| /* 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" |
| |
| |
| // bn_div_words divides a double-width |h|,|l| by |d| and returns the result, |
| // which must fit in a |BN_ULONG|. |
| OPENSSL_UNUSED 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); |
| l = (l & BN_MASK2l) << BN_BITS4; |
| } |
| |
| ret |= q; |
| return ret; |
| } |
| |
| 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(BN_CAN_USE_INLINE_ASM) && defined(OPENSSL_X86) |
| __asm__ volatile("divl %4" |
| : "=a"(*quotient_out), "=d"(*rem_out) |
| : "a"(n1), "d"(n0), "rm"(d0) |
| : "cc"); |
| #elif defined(BN_CAN_USE_INLINE_ASM) && defined(OPENSSL_X86_64) |
| __asm__ volatile("divq %4" |
| : "=a"(*quotient_out), "=d"(*rem_out) |
| : "a"(n1), "d"(n0), "rm"(d0) |
| : "cc"); |
| #else |
| #if defined(BN_CAN_DIVIDE_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 "quotient := numerator / divisor", rounding towards zero, |
| // and sets up |rem| such that "quotient * divisor + rem = numerator" holds. |
| // |
| // Thus: |
| // |
| // quotient->neg == numerator->neg ^ divisor->neg |
| // (unless the result is zero) |
| // rem->neg == numerator->neg |
| // (unless the remainder is zero) |
| // |
| // If |quotient| or |rem| is NULL, the respective value is not returned. |
| // |
| // This was specifically designed to contain fewer branches that may leak |
| // sensitive information; see "New Branch Prediction Vulnerabilities in OpenSSL |
| // and Necessary Software Countermeasures" by Onur Acıçmez, Shay Gueron, and |
| // Jean-Pierre Seifert. |
| int BN_div(BIGNUM *quotient, BIGNUM *rem, const BIGNUM *numerator, |
| const BIGNUM *divisor, BN_CTX *ctx) { |
| int norm_shift, loop; |
| BIGNUM wnum; |
| BN_ULONG *resp, *wnump; |
| BN_ULONG d0, d1; |
| int num_n, div_n; |
| |
| // This function relies on the historical minimal-width |BIGNUM| invariant. |
| // It is already not constant-time (constant-time reductions should use |
| // Montgomery logic), so we shrink all inputs and intermediate values to |
| // retain the previous behavior. |
| |
| // Invalid zero-padding would have particularly bad consequences. |
| int numerator_width = bn_minimal_width(numerator); |
| int divisor_width = bn_minimal_width(divisor); |
| if ((numerator_width > 0 && numerator->d[numerator_width - 1] == 0) || |
| (divisor_width > 0 && divisor->d[divisor_width - 1] == 0)) { |
| OPENSSL_PUT_ERROR(BN, BN_R_NOT_INITIALIZED); |
| return 0; |
| } |
| |
| if (BN_is_zero(divisor)) { |
| OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO); |
| return 0; |
| } |
| |
| BN_CTX_start(ctx); |
| BIGNUM *tmp = BN_CTX_get(ctx); |
| BIGNUM *snum = BN_CTX_get(ctx); |
| BIGNUM *sdiv = BN_CTX_get(ctx); |
| BIGNUM *res = NULL; |
| if (quotient == NULL) { |
| res = BN_CTX_get(ctx); |
| } else { |
| res = quotient; |
| } |
| if (sdiv == NULL || res == 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; |
| } |
| bn_set_minimal_width(sdiv); |
| sdiv->neg = 0; |
| norm_shift += BN_BITS2; |
| if (!BN_lshift(snum, numerator, norm_shift)) { |
| goto err; |
| } |
| bn_set_minimal_width(snum); |
| snum->neg = 0; |
| |
| // Since we don't want to have special-case logic for the case where snum is |
| // larger than sdiv, we pad snum with enough zeroes without changing its |
| // value. |
| if (snum->width <= sdiv->width + 1) { |
| if (!bn_wexpand(snum, sdiv->width + 2)) { |
| goto err; |
| } |
| for (int i = snum->width; i < sdiv->width + 2; i++) { |
| snum->d[i] = 0; |
| } |
| snum->width = sdiv->width + 2; |
| } else { |
| if (!bn_wexpand(snum, snum->width + 1)) { |
| goto err; |
| } |
| snum->d[snum->width] = 0; |
| snum->width++; |
| } |
| |
| div_n = sdiv->width; |
| num_n = snum->width; |
| 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.width = div_n; |
| // only needed when BN_ucmp messes up the values between width 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->width; |
| 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 |res|. |numerator| and |res| may alias, so we save |numerator->neg| |
| // for later. |
| const int numerator_neg = numerator->neg; |
| res->neg = (numerator_neg ^ divisor->neg); |
| if (!bn_wexpand(res, loop + 1)) { |
| goto err; |
| } |
| res->width = loop - 1; |
| resp = &(res->d[loop - 1]); |
| |
| // space for temp |
| if (!bn_wexpand(tmp, div_n + 1)) { |
| goto err; |
| } |
| |
| // if res->width == 0 then clear the neg value otherwise decrease |
| // the resp pointer |
| if (res->width == 0) { |
| res->neg = 0; |
| } else { |
| resp--; |
| } |
| |
| for (int 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, rm = 0; |
| |
| n0 = wnump[0]; |
| n1 = wnump[-1]; |
| if (n0 == d0) { |
| q = BN_MASK2; |
| } else { |
| // n0 < d0 |
| bn_div_rem_words(&q, &rm, n0, n1, d0); |
| |
| #ifdef BN_ULLONG |
| BN_ULLONG t2 = (BN_ULLONG)d1 * q; |
| for (;;) { |
| if (t2 <= ((((BN_ULLONG)rm) << BN_BITS2) | wnump[-2])) { |
| break; |
| } |
| q--; |
| rm += d0; |
| if (rm < d0) { |
| break; // don't let rm overflow |
| } |
| t2 -= d1; |
| } |
| #else // !BN_ULLONG |
| BN_ULONG t2l, t2h; |
| BN_UMULT_LOHI(t2l, t2h, d1, q); |
| for (;;) { |
| if (t2h < rm || |
| (t2h == rm && t2l <= wnump[-2])) { |
| break; |
| } |
| q--; |
| rm += d0; |
| if (rm < d0) { |
| break; // don't let rm 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_set_minimal_width(snum); |
| |
| if (rem != NULL) { |
| if (!BN_rshift(rem, snum, norm_shift)) { |
| goto err; |
| } |
| if (!BN_is_zero(rem)) { |
| rem->neg = numerator_neg; |
| } |
| } |
| |
| bn_set_minimal_width(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); |
| } |
| |
| BN_ULONG bn_reduce_once(BN_ULONG *r, const BN_ULONG *a, BN_ULONG carry, |
| const BN_ULONG *m, size_t num) { |
| assert(r != a); |
| // |r| = |a| - |m|. |bn_sub_words| performs the bulk of the subtraction, and |
| // then we apply the borrow to |carry|. |
| carry -= bn_sub_words(r, a, m, num); |
| // We know 0 <= |a| < 2*|m|, so -|m| <= |r| < |m|. |
| // |
| // If 0 <= |r| < |m|, |r| fits in |num| words and |carry| is zero. We then |
| // wish to select |r| as the answer. Otherwise -m <= r < 0 and we wish to |
| // return |r| + |m|, or |a|. |carry| must then be -1 or all ones. In both |
| // cases, |carry| is a suitable input to |bn_select_words|. |
| // |
| // Although |carry| may be one if it was one on input and |bn_sub_words| |
| // returns zero, this would give |r| > |m|, violating our input assumptions. |
| declassify_assert(carry + 1 <= 1); |
| bn_select_words(r, carry, a /* r < 0 */, r /* r >= 0 */, num); |
| return carry; |
| } |
| |
| BN_ULONG bn_reduce_once_in_place(BN_ULONG *r, BN_ULONG carry, const BN_ULONG *m, |
| BN_ULONG *tmp, size_t num) { |
| // See |bn_reduce_once| for why this logic works. |
| carry -= bn_sub_words(tmp, r, m, num); |
| declassify_assert(carry + 1 <= 1); |
| bn_select_words(r, carry, r /* tmp < 0 */, tmp /* tmp >= 0 */, num); |
| return carry; |
| } |
| |
| void bn_mod_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, |
| const BN_ULONG *m, BN_ULONG *tmp, size_t num) { |
| // r = a - b |
| BN_ULONG borrow = bn_sub_words(r, a, b, num); |
| // tmp = a - b + m |
| bn_add_words(tmp, r, m, num); |
| bn_select_words(r, 0 - borrow, tmp /* r < 0 */, r /* r >= 0 */, num); |
| } |
| |
| void bn_mod_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, |
| const BN_ULONG *m, BN_ULONG *tmp, size_t num) { |
| BN_ULONG carry = bn_add_words(r, a, b, num); |
| bn_reduce_once_in_place(r, carry, m, tmp, num); |
| } |
| |
| int bn_div_consttime(BIGNUM *quotient, BIGNUM *remainder, |
| const BIGNUM *numerator, const BIGNUM *divisor, |
| unsigned divisor_min_bits, BN_CTX *ctx) { |
| if (BN_is_negative(numerator) || BN_is_negative(divisor)) { |
| OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER); |
| return 0; |
| } |
| if (BN_is_zero(divisor)) { |
| OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO); |
| return 0; |
| } |
| |
| // This function implements long division in binary. It is not very efficient, |
| // but it is simple, easy to make constant-time, and performant enough for RSA |
| // key generation. |
| |
| int ret = 0; |
| BN_CTX_start(ctx); |
| BIGNUM *q = quotient, *r = remainder; |
| if (quotient == NULL || quotient == numerator || quotient == divisor) { |
| q = BN_CTX_get(ctx); |
| } |
| if (remainder == NULL || remainder == numerator || remainder == divisor) { |
| r = BN_CTX_get(ctx); |
| } |
| BIGNUM *tmp = BN_CTX_get(ctx); |
| if (q == NULL || r == NULL || tmp == NULL || |
| !bn_wexpand(q, numerator->width) || |
| !bn_wexpand(r, divisor->width) || |
| !bn_wexpand(tmp, divisor->width)) { |
| goto err; |
| } |
| |
| OPENSSL_memset(q->d, 0, numerator->width * sizeof(BN_ULONG)); |
| q->width = numerator->width; |
| q->neg = 0; |
| |
| OPENSSL_memset(r->d, 0, divisor->width * sizeof(BN_ULONG)); |
| r->width = divisor->width; |
| r->neg = 0; |
| |
| // Incorporate |numerator| into |r|, one bit at a time, reducing after each |
| // step. We maintain the invariant that |0 <= r < divisor| and |
| // |q * divisor + r = n| where |n| is the portion of |numerator| incorporated |
| // so far. |
| // |
| // First, we short-circuit the loop: if we know |divisor| has at least |
| // |divisor_min_bits| bits, the top |divisor_min_bits - 1| can be incorporated |
| // without reductions. This significantly speeds up |RSA_check_key|. For |
| // simplicity, we round down to a whole number of words. |
| declassify_assert(divisor_min_bits <= BN_num_bits(divisor)); |
| int initial_words = 0; |
| if (divisor_min_bits > 0) { |
| initial_words = (divisor_min_bits - 1) / BN_BITS2; |
| if (initial_words > numerator->width) { |
| initial_words = numerator->width; |
| } |
| OPENSSL_memcpy(r->d, numerator->d + numerator->width - initial_words, |
| initial_words * sizeof(BN_ULONG)); |
| } |
| |
| for (int i = numerator->width - initial_words - 1; i >= 0; i--) { |
| for (int bit = BN_BITS2 - 1; bit >= 0; bit--) { |
| // Incorporate the next bit of the numerator, by computing |
| // r = 2*r or 2*r + 1. Note the result fits in one more word. We store the |
| // extra word in |carry|. |
| BN_ULONG carry = bn_add_words(r->d, r->d, r->d, divisor->width); |
| r->d[0] |= (numerator->d[i] >> bit) & 1; |
| // |r| was previously fully-reduced, so we know: |
| // 2*0 <= r <= 2*(divisor-1) + 1 |
| // 0 <= r <= 2*divisor - 1 < 2*divisor. |
| // Thus |r| satisfies the preconditions for |bn_reduce_once_in_place|. |
| BN_ULONG subtracted = bn_reduce_once_in_place(r->d, carry, divisor->d, |
| tmp->d, divisor->width); |
| // The corresponding bit of the quotient is set iff we needed to subtract. |
| q->d[i] |= (~subtracted & 1) << bit; |
| } |
| } |
| |
| if ((quotient != NULL && !BN_copy(quotient, q)) || |
| (remainder != NULL && !BN_copy(remainder, r))) { |
| goto err; |
| } |
| |
| ret = 1; |
| |
| err: |
| BN_CTX_end(ctx); |
| return ret; |
| } |
| |
| static BIGNUM *bn_scratch_space_from_ctx(size_t width, BN_CTX *ctx) { |
| BIGNUM *ret = BN_CTX_get(ctx); |
| if (ret == NULL || |
| !bn_wexpand(ret, width)) { |
| return NULL; |
| } |
| ret->neg = 0; |
| ret->width = (int)width; |
| return ret; |
| } |
| |
| // bn_resized_from_ctx returns |bn| with width at least |width| or NULL on |
| // error. This is so it may be used with low-level "words" functions. If |
| // necessary, it allocates a new |BIGNUM| with a lifetime of the current scope |
| // in |ctx|, so the caller does not need to explicitly free it. |bn| must fit in |
| // |width| words. |
| static const BIGNUM *bn_resized_from_ctx(const BIGNUM *bn, size_t width, |
| BN_CTX *ctx) { |
| if ((size_t)bn->width >= width) { |
| // Any excess words must be zero. |
| assert(bn_fits_in_words(bn, width)); |
| return bn; |
| } |
| BIGNUM *ret = bn_scratch_space_from_ctx(width, ctx); |
| if (ret == NULL || |
| !BN_copy(ret, bn) || |
| !bn_resize_words(ret, width)) { |
| return NULL; |
| } |
| return ret; |
| } |
| |
| 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) { |
| BN_CTX *ctx = BN_CTX_new(); |
| int ok = ctx != NULL && |
| bn_mod_add_consttime(r, a, b, m, ctx); |
| BN_CTX_free(ctx); |
| return ok; |
| } |
| |
| int bn_mod_add_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| const BIGNUM *m, BN_CTX *ctx) { |
| BN_CTX_start(ctx); |
| a = bn_resized_from_ctx(a, m->width, ctx); |
| b = bn_resized_from_ctx(b, m->width, ctx); |
| BIGNUM *tmp = bn_scratch_space_from_ctx(m->width, ctx); |
| int ok = a != NULL && b != NULL && tmp != NULL && |
| bn_wexpand(r, m->width); |
| if (ok) { |
| bn_mod_add_words(r->d, a->d, b->d, m->d, tmp->d, m->width); |
| r->width = m->width; |
| r->neg = 0; |
| } |
| BN_CTX_end(ctx); |
| return ok; |
| } |
| |
| 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); |
| } |
| |
| int bn_mod_sub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| const BIGNUM *m, BN_CTX *ctx) { |
| BN_CTX_start(ctx); |
| a = bn_resized_from_ctx(a, m->width, ctx); |
| b = bn_resized_from_ctx(b, m->width, ctx); |
| BIGNUM *tmp = bn_scratch_space_from_ctx(m->width, ctx); |
| int ok = a != NULL && b != NULL && tmp != NULL && |
| bn_wexpand(r, m->width); |
| if (ok) { |
| bn_mod_sub_words(r->d, a->d, b->d, m->d, tmp->d, m->width); |
| r->width = m->width; |
| r->neg = 0; |
| } |
| BN_CTX_end(ctx); |
| return ok; |
| } |
| |
| int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, |
| const BIGNUM *m) { |
| BN_CTX *ctx = BN_CTX_new(); |
| int ok = ctx != NULL && |
| bn_mod_sub_consttime(r, a, b, m, ctx); |
| BN_CTX_free(ctx); |
| return ok; |
| } |
| |
| 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_consttime(r, r, n, (abs_m ? abs_m : m), ctx); |
| |
| BN_free(abs_m); |
| return ret; |
| } |
| |
| int bn_mod_lshift_consttime(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m, |
| BN_CTX *ctx) { |
| if (!BN_copy(r, a) || |
| !bn_resize_words(r, m->width)) { |
| return 0; |
| } |
| |
| BN_CTX_start(ctx); |
| BIGNUM *tmp = bn_scratch_space_from_ctx(m->width, ctx); |
| int ok = tmp != NULL; |
| if (ok) { |
| for (int i = 0; i < n; i++) { |
| bn_mod_add_words(r->d, r->d, r->d, m->d, tmp->d, m->width); |
| } |
| r->neg = 0; |
| } |
| BN_CTX_end(ctx); |
| return ok; |
| } |
| |
| int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m) { |
| BN_CTX *ctx = BN_CTX_new(); |
| int ok = ctx != NULL && |
| bn_mod_lshift_consttime(r, a, n, m, ctx); |
| BN_CTX_free(ctx); |
| return ok; |
| } |
| |
| 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_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, |
| BN_CTX *ctx) { |
| return bn_mod_add_consttime(r, a, a, m, ctx); |
| } |
| |
| int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m) { |
| BN_CTX *ctx = BN_CTX_new(); |
| int ok = ctx != NULL && |
| bn_mod_lshift1_consttime(r, a, m, ctx); |
| BN_CTX_free(ctx); |
| return ok; |
| } |
| |
| BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w) { |
| BN_ULONG ret = 0; |
| int i, j; |
| |
| if (!w) { |
| // actually this an error (division by zero) |
| return (BN_ULONG) - 1; |
| } |
| |
| if (a->width == 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->width - 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); |
| a->d[i] = d; |
| } |
| |
| bn_set_minimal_width(a); |
| ret >>= j; |
| return ret; |
| } |
| |
| BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w) { |
| #ifndef BN_CAN_DIVIDE_ULLONG |
| BN_ULONG ret = 0; |
| #else |
| BN_ULLONG ret = 0; |
| #endif |
| int i; |
| |
| if (w == 0) { |
| return (BN_ULONG) -1; |
| } |
| |
| #ifndef BN_CAN_DIVIDE_ULLONG |
| // If |w| is too long and we don't have |BN_ULLONG| division then we need to |
| // fall back to using |BN_div_word|. |
| if (w > ((BN_ULONG)1 << BN_BITS4)) { |
| BIGNUM *tmp = BN_dup(a); |
| if (tmp == NULL) { |
| return (BN_ULONG)-1; |
| } |
| ret = BN_div_word(tmp, w); |
| BN_free(tmp); |
| return ret; |
| } |
| #endif |
| |
| for (i = a->width - 1; i >= 0; i--) { |
| #ifndef BN_CAN_DIVIDE_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; |
| } |
| |
| int BN_mod_pow2(BIGNUM *r, const BIGNUM *a, size_t e) { |
| if (e == 0 || a->width == 0) { |
| BN_zero(r); |
| return 1; |
| } |
| |
| size_t num_words = 1 + ((e - 1) / BN_BITS2); |
| |
| // If |a| definitely has less than |e| bits, just BN_copy. |
| if ((size_t) a->width < num_words) { |
| return BN_copy(r, a) != NULL; |
| } |
| |
| // Otherwise, first make sure we have enough space in |r|. |
| // Note that this will fail if num_words > INT_MAX. |
| if (!bn_wexpand(r, num_words)) { |
| return 0; |
| } |
| |
| // Copy the content of |a| into |r|. |
| OPENSSL_memcpy(r->d, a->d, num_words * sizeof(BN_ULONG)); |
| |
| // If |e| isn't word-aligned, we have to mask off some of our bits. |
| size_t top_word_exponent = e % (sizeof(BN_ULONG) * 8); |
| if (top_word_exponent != 0) { |
| r->d[num_words - 1] &= (((BN_ULONG) 1) << top_word_exponent) - 1; |
| } |
| |
| // Fill in the remaining fields of |r|. |
| r->neg = a->neg; |
| r->width = (int) num_words; |
| bn_set_minimal_width(r); |
| return 1; |
| } |
| |
| int BN_nnmod_pow2(BIGNUM *r, const BIGNUM *a, size_t e) { |
| if (!BN_mod_pow2(r, a, e)) { |
| return 0; |
| } |
| |
| // If the returned value was non-negative, we're done. |
| if (BN_is_zero(r) || !r->neg) { |
| return 1; |
| } |
| |
| size_t num_words = 1 + (e - 1) / BN_BITS2; |
| |
| // Expand |r| to the size of our modulus. |
| if (!bn_wexpand(r, num_words)) { |
| return 0; |
| } |
| |
| // Clear the upper words of |r|. |
| OPENSSL_memset(&r->d[r->width], 0, (num_words - r->width) * BN_BYTES); |
| |
| // Set parameters of |r|. |
| r->neg = 0; |
| r->width = (int) num_words; |
| |
| // Now, invert every word. The idea here is that we want to compute 2^e-|x|, |
| // which is actually equivalent to the twos-complement representation of |x| |
| // in |e| bits, which is -x = ~x + 1. |
| for (int i = 0; i < r->width; i++) { |
| r->d[i] = ~r->d[i]; |
| } |
| |
| // If our exponent doesn't span the top word, we have to mask the rest. |
| size_t top_word_exponent = e % BN_BITS2; |
| if (top_word_exponent != 0) { |
| r->d[r->width - 1] &= (((BN_ULONG) 1) << top_word_exponent) - 1; |
| } |
| |
| // Keep the minimal-width invariant for |BIGNUM|. |
| bn_set_minimal_width(r); |
| |
| // Finally, add one, for the reason described above. |
| return BN_add(r, r, BN_value_one()); |
| } |