--- /dev/null
+/* 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);
+ 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__) || defined(__clang__))
+ __asm__ volatile("divl %4"
+ : "=a"(*quotient_out), "=d"(*rem_out)
+ : "a"(n1), "d"(n0), "rm"(d0)
+ : "cc");
+#elif !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
+ (defined(__GNUC__) || defined(__clang__))
+ __asm__ volatile("divq %4"
+ : "=a"(*quotient_out), "=d"(*rem_out)
+ : "a"(n1), "d"(n0), "rm"(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 "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 to 'res'
+ 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) {
+ // Keep a copy of the neg flag in numerator because if |rem| == |numerator|
+ // |BN_rshift| will overwrite it.
+ int neg = numerator->neg;
+ if (!BN_rshift(rem, snum, norm_shift)) {
+ goto err;
+ }
+ if (!BN_is_zero(rem)) {
+ rem->neg = 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_mod_sub_words sets |r| to |a| - |b| (mod |m|), using |tmp| as scratch
+// space. Each array is |num| words long. |a| and |b| must be < |m|. Any pair of
+// |r|, |a|, and |b| may alias.
+static 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);
+}
+
+// bn_mod_add_words sets |r| to |a| + |b| (mod |m|), using |tmp| as scratch
+// space. Each array is |num| words long. |a| and |b| must be < |m|. Any pair of
+// |r|, |a|, and |b| may alias.
+static 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) {
+ // tmp = a + b. Note the result fits in |num|+1 words. We store the extra word
+ // in |carry|.
+ BN_ULONG carry = bn_add_words(tmp, a, b, num);
+ // r = a + b - m. We use |bn_sub_words| to perform the bulk of the
+ // subtraction, and then apply the borrow to |carry|.
+ carry -= bn_sub_words(r, tmp, m, num);
+ // |a| and |b| were both fully-reduced, so we know:
+ //
+ // 0 + 0 - m <= r < m + m - m
+ // -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 |tmp|. |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 |bn_add_words| returns one and
+ // |bn_sub_words| returns zero, this would give |r| > |m|, which violates are
+ // input assumptions.
+ assert(carry == 0 || carry == (BN_ULONG)-1);
+ bn_select_words(r, carry, tmp /* r < 0 */, r /* r >= 0 */, num);
+}
+
+int bn_div_consttime(BIGNUM *quotient, BIGNUM *remainder,
+ const BIGNUM *numerator, const BIGNUM *divisor,
+ 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. At the start of each loop iteration, |r| < |divisor|
+ for (int i = numerator->width - 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;
+ // tmp = r - divisor. We use |bn_sub_words| to perform the bulk of the
+ // subtraction, and then apply the borrow to |carry|.
+ carry -= bn_sub_words(tmp->d, r->d, divisor->d, divisor->width);
+ // |r| was previously fully-reduced, so we know:
+ //
+ // 2*0 - divisor <= tmp <= 2*(divisor-1) + 1 - divisor
+ // -divisor <= tmp < divisor
+ //
+ // If 0 <= |tmp| < |divisor|, |tmp| fits in |divisor->width| and |carry|
+ // is zero. We then wish to select |tmp|. Otherwise,
+ // -|divisor| <= |tmp| < 0 and we wish to select |tmp| + |divisor|, which
+ // is |r|. |carry| must then be -1 (all ones). In both cases, |carry| is a
+ // suitable input to |bn_select_words|.
+ //
+ // Although |carry| may be one if |bn_add_words| returns one and
+ // |bn_sub_words| returns zero, this would give |r| > |d|, which violates
+ // the loop invariant.
+ bn_select_words(r->d, carry, r->d /* tmp < 0 */, tmp->d /* tmp >= 0 */,
+ divisor->width);
+ // The corresponding bit of the quotient is set iff we needed to subtract.
+ q->d[i] |= (~carry & 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 = 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;
+ }
+ 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;
+ }
+ 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)) {
+ return 0;
+ }
+ for (int i = 0; i < n; i++) {
+ if (!bn_mod_lshift1_consttime(r, r, m, ctx)) {
+ return 0;
+ }
+ }
+ return 1;
+}
+
+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());
+}
git://repos.xcallymotion.com / motion2.git / blobdiff