/* 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 #include #include #include #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; } #ifndef BN_ULLONG /* If |w| is too long and we don't have |BN_ULLONG| 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 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; }