2l, t2h;
- BN_UMULT_LOHI(t2l, t2h, d1, q);
- for (;;) {
- if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2]))) {
- break;
- }
- q--;
- rem += d0;
- if (rem < d0) {
- break; /* don't let rem overflow */
- }
- if (t2l < d1) {
- t2h--;
- }
- t2l -= d1;
- }
- #endif /* !BN_ULLONG */
- }
-
- l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
- tmp->d[div_n] = l0;
- wnum.d--;
- /* ingore top values of the bignums just sub the two
- * BN_ULONG arrays with bn_sub_words */
- if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
- /* Note: As we have considered only the leading
- * two BN_ULONGs in the calculation of q, sdiv * q
- * might be greater than wnum (but then (q-1) * sdiv
- * is less or equal than wnum)
- */
- q--;
- if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n)) {
- /* we can't have an overflow here (assuming
- * that q != 0, but if q == 0 then tmp is
- * zero anyway) */
- (*wnump)++;
- }
- }
- /* store part of the result */
- *resp = q;
- }
- bn_correct_top(snum);
- if (rm != NULL) {
- /* Keep a copy of the neg flag in num because if rm==num
- * BN_rshift() will overwrite it.
- */
- int neg = num->neg;
- if (!BN_rshift(rm, snum, norm_shift)) {
- goto err;
- }
- if (!BN_is_zero(rm)) {
- rm->neg = neg;
- }
- }
- if (no_branch) {
- bn_correct_top(res);
- }
- BN_CTX_end(ctx);
- return 1;
-
- err:
- BN_CTX_end(ctx);
- return 0;
- }
-
- int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx) {
- if (!(BN_mod(r, m, d, ctx))) {
- return 0;
- }
- if (!r->neg) {
- return 1;
- }
-
- /* now -|d| < r < 0, so we have to set r := r + |d|. */
- return (d->neg ? BN_sub : BN_add)(r, r, d);
- }
-
- int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
- BN_CTX *ctx) {
- if (!BN_add(r, a, b)) {
- return 0;
- }
- return BN_nnmod(r, r, m, ctx);
- }
-
- int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
- const BIGNUM *m) {
- if (!BN_uadd(r, a, b)) {
- return 0;
- }
- if (BN_ucmp(r, m) >= 0) {
- return BN_usub(r, r, m);
- }
- return 1;
- }
-
- int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
- BN_CTX *ctx) {
- if (!BN_sub(r, a, b)) {
- return 0;
- }
- return BN_nnmod(r, r, m, ctx);
- }
-
- /* BN_mod_sub variant that may be used if both a and b are non-negative
- * and less than m */
- int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
- const BIGNUM *m) {
- if (!BN_sub(r, a, b)) {
- return 0;
- }
- if (r->neg) {
- return BN_add(r, r, m);
- }
- return 1;
- }
-
- int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
- BN_CTX *ctx) {
- BIGNUM *t;
- int ret = 0;
-
- BN_CTX_start(ctx);
- t = BN_CTX_get(ctx);
- if (t == NULL) {
- goto err;
- }
-
- if (a == b) {
- if (!BN_sqr(t, a, ctx)) {
- goto err;
- }
- } else {
- if (!BN_mul(t, a, b, ctx)) {
- goto err;
- }
- }
-
- if (!BN_nnmod(r, t, m, ctx)) {
- goto err;
- }
-
- ret = 1;
-
- err:
- BN_CTX_end(ctx);
- return ret;
- }
-
- int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx) {
- if (!BN_sqr(r, a, ctx)) {
- return 0;
- }
-
- /* r->neg == 0, thus we don't need BN_nnmod */
- return BN_mod(r, r, m, ctx);
- }
-
- int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
- BN_CTX *ctx) {
- BIGNUM *abs_m = NULL;
- int ret;
-
- if (!BN_nnmod(r, a, m, ctx)) {
- return 0;
- }
-
- if (m->neg) {
- abs_m = BN_dup(m);
- if (abs_m == NULL) {
- return 0;
- }
- abs_m->neg = 0;
- }
-
- ret = BN_mod_lshift_quick(r, r, n, (abs_m ? abs_m : m));
-
- BN_free(abs_m);
- return ret;
- }
-
- int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m) {
- if (r != a) {
- if (BN_copy(r, a) == NULL) {
- return 0;
- }
- }
-
- while (n > 0) {
- int max_shift;
-
- /* 0 < r < m */
- max_shift = BN_num_bits(m) - BN_num_bits(r);
- /* max_shift >= 0 */
-
- if (max_shift < 0) {
- OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED);
- return 0;
- }
-
- if (max_shift > n) {
- max_shift = n;
- }
-
- if (max_shift) {
- if (!BN_lshift(r, r, max_shift)) {
- return 0;
- }
- n -= max_shift;
- } else {
- if (!BN_lshift1(r, r)) {
- return 0;
- }
- --n;
- }
-
- /* BN_num_bits(r) <= BN_num_bits(m) */
- if (BN_cmp(r, m) >= 0) {
- if (!BN_sub(r, r, m)) {
- return 0;
- }
- }
- }
-
- return 1;
- }
-
- int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx) {
- if (!BN_lshift1(r, a)) {
- return 0;
- }
-
- return BN_nnmod(r, r, m, ctx);
- }
-
- int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m) {
- if (!BN_lshift1(r, a)) {
- return 0;
- }
- if (BN_cmp(r, m) >= 0) {
- return BN_sub(r, r, m);
- }
-
- return 1;
- }
-
- BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w) {
- BN_ULONG ret = 0;
- int i, j;
-
- w &= BN_MASK2;
-
- if (!w) {
- /* actually this an error (division by zero) */
- return (BN_ULONG) - 1;
- }
-
- if (a->top == 0) {
- return 0;
- }
-
- /* normalize input for |bn_div_rem_words|. */
- j = BN_BITS2 - BN_num_bits_word(w);
- w <<= j;
- if (!BN_lshift(a, a, j)) {
- return (BN_ULONG) - 1;
- }
-
- for (i = a->top - 1; i >= 0; i--) {
- BN_ULONG l = a->d[i];
- BN_ULONG d;
- BN_ULONG unused_rem;
- bn_div_rem_words(&d, &unused_rem, ret, l, w);
- ret = (l - ((d * w) & BN_MASK2)) & BN_MASK2;
- a->d[i] = d;
- }
-
- if ((a->top > 0) && (a->d[a->top - 1] == 0)) {
- a->top--;
- }
-
- ret >>= j;
- return ret;
- }
-
- BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w) {
- #ifndef BN_ULLONG
- BN_ULONG ret = 0;
- #else
- BN_ULLONG ret = 0;
- #endif
- int i;
-
- if (w == 0) {
- return (BN_ULONG) -1;
- }
-
- w &= BN_MASK2;
- for (i = a->top - 1; i >= 0; i--) {
- #ifndef BN_ULLONG
- ret = ((ret << BN_BITS4) | ((a->d[i] >> BN_BITS4) & BN_MASK2l)) % w;
- ret = ((ret << BN_BITS4) | (a->d[i] & BN_MASK2l)) % w;
- #else
- ret = (BN_ULLONG)(((ret << (BN_ULLONG)BN_BITS2) | a->d[i]) % (BN_ULLONG)w);
- #endif
- }
- return (BN_ULONG)ret;
- }
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