/* $OpenBSD: bn_recp.c,v 1.34 2025/05/10 05:54:38 tb 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 "bn_local.h" #include "err_local.h" struct bn_recp_ctx_st { BIGNUM *N; /* the divisor */ BIGNUM *Nr; /* the reciprocal 2^shift / N */ int num_bits; /* number of bits in N */ int shift; } /* BN_RECP_CTX */; BN_RECP_CTX * BN_RECP_CTX_create(const BIGNUM *N) { BN_RECP_CTX *recp; if ((recp = calloc(1, sizeof(*recp))) == NULL) goto err; if ((recp->N = BN_dup(N)) == NULL) goto err; BN_set_negative(recp->N, 0); recp->num_bits = BN_num_bits(recp->N); if ((recp->Nr = BN_new()) == NULL) goto err; return recp; err: BN_RECP_CTX_free(recp); return NULL; } void BN_RECP_CTX_free(BN_RECP_CTX *recp) { if (recp == NULL) return; BN_free(recp->N); BN_free(recp->Nr); freezero(recp, sizeof(*recp)); } int BN_div_reciprocal(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, BN_RECP_CTX *recp, BN_CTX *ctx) { int i, j, ret = 0; BIGNUM *a, *b, *d, *r; if (BN_ucmp(m, recp->N) < 0) { if (dv != NULL) BN_zero(dv); if (rem != NULL) return bn_copy(rem, m); return 1; } BN_CTX_start(ctx); if ((a = BN_CTX_get(ctx)) == NULL) goto err; if ((b = BN_CTX_get(ctx)) == NULL) goto err; if ((d = dv) == NULL) d = BN_CTX_get(ctx); if (d == NULL) goto err; if ((r = rem) == NULL) r = BN_CTX_get(ctx); if (r == NULL) goto err; /* * We want the remainder. Given input of ABCDEF / ab we need to * multiply ABCDEF by 3 digits 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; /* Compute Nr := (1 << i) / N if necessary. */ if (i != recp->shift) { BN_zero(recp->Nr); if (!BN_set_bit(recp->Nr, i)) goto err; if (!BN_div_ct(recp->Nr, NULL, recp->Nr, recp->N, ctx)) goto err; recp->shift = i; } /* * d := |((m >> BN_num_bits(N)) * recp->Nr) >> (i - BN_num_bits(N))| * = |((m >> BN_num_bits(N)) * (1 << i) / N) >> (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 BN_set_negative(r, m->neg); BN_set_negative(d, m->neg ^ recp->N->neg); ret = 1; err: BN_CTX_end(ctx); return ret; } /* Compute r = (x * y) % m. */ int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y, BN_RECP_CTX *recp, BN_CTX *ctx) { if (!BN_mul(r, x, y, ctx)) return 0; return BN_div_reciprocal(NULL, r, r, recp, ctx); } /* Compute r = x^2 % m. */ int BN_mod_sqr_reciprocal(BIGNUM *r, const BIGNUM *x, BN_RECP_CTX *recp, BN_CTX *ctx) { if (!BN_sqr(r, x, ctx)) return 0; return BN_div_reciprocal(NULL, r, r, recp, ctx); }
