#include "bn.h" #ifndef WITH_LIBCRYPTO //FIXME Not checked on threadsafety yet; after checking please remove this line /* crypto/bn/bn_exp.c */ /* 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 license 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 license * [including the GNU Public License.] */ /* ==================================================================== * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved. * * 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 above 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 acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" * * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to * endorse or promote products derived from this software without * prior written permission. For written permission, please contact * openssl-core@openssl.org. * * 5. Products derived from this software may not be called "OpenSSL" * nor may "OpenSSL" appear in their names without prior written * permission of the OpenSSL Project. * * 6. Redistributions of any form whatsoever must retain the following * acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit (http://www.openssl.org/)" * * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY * EXPRESSED 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 OpenSSL PROJECT OR * ITS 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. * ==================================================================== * * This product includes cryptographic software written by Eric Young * (eay@cryptsoft.com). This product includes software written by Tim * Hudson (tjh@cryptsoft.com). * */ #include #include "bn_lcl.h" #define TABLE_SIZE 32 /* slow but works */ int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx) { BIGNUM *t; int r = 0; bn_check_top(a); bn_check_top(b); bn_check_top(m); BN_CTX_start(ctx); if((t = BN_CTX_get(ctx)) == 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_mod(ret, t, m, ctx)) { goto err; } r = 1; err: BN_CTX_end(ctx); return (r); } int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx) { int ret; bn_check_top(a); bn_check_top(p); bn_check_top(m); ret = BN_mod_exp_simple(r, a, p, m, ctx); return (ret); } /* The old fallback, simple version :-) */ int BN_mod_exp_simple(BIGNUM *r, BIGNUM *a, const BIGNUM *p, const BIGNUM *m, BN_CTX *ctx) { int i, j = 0, bits, ret = 0, wstart = 0, wend = 0, window, wvalue = 0, ts = 0; int start = 1; BIGNUM *d; BIGNUM val[TABLE_SIZE]; bits = BN_num_bits(p); if(bits == 0) { BN_one(r); return (1); } BN_CTX_start(ctx); if((d = BN_CTX_get(ctx)) == NULL) { goto err; } BN_init(&(val[0])); ts = 1; if(!BN_mod(&(val[0]), a, m, ctx)) { goto err; } /* 1 */ window = BN_window_bits_for_exponent_size(bits); if(window > 1) { if(!BN_mod_mul(d, &(val[0]), &(val[0]), m, ctx)) { goto err; } /* 2 */ j = 1 << (window - 1); for(i = 1; i < j; i++) { BN_init(&(val[i])); if(!BN_mod_mul(&(val[i]), &(val[i - 1]), d, m, ctx)) { goto err; } } ts = i; } start = 1; /* This is used to avoid multiplication etc * when there is only the value '1' in the * buffer. */ wstart = bits - 1; /* The top bit of the window */ if(!BN_one(r)) { goto err; } for(;;) { if(BN_is_bit_set(p, wstart) == 0) { if(!start) if(!BN_mod_mul(r, r, r, m, ctx)) { goto err; } if(wstart == 0) { break; } wstart--; continue; } /* We now have wstart on a 'set' bit, we now need to work out * how bit a window to do. To do this we need to scan * forward until the last set bit before the end of the * window */ j = wstart; wvalue = 1; wend = 0; for(i = 1; i < window; i++) { if(wstart - i < 0) { break; } if(BN_is_bit_set(p, wstart - i)) { wvalue <<= (i - wend); wvalue |= 1; wend = i; } } /* wend is the size of the current window */ j = wend + 1; /* add the 'bytes above' */ if(!start) for(i = 0; i < j; i++) { if(!BN_mod_mul(r, r, r, m, ctx)) { goto err; } } /* wvalue will be an odd number < 2^window */ if(!BN_mod_mul(r, r, &(val[wvalue >> 1]), m, ctx)) { goto err; } /* move the 'window' down further */ wstart -= wend + 1; wvalue = 0; start = 0; if(wstart < 0) { break; } } ret = 1; err: BN_CTX_end(ctx); for(i = 0; i < ts; i++) { BN_clear_free(&(val[i])); } return (ret); } int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx) { /* like BN_mod, but returns non-negative remainder * (i.e., 0 <= r < |d| always holds) */ 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); } /* solves ax == 1 (mod n) */ BIGNUM * BN_mod_inverse(BIGNUM *ret, BIGNUM *a, const BIGNUM *n, BN_CTX *ctx) { BIGNUM *A, *B, *X, *Y, *M, *D, *T = NULL; int sign; bn_check_top(a); bn_check_top(n); BN_CTX_start(ctx); A = BN_CTX_get(ctx); B = BN_CTX_get(ctx); X = BN_CTX_get(ctx); D = BN_CTX_get(ctx); M = BN_CTX_get(ctx); Y = BN_CTX_get(ctx); T = BN_CTX_get(ctx); if (T == NULL) goto err; if (ret == NULL) goto err; BN_one(X); BN_zero(Y); if (BN_copy(B, a) == NULL) goto err; if (BN_copy(A, n) == NULL) goto err; A->neg = 0; if (B->neg || (BN_ucmp(B, A) >= 0)) { if (!BN_nnmod(B, B, A, ctx)) goto err; } sign = -1; /* From B = a mod |n|, A = |n| it follows that * * 0 <= B < A, * -sign*X*a == B (mod |n|), * sign*Y*a == A (mod |n|). */ if (BN_is_odd(n) && (BN_num_bits(n) <= (BN_BITS <= 32 ? 450 : 2048))) { /* Binary inversion algorithm; requires odd modulus. * This is faster than the general algorithm if the modulus * is sufficiently small (about 400 .. 500 bits on 32-bit * sytems, but much more on 64-bit systems) */ int shift; while (!BN_is_zero(B)) { /* * 0 < B < |n|, * 0 < A <= |n|, * (1) -sign*X*a == B (mod |n|), * (2) sign*Y*a == A (mod |n|) */ /* Now divide B by the maximum possible power of two in the integers, * and divide X by the same value mod |n|. * When we're done, (1) still holds. */ shift = 0; while (!BN_is_bit_set(B, shift)) /* note that 0 < B */ { shift++; if (BN_is_odd(X)) { if (!BN_uadd(X, X, n)) goto err; } /* now X is even, so we can easily divide it by two */ if (!BN_rshift1(X, X)) goto err; } if (shift > 0) { if (!BN_rshift(B, B, shift)) goto err; } /* Same for A and Y. Afterwards, (2) still holds. */ shift = 0; while (!BN_is_bit_set(A, shift)) /* note that 0 < A */ { shift++; if (BN_is_odd(Y)) { if (!BN_uadd(Y, Y, n)) goto err; } /* now Y is even */ if (!BN_rshift1(Y, Y)) goto err; } if (shift > 0) { if (!BN_rshift(A, A, shift)) goto err; } /* We still have (1) and (2). * Both A and B are odd. * The following computations ensure that * * 0 <= B < |n|, * 0 < A < |n|, * (1) -sign*X*a == B (mod |n|), * (2) sign*Y*a == A (mod |n|), * * and that either A or B is even in the next iteration. */ if (BN_ucmp(B, A) >= 0) { /* -sign*(X + Y)*a == B - A (mod |n|) */ if (!BN_uadd(X, X, Y)) goto err; /* NB: we could use BN_mod_add_quick(X, X, Y, n), but that * actually makes the algorithm slower */ if (!BN_usub(B, B, A)) goto err; } else { /* sign*(X + Y)*a == A - B (mod |n|) */ if (!BN_uadd(Y, Y, X)) goto err; /* as above, BN_mod_add_quick(Y, Y, X, n) would slow things down */ if (!BN_usub(A, A, B)) goto err; } } } else { /* general inversion algorithm */ while (!BN_is_zero(B)) { BIGNUM *tmp; /* * 0 < B < A, * (*) -sign*X*a == B (mod |n|), * sign*Y*a == A (mod |n|) */ /* (D, M) : = (A/B, A%B) ... */ if (BN_num_bits(A) == BN_num_bits(B)) { if (!BN_one(D)) goto err; if (!BN_sub(M, A, B)) goto err; } else if (BN_num_bits(A) == BN_num_bits(B) + 1) { /* A/B is 1, 2, or 3 */ if (!BN_lshift1(T, B)) goto err; if (BN_ucmp(A, T) < 0) { /* A < 2*B, so D = 1 */ if (!BN_one(D)) goto err; if (!BN_sub(M, A, B)) goto err; } else { /* A >= 2*B, so D = 2 or D = 3 */ if (!BN_sub(M, A, T)) goto err; if (!BN_add(D, T, B)) goto err; /* use D ( := 3 * B) as temp */ if (BN_ucmp(A, D) < 0) { /* A < 3*B, so D = 2 */ if (!BN_set_word(D, 2)) goto err; /* M ( = A - 2*B) already has the correct value */ } else { /* only D = 3 remains */ if (!BN_set_word(D, 3)) goto err; /* currently M = A - 2 * B, * but we need M = A - 3 * B */ if (!BN_sub(M, M, B)) goto err; } } } else { if (!BN_div(D, M, A, B, ctx)) goto err; } /* Now * A = D*B + M; * thus we have * (**) sign*Y*a == D*B + M (mod |n|). */ tmp = A; /* keep the BIGNUM object, the value does not matter */ /* (A, B) : = (B, A mod B) ... */ A = B; B = M; /* ... so we have 0 <= B < A again */ /* Since the former M is now B and the former B is now A, * (**) translates into * sign*Y*a == D*A + B (mod |n|), * i.e. * sign*Y*a - D*A == B (mod |n|). * Similarly, (*) translates into * -sign*X*a == A (mod |n|). * * Thus, * sign*Y*a + D*sign*X*a == B (mod |n|), * i.e. * sign*(Y + D*X)*a == B (mod |n|). * * So if we set (X, Y, sign) : = (Y + D*X, X, -sign), we arrive back at * -sign*X*a == B (mod |n|), * sign*Y*a == A (mod |n|). * Note that X and Y stay non-negative all the time. */ /* most of the time D is very small, so we can optimize tmp : = D*X+Y */ if (BN_is_one(D)) { if (!BN_add(tmp, X, Y)) goto err; } else { if (BN_is_word(D, 2)) { if (!BN_lshift1(tmp, X)) goto err; } else if (BN_is_word(D, 4)) { if (!BN_lshift(tmp, X, 2)) goto err; } else if (D->top == 1) { if (!BN_copy(tmp, X)) goto err; if (!BN_mul_word(tmp, D->d[0])) goto err; } else { if (!BN_mul(tmp, D, X, ctx)) goto err; } if (!BN_add(tmp, tmp, Y)) goto err; } M = Y; /* keep the BIGNUM object, the value does not matter */ Y = X; X = tmp; sign = -sign; } } /* * The while loop (Euclid's algorithm) ends when * A == gcd(a, n); * we have * sign*Y*a == A (mod |n|), * where Y is non-negative. */ if (sign < 0) { if (!BN_sub(Y, n, Y)) goto err; } /* Now Y*a == A (mod |n|). */ if (BN_is_one(A)) { /* Y*a == 1 (mod |n|) */ if (!Y->neg && BN_ucmp(Y, n) < 0) { if (!BN_copy(ret, Y)) goto err; } else { if (!BN_nnmod(ret, Y, n, ctx)) goto err; } } else { goto err; } err: BN_CTX_end(ctx); return (ret); } #endif