| /* 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 <limits.h> |
| #include <openssl/err.h> |
| |
| #include "internal.h" |
| |
| |
| #define asm __asm__ |
| |
| #if !defined(OPENSSL_NO_ASM) |
| # if defined(__GNUC__) && __GNUC__>=2 |
| # if defined(OPENSSL_X86) |
| /* |
| * There were two reasons for implementing this template: |
| * - GNU C generates a call to a function (__udivdi3 to be exact) |
| * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to |
| * understand why...); |
| * - divl doesn't only calculate quotient, but also leaves |
| * remainder in %edx which we can definitely use here:-) |
| * |
| * <appro@fy.chalmers.se> |
| */ |
| #undef div_asm |
| # define div_asm(n0,n1,d0) \ |
| ({ asm volatile ( \ |
| "divl %4" \ |
| : "=a"(q), "=d"(rem) \ |
| : "a"(n1), "d"(n0), "g"(d0) \ |
| : "cc"); \ |
| q; \ |
| }) |
| # define REMAINDER_IS_ALREADY_CALCULATED |
| # elif defined(OPENSSL_X86_64) |
| /* |
| * Same story here, but it's 128-bit by 64-bit division. Wow! |
| * <appro@fy.chalmers.se> |
| */ |
| # undef div_asm |
| # define div_asm(n0,n1,d0) \ |
| ({ asm volatile ( \ |
| "divq %4" \ |
| : "=a"(q), "=d"(rem) \ |
| : "a"(n1), "d"(n0), "g"(d0) \ |
| : "cc"); \ |
| q; \ |
| }) |
| # define REMAINDER_IS_ALREADY_CALCULATED |
| # endif /* __<cpu> */ |
| # endif /* __GNUC__ */ |
| #endif /* OPENSSL_NO_ASM */ |
| |
| /* 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_div, 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_div, 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 */ |
| #ifdef BN_LLONG |
| BN_ULLONG t2; |
| |
| #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(div_asm) |
| q = (BN_ULONG)(((((BN_ULLONG)n0) << BN_BITS2) | n1) / d0); |
| #else |
| q = div_asm(n0, n1, d0); |
| #endif |
| |
| #ifndef REMAINDER_IS_ALREADY_CALCULATED |
| /* rem doesn't have to be BN_ULLONG. The least we know it's less that d0, |
| * isn't it? */ |
| rem = (n1 - q * d0) & BN_MASK2; |
| #endif |
| |
| 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_LLONG */ |
| BN_ULONG t2l, t2h; |
| |
| #if defined(div_asm) |
| q = div_asm(n0, n1, d0); |
| #else |
| q = bn_div_words(n0, n1, d0); |
| #endif |
| |
| #ifndef REMAINDER_IS_ALREADY_CALCULATED |
| rem = (n1 - q * d0) & BN_MASK2; |
| #endif |
| |
| #if defined(BN_UMULT_LOHI) |
| BN_UMULT_LOHI(t2l, t2h, d1, q); |
| #elif defined(BN_UMULT_HIGH) |
| t2l = d1 * q; |
| t2h = BN_UMULT_HIGH(d1, q); |
| #else |
| { |
| BN_ULONG ql, qh; |
| t2l = LBITS(d1); |
| t2h = HBITS(d1); |
| ql = LBITS(q); |
| qh = HBITS(q); |
| mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */ |
| } |
| #endif |
| |
| 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_LLONG */ |
| } |
| |
| 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; |
| BN_rshift(rm, snum, norm_shift); |
| 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)); |
| |
| if (abs_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_mod_lshift_quick, 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 (so bn_div_words doesn't complain) */ |
| 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, d; |
| |
| l = a->d[i]; |
| d = bn_div_words(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_LLONG |
| 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_LLONG |
| 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; |
| } |