/* 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_CAN_DIVIDE_ULLONG) && !defined(BN_CAN_USE_INLINE_ASM) // 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_CAN_DIVIDE_ULLONG) && !defined(BN_CAN_USE_INLINE_ASM) 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 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_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. assert(carry == 0 || carry == (BN_ULONG)-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); assert(carry == 0 || carry == (BN_ULONG)-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, 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; // |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 = 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)) { 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()); }