/* 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.] */ /* ==================================================================== * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. * * Portions of the attached software ("Contribution") are developed by * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. * * The Contribution is licensed pursuant to the Eric Young open source * license provided above. * * The binary polynomial arithmetic software is originally written by * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems * Laboratories. */ #include #include #include #include #include #include "internal.h" static const int num0 = 100; /* number of tests */ static const int num1 = 50; /* additional tests for some functions */ static const int num2 = 5; /* number of tests for slow functions */ int test_add(BIO *bp); int test_sub(BIO *bp); int test_lshift1(BIO *bp); int test_lshift(BIO *bp, BN_CTX *ctx, BIGNUM *a_); int test_rshift1(BIO *bp); int test_rshift(BIO *bp, BN_CTX *ctx); int test_sqr(BIO *bp, BN_CTX *ctx); int test_mul(BIO *bp); int test_div(BIO *bp, BN_CTX *ctx); int rand_neg(void); int test_div_word(BIO *bp); int test_mont(BIO *bp, BN_CTX *ctx); int test_mod(BIO *bp, BN_CTX *ctx); int test_mod_mul(BIO *bp, BN_CTX *ctx); int test_mod_exp(BIO *bp, BN_CTX *ctx); int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx); int test_exp(BIO *bp, BN_CTX *ctx); int test_mod_sqrt(BIO *bp, BN_CTX *ctx); static int test_exp_mod_zero(); int test_small_prime(BIO *bp,BN_CTX *ctx); int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx); int test_sqrt(BIO *bp, BN_CTX *ctx); #if 0 int test_gf2m_add(BIO *bp); int test_gf2m_mod(BIO *bp); int test_gf2m_mod_mul(BIO *bp, BN_CTX *ctx); int test_gf2m_mod_sqr(BIO *bp, BN_CTX *ctx); int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx); int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx); int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx); int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx); int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx); #endif static int results = 0; static unsigned char lst[] = "\xC6\x4F\x43\x04\x2A\xEA\xCA\x6E\x58\x36\x80\x5B\xE8\xC9" "\x9B\x04\x5D\x48\x36\xC2\xFD\x16\xC9\x64\xF0"; static void ERR_print_errors_fp(FILE *out) { } static void message(BIO *out, char *m) { BIO_puts(out, "print \"test "); BIO_puts(out, m); BIO_puts(out, "\\n\"\n"); } int main(int argc, char *argv[]) { BN_CTX *ctx; BIO *out = NULL; char *outfile = NULL; results = 0; argc--; argv++; while (argc >= 1) { if (strcmp(*argv, "-results") == 0) results = 1; else if (strcmp(*argv, "-out") == 0) { if (--argc < 1) break; outfile = *(++argv); } argc--; argv++; } ctx = BN_CTX_new(); if (ctx == NULL) return 1; out = BIO_new(BIO_s_file()); if (out == NULL) { return 1; } if (outfile == NULL) { BIO_set_fp(out, stdout, BIO_NOCLOSE); } else { if (!BIO_write_filename(out, outfile)) { perror(outfile); return 1; } } if (!results) BIO_puts(out, "obase=16\nibase=16\n"); message(out, "BN_add"); if (!test_add(out)) goto err; (void)BIO_flush(out); message(out, "BN_sub"); if (!test_sub(out)) goto err; (void)BIO_flush(out); message(out, "BN_lshift1"); if (!test_lshift1(out)) goto err; (void)BIO_flush(out); message(out, "BN_lshift (fixed)"); if (!test_lshift(out, ctx, BN_bin2bn(lst, sizeof(lst) - 1, NULL))) goto err; (void)BIO_flush(out); message(out, "BN_lshift"); if (!test_lshift(out, ctx, NULL)) goto err; (void)BIO_flush(out); message(out, "BN_rshift1"); if (!test_rshift1(out)) goto err; (void)BIO_flush(out); message(out, "BN_rshift"); if (!test_rshift(out, ctx)) goto err; (void)BIO_flush(out); message(out, "BN_sqr"); if (!test_sqr(out, ctx)) goto err; (void)BIO_flush(out); message(out, "BN_mul"); if (!test_mul(out)) goto err; (void)BIO_flush(out); message(out, "BN_div"); if (!test_div(out, ctx)) goto err; (void)BIO_flush(out); message(out, "BN_div_word"); if (!test_div_word(out)) goto err; (void)BIO_flush(out); message(out, "BN_mod"); if (!test_mod(out, ctx)) goto err; (void)BIO_flush(out); message(out, "BN_mod_mul"); if (!test_mod_mul(out, ctx)) goto err; (void)BIO_flush(out); message(out, "BN_mont"); if (!test_mont(out, ctx)) goto err; (void)BIO_flush(out); message(out, "BN_mod_exp"); if (!test_mod_exp(out, ctx)) goto err; (void)BIO_flush(out); message(out, "BN_mod_exp_mont_consttime"); if (!test_mod_exp_mont_consttime(out, ctx) || !test_mod_exp_mont5(out, ctx)) { goto err; } (void)BIO_flush(out); message(out, "BN_exp"); if (!test_exp(out, ctx) || !test_exp_mod_zero()) { goto err; } (void)BIO_flush(out); message(out, "BN_mod_sqrt"); if (!test_mod_sqrt(out, ctx)) goto err; (void)BIO_flush(out); message(out, "Small prime generation"); if (!test_small_prime(out, ctx)) goto err; (void)BIO_flush(out); message(out, "BN_sqrt"); if (!test_sqrt(out, ctx)) goto err; (void)BIO_flush(out); BN_CTX_free(ctx); BIO_free(out); printf("PASS\n"); return 0; err: BIO_puts(out, "1\n"); /* make sure the Perl script fed by bc notices * the failure, see test_bn in test/Makefile.ssl*/ (void)BIO_flush(out); return 1; } int test_add(BIO *bp) { BIGNUM a, b, c; int i; BN_init(&a); BN_init(&b); BN_init(&c); BN_rand(&a, 512, 0, 0); for (i = 0; i < num0; i++) { BN_rand(&b, 450 + i, 0, 0); a.neg = rand_neg(); b.neg = rand_neg(); BN_add(&c, &a, &b); if (bp != NULL) { if (!results) { BN_print(bp, &a); BIO_puts(bp, " + "); BN_print(bp, &b); BIO_puts(bp, " - "); } BN_print(bp, &c); BIO_puts(bp, "\n"); } a.neg = !a.neg; b.neg = !b.neg; BN_add(&c, &c, &b); BN_add(&c, &c, &a); if (!BN_is_zero(&c)) { fprintf(stderr, "Add test failed!\n"); return 0; } } BN_free(&a); BN_free(&b); BN_free(&c); return (1); } int test_sub(BIO *bp) { BIGNUM a, b, c; int i; BN_init(&a); BN_init(&b); BN_init(&c); for (i = 0; i < num0 + num1; i++) { if (i < num1) { BN_rand(&a, 512, 0, 0); BN_copy(&b, &a); if (BN_set_bit(&a, i) == 0) return (0); BN_add_word(&b, i); } else { BN_rand(&b, 400 + i - num1, 0, 0); a.neg = rand_neg(); b.neg = rand_neg(); } BN_sub(&c, &a, &b); if (bp != NULL) { if (!results) { BN_print(bp, &a); BIO_puts(bp, " - "); BN_print(bp, &b); BIO_puts(bp, " - "); } BN_print(bp, &c); BIO_puts(bp, "\n"); } BN_add(&c, &c, &b); BN_sub(&c, &c, &a); if (!BN_is_zero(&c)) { fprintf(stderr, "Subtract test failed!\n"); return 0; } } BN_free(&a); BN_free(&b); BN_free(&c); return (1); } int test_div(BIO *bp, BN_CTX *ctx) { BIGNUM a, b, c, d, e; int i; BN_init(&a); BN_init(&b); BN_init(&c); BN_init(&d); BN_init(&e); for (i = 0; i < num0 + num1; i++) { if (i < num1) { BN_rand(&a, 400, 0, 0); BN_copy(&b, &a); BN_lshift(&a, &a, i); BN_add_word(&a, i); } else BN_rand(&b, 50 + 3 * (i - num1), 0, 0); a.neg = rand_neg(); b.neg = rand_neg(); BN_div(&d, &c, &a, &b, ctx); if (bp != NULL) { if (!results) { BN_print(bp, &a); BIO_puts(bp, " / "); BN_print(bp, &b); BIO_puts(bp, " - "); } BN_print(bp, &d); BIO_puts(bp, "\n"); if (!results) { BN_print(bp, &a); BIO_puts(bp, " % "); BN_print(bp, &b); BIO_puts(bp, " - "); } BN_print(bp, &c); BIO_puts(bp, "\n"); } BN_mul(&e, &d, &b, ctx); BN_add(&d, &e, &c); BN_sub(&d, &d, &a); if (!BN_is_zero(&d)) { fprintf(stderr, "Division test failed!\n"); return 0; } } BN_free(&a); BN_free(&b); BN_free(&c); BN_free(&d); BN_free(&e); return (1); } int test_lshift1(BIO *bp) { BIGNUM *a, *b, *c; int i; a = BN_new(); b = BN_new(); c = BN_new(); BN_rand(a, 200, 0, 0); /**/ a->neg = rand_neg(); for (i = 0; i < num0; i++) { BN_lshift1(b, a); if (bp != NULL) { if (!results) { BN_print(bp, a); BIO_puts(bp, " * 2"); BIO_puts(bp, " - "); } BN_print(bp, b); BIO_puts(bp, "\n"); } BN_add(c, a, a); BN_sub(a, b, c); if (!BN_is_zero(a)) { fprintf(stderr, "Left shift one test failed!\n"); return 0; } BN_copy(a, b); } BN_free(a); BN_free(b); BN_free(c); return (1); } int test_rshift(BIO *bp, BN_CTX *ctx) { BIGNUM *a, *b, *c, *d, *e; int i; a = BN_new(); b = BN_new(); c = BN_new(); d = BN_new(); e = BN_new(); BN_one(c); BN_rand(a, 200, 0, 0); /**/ a->neg = rand_neg(); for (i = 0; i < num0; i++) { BN_rshift(b, a, i + 1); BN_add(c, c, c); if (bp != NULL) { if (!results) { BN_print(bp, a); BIO_puts(bp, " / "); BN_print(bp, c); BIO_puts(bp, " - "); } BN_print(bp, b); BIO_puts(bp, "\n"); } BN_div(d, e, a, c, ctx); BN_sub(d, d, b); if (!BN_is_zero(d)) { fprintf(stderr, "Right shift test failed!\n"); return 0; } } BN_free(a); BN_free(b); BN_free(c); BN_free(d); BN_free(e); return (1); } int test_rshift1(BIO *bp) { BIGNUM *a, *b, *c; int i; a = BN_new(); b = BN_new(); c = BN_new(); BN_rand(a, 200, 0, 0); /**/ a->neg = rand_neg(); for (i = 0; i < num0; i++) { BN_rshift1(b, a); if (bp != NULL) { if (!results) { BN_print(bp, a); BIO_puts(bp, " / 2"); BIO_puts(bp, " - "); } BN_print(bp, b); BIO_puts(bp, "\n"); } BN_sub(c, a, b); BN_sub(c, c, b); if (!BN_is_zero(c) && !BN_abs_is_word(c, 1)) { fprintf(stderr, "Right shift one test failed!\n"); return 0; } BN_copy(a, b); } BN_free(a); BN_free(b); BN_free(c); return (1); } int test_lshift(BIO *bp, BN_CTX *ctx, BIGNUM *a_) { BIGNUM *a, *b, *c, *d; int i; b = BN_new(); c = BN_new(); d = BN_new(); BN_one(c); if (a_) a = a_; else { a = BN_new(); BN_rand(a, 200, 0, 0); /**/ a->neg = rand_neg(); } for (i = 0; i < num0; i++) { BN_lshift(b, a, i + 1); BN_add(c, c, c); if (bp != NULL) { if (!results) { BN_print(bp, a); BIO_puts(bp, " * "); BN_print(bp, c); BIO_puts(bp, " - "); } BN_print(bp, b); BIO_puts(bp, "\n"); } BN_mul(d, a, c, ctx); BN_sub(d, d, b); if (!BN_is_zero(d)) { fprintf(stderr, "Left shift test failed!\n"); fprintf(stderr, "a="); BN_print_fp(stderr, a); fprintf(stderr, "\nb="); BN_print_fp(stderr, b); fprintf(stderr, "\nc="); BN_print_fp(stderr, c); fprintf(stderr, "\nd="); BN_print_fp(stderr, d); fprintf(stderr, "\n"); return 0; } } BN_free(a); BN_free(b); BN_free(c); BN_free(d); return (1); } int test_mul(BIO *bp) { BIGNUM a, b, c, d, e; int i; BN_CTX *ctx; ctx = BN_CTX_new(); if (ctx == NULL) abort(); BN_init(&a); BN_init(&b); BN_init(&c); BN_init(&d); BN_init(&e); for (i = 0; i < num0 + num1; i++) { if (i <= num1) { BN_rand(&a, 100, 0, 0); BN_rand(&b, 100, 0, 0); } else BN_rand(&b, i - num1, 0, 0); a.neg = rand_neg(); b.neg = rand_neg(); BN_mul(&c, &a, &b, ctx); if (bp != NULL) { if (!results) { BN_print(bp, &a); BIO_puts(bp, " * "); BN_print(bp, &b); BIO_puts(bp, " - "); } BN_print(bp, &c); BIO_puts(bp, "\n"); } BN_div(&d, &e, &c, &a, ctx); BN_sub(&d, &d, &b); if (!BN_is_zero(&d) || !BN_is_zero(&e)) { fprintf(stderr, "Multiplication test failed!\n"); return 0; } } BN_free(&a); BN_free(&b); BN_free(&c); BN_free(&d); BN_free(&e); BN_CTX_free(ctx); return (1); } int test_sqr(BIO *bp, BN_CTX *ctx) { BIGNUM a, c, d, e; int i; BN_init(&a); BN_init(&c); BN_init(&d); BN_init(&e); for (i = 0; i < num0; i++) { BN_rand(&a, 40 + i * 10, 0, 0); a.neg = rand_neg(); BN_sqr(&c, &a, ctx); if (bp != NULL) { if (!results) { BN_print(bp, &a); BIO_puts(bp, " * "); BN_print(bp, &a); BIO_puts(bp, " - "); } BN_print(bp, &c); BIO_puts(bp, "\n"); } BN_div(&d, &e, &c, &a, ctx); BN_sub(&d, &d, &a); if (!BN_is_zero(&d) || !BN_is_zero(&e)) { fprintf(stderr, "Square test failed!\n"); return 0; } } BN_free(&a); BN_free(&c); BN_free(&d); BN_free(&e); return (1); } int rand_neg(void) { static unsigned int neg = 0; static int sign[8] = {0, 0, 0, 1, 1, 0, 1, 1}; return (sign[(neg++) % 8]); } static void print_word(BIO *bp, BN_ULONG w) { #ifdef OPENSSL_64_BIT if (sizeof(w) > sizeof(unsigned long)) { unsigned long h = (unsigned long)(w >> 32), l = (unsigned long)(w); if (h) BIO_printf(bp, "%lX%08lX", h, l); else BIO_printf(bp, "%lX", l); return; } #endif BIO_printf(bp, BN_HEX_FMT1, w); } int test_div_word(BIO *bp) { BIGNUM a, b; BN_ULONG r, s; int i; BN_init(&a); BN_init(&b); for (i = 0; i < num0; i++) { do { BN_rand(&a, 512, -1, 0); BN_rand(&b, BN_BITS2, -1, 0); s = b.d[0]; } while (!s); BN_copy(&b, &a); r = BN_div_word(&b, s); if (bp != NULL) { if (!results) { BN_print(bp, &a); BIO_puts(bp, " / "); print_word(bp, s); BIO_puts(bp, " - "); } BN_print(bp, &b); BIO_puts(bp, "\n"); if (!results) { BN_print(bp, &a); BIO_puts(bp, " % "); print_word(bp, s); BIO_puts(bp, " - "); } print_word(bp, r); BIO_puts(bp, "\n"); } BN_mul_word(&b, s); BN_add_word(&b, r); BN_sub(&b, &a, &b); if (!BN_is_zero(&b)) { fprintf(stderr, "Division (word) test failed!\n"); return 0; } } BN_free(&a); BN_free(&b); return (1); } int test_mont(BIO *bp, BN_CTX *ctx) { BIGNUM a, b, c, d, A, B; BIGNUM n; int i; BN_MONT_CTX *mont; BN_init(&a); BN_init(&b); BN_init(&c); BN_init(&d); BN_init(&A); BN_init(&B); BN_init(&n); mont = BN_MONT_CTX_new(); if (mont == NULL) return 0; BN_rand(&a, 100, 0, 0); /**/ BN_rand(&b, 100, 0, 0); /**/ for (i = 0; i < num2; i++) { int bits = (200 * (i + 1)) / num2; if (bits == 0) continue; BN_rand(&n, bits, 0, 1); BN_MONT_CTX_set(mont, &n, ctx); BN_nnmod(&a, &a, &n, ctx); BN_nnmod(&b, &b, &n, ctx); BN_to_montgomery(&A, &a, mont, ctx); BN_to_montgomery(&B, &b, mont, ctx); BN_mod_mul_montgomery(&c, &A, &B, mont, ctx); /**/ BN_from_montgomery(&A, &c, mont, ctx); /**/ if (bp != NULL) { if (!results) { #ifdef undef fprintf(stderr, "%d * %d %% %d\n", BN_num_bits(&a), BN_num_bits(&b), BN_num_bits(mont->N)); #endif BN_print(bp, &a); BIO_puts(bp, " * "); BN_print(bp, &b); BIO_puts(bp, " % "); BN_print(bp, &(mont->N)); BIO_puts(bp, " - "); } BN_print(bp, &A); BIO_puts(bp, "\n"); } BN_mod_mul(&d, &a, &b, &n, ctx); BN_sub(&d, &d, &A); if (!BN_is_zero(&d)) { fprintf(stderr, "Montgomery multiplication test failed!\n"); return 0; } } BN_MONT_CTX_free(mont); BN_free(&a); BN_free(&b); BN_free(&c); BN_free(&d); BN_free(&A); BN_free(&B); BN_free(&n); return (1); } int test_mod(BIO *bp, BN_CTX *ctx) { BIGNUM *a, *b, *c, *d, *e; int i; a = BN_new(); b = BN_new(); c = BN_new(); d = BN_new(); e = BN_new(); BN_rand(a, 1024, 0, 0); /**/ for (i = 0; i < num0; i++) { BN_rand(b, 450 + i * 10, 0, 0); /**/ a->neg = rand_neg(); b->neg = rand_neg(); BN_mod(c, a, b, ctx); /**/ if (bp != NULL) { if (!results) { BN_print(bp, a); BIO_puts(bp, " % "); BN_print(bp, b); BIO_puts(bp, " - "); } BN_print(bp, c); BIO_puts(bp, "\n"); } BN_div(d, e, a, b, ctx); BN_sub(e, e, c); if (!BN_is_zero(e)) { fprintf(stderr, "Modulo test failed!\n"); return 0; } } BN_free(a); BN_free(b); BN_free(c); BN_free(d); BN_free(e); return (1); } int test_mod_mul(BIO *bp, BN_CTX *ctx) { BIGNUM *a, *b, *c, *d, *e; int i, j; a = BN_new(); b = BN_new(); c = BN_new(); d = BN_new(); e = BN_new(); for (j = 0; j < 3; j++) { BN_rand(c, 1024, 0, 0); /**/ for (i = 0; i < num0; i++) { BN_rand(a, 475 + i * 10, 0, 0); /**/ BN_rand(b, 425 + i * 11, 0, 0); /**/ a->neg = rand_neg(); b->neg = rand_neg(); if (!BN_mod_mul(e, a, b, c, ctx)) { unsigned long l; while ((l = ERR_get_error())) fprintf(stderr, "ERROR:%s\n", ERR_error_string(l, NULL)); abort(); } if (bp != NULL) { if (!results) { BN_print(bp, a); BIO_puts(bp, " * "); BN_print(bp, b); BIO_puts(bp, " % "); BN_print(bp, c); if ((a->neg ^ b->neg) && !BN_is_zero(e)) { /* If (a*b) % c is negative, c must be added * in order to obtain the normalized remainder * (new with OpenSSL 0.9.7, previous versions of * BN_mod_mul could generate negative results) */ BIO_puts(bp, " + "); BN_print(bp, c); } BIO_puts(bp, " - "); } BN_print(bp, e); BIO_puts(bp, "\n"); } BN_mul(d, a, b, ctx); BN_sub(d, d, e); BN_div(a, b, d, c, ctx); if (!BN_is_zero(b)) { fprintf(stderr, "Modulo multiply test failed!\n"); ERR_print_errors_fp(stderr); return 0; } } } BN_free(a); BN_free(b); BN_free(c); BN_free(d); BN_free(e); return (1); } int test_mod_exp(BIO *bp, BN_CTX *ctx) { BIGNUM *a, *b, *c, *d, *e; int i; a = BN_new(); b = BN_new(); c = BN_new(); d = BN_new(); e = BN_new(); BN_rand(c, 30, 0, 1); /* must be odd for montgomery */ for (i = 0; i < num2; i++) { BN_rand(a, 20 + i * 5, 0, 0); /**/ BN_rand(b, 2 + i, 0, 0); /**/ if (!BN_mod_exp(d, a, b, c, ctx)) return (0); if (bp != NULL) { if (!results) { BN_print(bp, a); BIO_puts(bp, " ^ "); BN_print(bp, b); BIO_puts(bp, " % "); BN_print(bp, c); BIO_puts(bp, " - "); } BN_print(bp, d); BIO_puts(bp, "\n"); } BN_exp(e, a, b, ctx); BN_sub(e, e, d); BN_div(a, b, e, c, ctx); if (!BN_is_zero(b)) { fprintf(stderr, "Modulo exponentiation test failed!\n"); return 0; } } BN_free(a); BN_free(b); BN_free(c); BN_free(d); BN_free(e); return (1); } int test_mod_exp_mont_consttime(BIO *bp, BN_CTX *ctx) { BIGNUM *a, *b, *c, *d, *e; int i; a = BN_new(); b = BN_new(); c = BN_new(); d = BN_new(); e = BN_new(); BN_rand(c, 30, 0, 1); /* must be odd for montgomery */ for (i = 0; i < num2; i++) { BN_rand(a, 20 + i * 5, 0, 0); /**/ BN_rand(b, 2 + i, 0, 0); /**/ if (!BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL)) return (00); if (bp != NULL) { if (!results) { BN_print(bp, a); BIO_puts(bp, " ^ "); BN_print(bp, b); BIO_puts(bp, " % "); BN_print(bp, c); BIO_puts(bp, " - "); } BN_print(bp, d); BIO_puts(bp, "\n"); } BN_exp(e, a, b, ctx); BN_sub(e, e, d); BN_div(a, b, e, c, ctx); if (!BN_is_zero(b)) { fprintf(stderr, "Modulo exponentiation test failed!\n"); return 0; } } BN_free(a); BN_free(b); BN_free(c); BN_free(d); BN_free(e); return (1); } /* Test constant-time modular exponentiation with 1024-bit inputs, * which on x86_64 cause a different code branch to be taken. */ int test_mod_exp_mont5(BIO *bp, BN_CTX *ctx) { BIGNUM *a, *p, *m, *d, *e; BN_MONT_CTX *mont; a = BN_new(); p = BN_new(); m = BN_new(); d = BN_new(); e = BN_new(); mont = BN_MONT_CTX_new(); BN_rand(m, 1024, 0, 1); /* must be odd for montgomery */ /* Zero exponent */ BN_rand(a, 1024, 0, 0); BN_zero(p); if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL)) return 0; if (!BN_is_one(d)) { fprintf(stderr, "Modular exponentiation test failed!\n"); return 0; } /* Zero input */ BN_rand(p, 1024, 0, 0); BN_zero(a); if (!BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL)) return 0; if (!BN_is_zero(d)) { fprintf(stderr, "Modular exponentiation test failed!\n"); return 0; } /* Craft an input whose Montgomery representation is 1, * i.e., shorter than the modulus m, in order to test * the const time precomputation scattering/gathering. */ BN_one(a); BN_MONT_CTX_set(mont, m, ctx); if (!BN_from_montgomery(e, a, mont, ctx) || !BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL) || !BN_mod_exp(a, e, p, m, ctx)) { return 0; } if (BN_cmp(a, d) != 0) { fprintf(stderr, "Modular exponentiation test failed!\n"); return 0; } /* Finally, some regular test vectors. */ BN_rand(e, 1024, 0, 0); if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL)) return 0; if (!BN_mod_exp(a, e, p, m, ctx)) return 0; if (BN_cmp(a, d) != 0) { fprintf(stderr, "Modular exponentiation test failed!\n"); return 0; } BN_MONT_CTX_free(mont); BN_free(a); BN_free(p); BN_free(m); BN_free(d); BN_free(e); return (1); } int test_exp(BIO *bp, BN_CTX *ctx) { BIGNUM *a, *b, *d, *e, *one; int i; a = BN_new(); b = BN_new(); d = BN_new(); e = BN_new(); one = BN_new(); BN_one(one); for (i = 0; i < num2; i++) { BN_rand(a, 20 + i * 5, 0, 0); /**/ BN_rand(b, 2 + i, 0, 0); /**/ if (BN_exp(d, a, b, ctx) <= 0) return (0); if (bp != NULL) { if (!results) { BN_print(bp, a); BIO_puts(bp, " ^ "); BN_print(bp, b); BIO_puts(bp, " - "); } BN_print(bp, d); BIO_puts(bp, "\n"); } BN_one(e); for (; !BN_is_zero(b); BN_sub(b, b, one)) BN_mul(e, e, a, ctx); BN_sub(e, e, d); if (!BN_is_zero(e)) { fprintf(stderr, "Exponentiation test failed!\n"); return 0; } } BN_free(a); BN_free(b); BN_free(d); BN_free(e); BN_free(one); return (1); } /* test_exp_mod_zero tests that x**0 mod 1 == 0. */ static int test_exp_mod_zero() { BIGNUM a, p, m; BIGNUM r; BN_CTX *ctx = BN_CTX_new(); int ret = 0; BN_init(&m); BN_one(&m); BN_init(&a); BN_one(&a); BN_init(&p); BN_zero(&p); BN_init(&r); BN_mod_exp(&r, &a, &p, &m, ctx); BN_CTX_free(ctx); if (BN_is_zero(&r)) { ret = 1; } else { printf("1**0 mod 1 = "); BN_print_fp(stdout, &r); printf(", should be 0\n"); } BN_free(&r); BN_free(&a); BN_free(&p); BN_free(&m); return ret; } static int genprime_cb(int p, int n, BN_GENCB *arg) { char c = '*'; if (p == 0) c = '.'; if (p == 1) c = '+'; if (p == 2) c = '*'; if (p == 3) c = '\n'; putc(c, stdout); fflush(stdout); return 1; } int test_mod_sqrt(BIO *bp, BN_CTX *ctx) { BN_GENCB cb; BIGNUM *a, *p, *r; int i, j; int ret = 0; a = BN_new(); p = BN_new(); r = BN_new(); if (a == NULL || p == NULL || r == NULL) goto err; BN_GENCB_set(&cb, genprime_cb, NULL); for (i = 0; i < 16; i++) { if (i < 8) { unsigned primes[8] = {2, 3, 5, 7, 11, 13, 17, 19}; if (!BN_set_word(p, primes[i])) goto err; } else { if (!BN_set_word(a, 32)) goto err; if (!BN_set_word(r, 2 * i + 1)) goto err; if (!BN_generate_prime_ex(p, 256, 0, a, r, &cb)) goto err; putc('\n', stdout); } p->neg = rand_neg(); for (j = 0; j < num2; j++) { /* construct 'a' such that it is a square modulo p, * but in general not a proper square and not reduced modulo p */ if (!BN_rand(r, 256, 0, 3)) goto err; if (!BN_nnmod(r, r, p, ctx)) goto err; if (!BN_mod_sqr(r, r, p, ctx)) goto err; if (!BN_rand(a, 256, 0, 3)) goto err; if (!BN_nnmod(a, a, p, ctx)) goto err; if (!BN_mod_sqr(a, a, p, ctx)) goto err; if (!BN_mul(a, a, r, ctx)) goto err; if (rand_neg()) if (!BN_sub(a, a, p)) goto err; if (!BN_mod_sqrt(r, a, p, ctx)) goto err; if (!BN_mod_sqr(r, r, p, ctx)) goto err; if (!BN_nnmod(a, a, p, ctx)) goto err; if (BN_cmp(a, r) != 0) { fprintf(stderr, "BN_mod_sqrt failed: a = "); BN_print_fp(stderr, a); fprintf(stderr, ", r = "); BN_print_fp(stderr, r); fprintf(stderr, ", p = "); BN_print_fp(stderr, p); fprintf(stderr, "\n"); goto err; } putc('.', stdout); fflush(stdout); } putc('\n', stdout); fflush(stderr); } ret = 1; err: if (a != NULL) BN_free(a); if (p != NULL) BN_free(p); if (r != NULL) BN_free(r); return ret; } int test_small_prime(BIO *bp, BN_CTX *ctx) { static const int bits = 10; int ret = 0; BIGNUM r; BN_init(&r); if (!BN_generate_prime_ex(&r, bits, 0, NULL, NULL, NULL)) { goto err; } if (BN_num_bits(&r) != bits) { BIO_printf(bp, "Expected %d bit prime, got %d bit number\n", bits, BN_num_bits(&r)); goto err; } ret = 1; err: BN_free(&r); return ret; } int test_sqrt(BIO *bp, BN_CTX *ctx) { BIGNUM *n = BN_new(), *nn = BN_new(), *sqrt = BN_new(); unsigned i; /* Test some random squares. */ for (i = 0; i < 100; i++) { if (!BN_rand(n, 1024 /* bit length */, -1 /* no modification of top bits */, 0 /* don't modify bottom bit */) || !BN_mul(nn, n, n, ctx) || !BN_sqrt(sqrt, nn, ctx)) { BIO_print_errors_fp(stderr); return 0; } if (BN_cmp(n, sqrt) != 0) { fprintf(stderr, "Bad result from BN_sqrt.\n"); return 0; } } /* Test some non-squares */ for (i = 0; i < 100; i++) { if (!BN_rand(n, 1024 /* bit length */, -1 /* no modification of top bits */, 0 /* don't modify bottom bit */) || !BN_mul(nn, n, n, ctx) || !BN_add(nn, nn, BN_value_one())) { BIO_print_errors_fp(stderr); return 0; } if (BN_sqrt(sqrt, nn, ctx)) { char *nn_str = BN_bn2dec(nn); fprintf(stderr, "BIO_sqrt didn't fail on a non-square: %s\n", nn_str); OPENSSL_free(nn_str); } } BN_free(n); BN_free(sqrt); BN_free(nn); return 1; }