/* $OpenBSD: bn_recp.c,v 1.15 2017/01/29 17:49:22 beck Exp $ */ /* 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 <stdio.h> #include <openssl/err.h> #include "bn_lcl.h" void BN_RECP_CTX_init(BN_RECP_CTX *recp) { BN_init(&(recp->N)); BN_init(&(recp->Nr)); recp->num_bits = 0; recp->flags = 0; } BN_RECP_CTX * BN_RECP_CTX_new(void) { BN_RECP_CTX *ret; if ((ret = malloc(sizeof(BN_RECP_CTX))) == NULL) return (NULL); BN_RECP_CTX_init(ret); ret->flags = BN_FLG_MALLOCED; return (ret); } void BN_RECP_CTX_free(BN_RECP_CTX *recp) { if (recp == NULL) return; BN_free(&(recp->N)); BN_free(&(recp->Nr)); if (recp->flags & BN_FLG_MALLOCED) free(recp); } int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx) { if (!BN_copy(&(recp->N), d)) return 0; BN_zero(&(recp->Nr)); recp->num_bits = BN_num_bits(d); recp->shift = 0; return (1); } int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y, BN_RECP_CTX *recp, BN_CTX *ctx) { int ret = 0; BIGNUM *a; const BIGNUM *ca; BN_CTX_start(ctx); if ((a = BN_CTX_get(ctx)) == NULL) goto err; if (y != NULL) { if (x == y) { if (!BN_sqr(a, x, ctx)) goto err; } else { if (!BN_mul(a, x, y, ctx)) goto err; } ca = a; } else ca = x; /* Just do the mod */ ret = BN_div_recp(NULL, r, ca, recp, ctx); err: BN_CTX_end(ctx); bn_check_top(r); return (ret); } int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, BN_RECP_CTX *recp, BN_CTX *ctx) { int i, j, ret = 0; BIGNUM *a, *b, *d, *r; BN_CTX_start(ctx); a = BN_CTX_get(ctx); b = BN_CTX_get(ctx); if (dv != NULL) d = dv; else d = BN_CTX_get(ctx); if (rem != NULL) r = rem; else r = BN_CTX_get(ctx); if (a == NULL || b == NULL || d == NULL || r == NULL) goto err; if (BN_ucmp(m, &(recp->N)) < 0) { BN_zero(d); if (!BN_copy(r, m)) { BN_CTX_end(ctx); return 0; } BN_CTX_end(ctx); return (1); } /* We want the remainder * Given input of ABCDEF / ab * we need multiply ABCDEF by 3 digests of the reciprocal of ab * */ /* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */ i = BN_num_bits(m); j = recp->num_bits << 1; if (j > i) i = j; /* Nr := round(2^i / N) */ if (i != recp->shift) recp->shift = BN_reciprocal(&(recp->Nr), &(recp->N), i, ctx); /* BN_reciprocal returns i, or -1 for an error */ if (recp->shift == -1) goto err; /* d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - BN_num_bits(N)))| * = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - BN_num_bits(N)))| * <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)| * = |m/N| */ if (!BN_rshift(a, m, recp->num_bits)) goto err; if (!BN_mul(b, a,&(recp->Nr), ctx)) goto err; if (!BN_rshift(d, b, i - recp->num_bits)) goto err; d->neg = 0; if (!BN_mul(b, &(recp->N), d, ctx)) goto err; if (!BN_usub(r, m, b)) goto err; r->neg = 0; #if 1 j = 0; while (BN_ucmp(r, &(recp->N)) >= 0) { if (j++ > 2) { BNerror(BN_R_BAD_RECIPROCAL); goto err; } if (!BN_usub(r, r, &(recp->N))) goto err; if (!BN_add_word(d, 1)) goto err; } #endif r->neg = BN_is_zero(r) ? 0 : m->neg; d->neg = m->neg^recp->N.neg; ret = 1; err: BN_CTX_end(ctx); bn_check_top(dv); bn_check_top(rem); return (ret); } /* len is the expected size of the result * We actually calculate with an extra word of precision, so * we can do faster division if the remainder is not required. */ /* r := 2^len / m */ int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx) { int ret = -1; BIGNUM *t; BN_CTX_start(ctx); if ((t = BN_CTX_get(ctx)) == NULL) goto err; if (!BN_set_bit(t, len)) goto err; if (!BN_div_ct(r, NULL, t,m, ctx)) goto err; ret = len; err: bn_check_top(r); BN_CTX_end(ctx); return (ret); }
