--- /dev/null
+/*
+ * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
+ *
+ * Licensed under the OpenSSL license (the "License"). You may not use
+ * this file except in compliance with the License. You can obtain a copy
+ * in the file LICENSE in the source distribution or at
+ * https://www.openssl.org/source/license.html
+ */
+
+/* ====================================================================
+ * 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 <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "e_os.h"
+
+#include <openssl/bio.h>
+#include <openssl/bn.h>
+#include <openssl/rand.h>
+#include <openssl/x509.h>
+#include <openssl/err.h>
+
+/*
+ * In bn_lcl.h, bn_expand() is defined as a static ossl_inline function.
+ * This is fine in itself, it will end up as an unused static function in
+ * the worst case. However, it referenses bn_expand2(), which is a private
+ * function in libcrypto and therefore unavailable on some systems. This
+ * may result in a linker error because of unresolved symbols.
+ *
+ * To avoid this, we define a dummy variant of bn_expand2() here, and to
+ * avoid possible clashes with libcrypto, we rename it first, using a macro.
+ */
+#define bn_expand2 dummy_bn_expand2
+BIGNUM *bn_expand2(BIGNUM *b, int words);
+BIGNUM *bn_expand2(BIGNUM *b, int words) { return NULL; }
+
+#include "../crypto/bn/bn_lcl.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_div(BIO *bp, BN_CTX *ctx);
+int test_div_word(BIO *bp);
+int test_div_recp(BIO *bp, BN_CTX *ctx);
+int test_mul(BIO *bp);
+int test_sqr(BIO *bp, BN_CTX *ctx);
+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_mod_exp_mont5(BIO *bp, BN_CTX *ctx);
+int test_exp(BIO *bp, BN_CTX *ctx);
+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);
+int test_kron(BIO *bp, BN_CTX *ctx);
+int test_sqrt(BIO *bp, BN_CTX *ctx);
+int test_small_prime(BIO *bp, BN_CTX *ctx);
+int test_bn2dec(BIO *bp);
+int rand_neg(void);
+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 const char rnd_seed[] =
+ "string to make the random number generator think it has entropy";
+
+static void message(BIO *out, char *m)
+{
+ fprintf(stderr, "test %s\n", 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;
+ char *outfile = NULL;
+
+ CRYPTO_set_mem_debug(1);
+ CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
+
+ results = 0;
+
+ RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
+
+ 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)
+ EXIT(1);
+
+ out = BIO_new(BIO_s_file());
+ if (out == NULL)
+ EXIT(1);
+ if (outfile == NULL) {
+ BIO_set_fp(out, stdout, BIO_NOCLOSE | BIO_FP_TEXT);
+ } else {
+ if (!BIO_write_filename(out, outfile)) {
+ perror(outfile);
+ EXIT(1);
+ }
+ }
+#ifdef OPENSSL_SYS_VMS
+ {
+ BIO *tmpbio = BIO_new(BIO_f_linebuffer());
+ out = BIO_push(tmpbio, out);
+ }
+#endif
+
+ 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_div_recp");
+ if (!test_div_recp(out, ctx))
+ 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))
+ goto err;
+ if (!test_mod_exp_mont5(out, ctx))
+ goto err;
+ (void)BIO_flush(out);
+
+ message(out, "BN_exp");
+ if (!test_exp(out, ctx))
+ goto err;
+ (void)BIO_flush(out);
+
+ message(out, "BN_kronecker");
+ if (!test_kron(out, ctx))
+ goto err;
+ (void)BIO_flush(out);
+
+ message(out, "BN_mod_sqrt");
+ if (!test_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_bn2dec");
+ if (!test_bn2dec(out))
+ goto err;
+ (void)BIO_flush(out);
+
+#ifndef OPENSSL_NO_EC2M
+ message(out, "BN_GF2m_add");
+ if (!test_gf2m_add(out))
+ goto err;
+ (void)BIO_flush(out);
+
+ message(out, "BN_GF2m_mod");
+ if (!test_gf2m_mod(out))
+ goto err;
+ (void)BIO_flush(out);
+
+ message(out, "BN_GF2m_mod_mul");
+ if (!test_gf2m_mod_mul(out, ctx))
+ goto err;
+ (void)BIO_flush(out);
+
+ message(out, "BN_GF2m_mod_sqr");
+ if (!test_gf2m_mod_sqr(out, ctx))
+ goto err;
+ (void)BIO_flush(out);
+
+ message(out, "BN_GF2m_mod_inv");
+ if (!test_gf2m_mod_inv(out, ctx))
+ goto err;
+ (void)BIO_flush(out);
+
+ message(out, "BN_GF2m_mod_div");
+ if (!test_gf2m_mod_div(out, ctx))
+ goto err;
+ (void)BIO_flush(out);
+
+ message(out, "BN_GF2m_mod_exp");
+ if (!test_gf2m_mod_exp(out, ctx))
+ goto err;
+ (void)BIO_flush(out);
+
+ message(out, "BN_GF2m_mod_sqrt");
+ if (!test_gf2m_mod_sqrt(out, ctx))
+ goto err;
+ (void)BIO_flush(out);
+
+ message(out, "BN_GF2m_mod_solve_quad");
+ if (!test_gf2m_mod_solve_quad(out, ctx))
+ goto err;
+ (void)BIO_flush(out);
+#endif
+ BN_CTX_free(ctx);
+ BIO_free(out);
+
+ ERR_print_errors_fp(stderr);
+
+#ifndef OPENSSL_NO_CRYPTO_MDEBUG
+ if (CRYPTO_mem_leaks_fp(stderr) <= 0)
+ EXIT(1);
+#endif
+ EXIT(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);
+ BN_CTX_free(ctx);
+ BIO_free(out);
+
+ ERR_print_errors_fp(stderr);
+ EXIT(1);
+}
+
+int test_add(BIO *bp)
+{
+ BIGNUM *a, *b, *c;
+ int i;
+
+ a = BN_new();
+ b = BN_new();
+ c = BN_new();
+
+ BN_bntest_rand(a, 512, 0, 0);
+ for (i = 0; i < num0; i++) {
+ BN_bntest_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;
+
+ a = BN_new();
+ b = BN_new();
+ c = BN_new();
+
+ for (i = 0; i < num0 + num1; i++) {
+ if (i < num1) {
+ BN_bntest_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_bntest_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;
+
+ a = BN_new();
+ b = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+
+ BN_one(a);
+ BN_zero(b);
+
+ if (BN_div(d, c, a, b, ctx)) {
+ fprintf(stderr, "Division by zero succeeded!\n");
+ return 0;
+ }
+
+ for (i = 0; i < num0 + num1; i++) {
+ if (i < num1) {
+ BN_bntest_rand(a, 400, 0, 0);
+ BN_copy(b, a);
+ BN_lshift(a, a, i);
+ BN_add_word(a, i);
+ } else
+ BN_bntest_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);
+}
+
+static void print_word(BIO *bp, BN_ULONG w)
+{
+ int i = sizeof(w) * 8;
+ char *fmt = NULL;
+ unsigned char byte;
+
+ do {
+ i -= 8;
+ byte = (unsigned char)(w >> i);
+ if (fmt == NULL)
+ fmt = byte ? "%X" : NULL;
+ else
+ fmt = "%02X";
+
+ if (fmt != NULL)
+ BIO_printf(bp, fmt, byte);
+ } while (i);
+
+ /* If we haven't printed anything, at least print a zero! */
+ if (fmt == NULL)
+ BIO_printf(bp, "0");
+}
+
+int test_div_word(BIO *bp)
+{
+ BIGNUM *a, *b;
+ BN_ULONG r, rmod, s;
+ int i;
+
+ a = BN_new();
+ b = BN_new();
+
+ for (i = 0; i < num0; i++) {
+ do {
+ BN_bntest_rand(a, 512, -1, 0);
+ BN_bntest_rand(b, BN_BITS2, -1, 0);
+ } while (BN_is_zero(b));
+
+ s = b->d[0];
+ BN_copy(b, a);
+ rmod = BN_mod_word(b, s);
+ r = BN_div_word(b, s);
+
+ if (rmod != r) {
+ fprintf(stderr, "Mod (word) test failed!\n");
+ return 0;
+ }
+
+ 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_div_recp(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b, *c, *d, *e;
+ BN_RECP_CTX *recp;
+ int i;
+
+ recp = BN_RECP_CTX_new();
+ a = BN_new();
+ b = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+
+ for (i = 0; i < num0 + num1; i++) {
+ if (i < num1) {
+ BN_bntest_rand(a, 400, 0, 0);
+ BN_copy(b, a);
+ BN_lshift(a, a, i);
+ BN_add_word(a, i);
+ } else
+ BN_bntest_rand(b, 50 + 3 * (i - num1), 0, 0);
+ a->neg = rand_neg();
+ b->neg = rand_neg();
+ BN_RECP_CTX_set(recp, b, ctx);
+ BN_div_recp(d, c, a, recp, 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, "Reciprocal division test failed!\n");
+ fprintf(stderr, "a=");
+ BN_print_fp(stderr, a);
+ fprintf(stderr, "\nb=");
+ BN_print_fp(stderr, b);
+ fprintf(stderr, "\n");
+ return 0;
+ }
+ }
+ BN_free(a);
+ BN_free(b);
+ BN_free(c);
+ BN_free(d);
+ BN_free(e);
+ BN_RECP_CTX_free(recp);
+ 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)
+ EXIT(1);
+
+ a = BN_new();
+ b = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+
+ for (i = 0; i < num0 + num1; i++) {
+ if (i <= num1) {
+ BN_bntest_rand(a, 100, 0, 0);
+ BN_bntest_rand(b, 100, 0, 0);
+ } else
+ BN_bntest_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, ret = 0;
+
+ a = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+ if (a == NULL || c == NULL || d == NULL || e == NULL) {
+ goto err;
+ }
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_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");
+ goto err;
+ }
+ }
+
+ /* Regression test for a BN_sqr overflow bug. */
+ BN_hex2bn(&a,
+ "80000000000000008000000000000001"
+ "FFFFFFFFFFFFFFFE0000000000000000");
+ 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_mul(d, a, a, ctx);
+ if (BN_cmp(c, d)) {
+ fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
+ "different results!\n");
+ goto err;
+ }
+
+ /* Regression test for a BN_sqr overflow bug. */
+ BN_hex2bn(&a,
+ "80000000000000000000000080000001"
+ "FFFFFFFE000000000000000000000000");
+ 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_mul(d, a, a, ctx);
+ if (BN_cmp(c, d)) {
+ fprintf(stderr, "Square test failed: BN_sqr and BN_mul produce "
+ "different results!\n");
+ goto err;
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(c);
+ BN_free(d);
+ BN_free(e);
+ return ret;
+}
+
+int test_mont(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b, *c, *d, *A, *B;
+ BIGNUM *n;
+ int i;
+ BN_MONT_CTX *mont;
+
+ a = BN_new();
+ b = BN_new();
+ c = BN_new();
+ d = BN_new();
+ A = BN_new();
+ B = BN_new();
+ n = BN_new();
+
+ mont = BN_MONT_CTX_new();
+ if (mont == NULL)
+ return 0;
+
+ BN_zero(n);
+ if (BN_MONT_CTX_set(mont, n, ctx)) {
+ fprintf(stderr, "BN_MONT_CTX_set succeeded for zero modulus!\n");
+ return 0;
+ }
+
+ BN_set_word(n, 16);
+ if (BN_MONT_CTX_set(mont, n, ctx)) {
+ fprintf(stderr, "BN_MONT_CTX_set succeeded for even modulus!\n");
+ return 0;
+ }
+
+ BN_bntest_rand(a, 100, 0, 0);
+ BN_bntest_rand(b, 100, 0, 0);
+ for (i = 0; i < num2; i++) {
+ int bits = (200 * (i + 1)) / num2;
+
+ if (bits == 0)
+ continue;
+ BN_bntest_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) {
+ 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;
+ }
+ }
+
+ /* Regression test for carry bug in mulx4x_mont */
+ BN_hex2bn(&a,
+ "7878787878787878787878787878787878787878787878787878787878787878"
+ "7878787878787878787878787878787878787878787878787878787878787878"
+ "7878787878787878787878787878787878787878787878787878787878787878"
+ "7878787878787878787878787878787878787878787878787878787878787878");
+ BN_hex2bn(&b,
+ "095D72C08C097BA488C5E439C655A192EAFB6380073D8C2664668EDDB4060744"
+ "E16E57FB4EDB9AE10A0CEFCDC28A894F689A128379DB279D48A2E20849D68593"
+ "9B7803BCF46CEBF5C533FB0DD35B080593DE5472E3FE5DB951B8BFF9B4CB8F03"
+ "9CC638A5EE8CDD703719F8000E6A9F63BEED5F2FCD52FF293EA05A251BB4AB81");
+ BN_hex2bn(&n,
+ "D78AF684E71DB0C39CFF4E64FB9DB567132CB9C50CC98009FEB820B26F2DED9B"
+ "91B9B5E2B83AE0AE4EB4E0523CA726BFBE969B89FD754F674CE99118C3F2D1C5"
+ "D81FDC7C54E02B60262B241D53C040E99E45826ECA37A804668E690E1AFC1CA4"
+ "2C9A15D84D4954425F0B7642FC0BD9D7B24E2618D2DCC9B729D944BADACFDDAF");
+ BN_MONT_CTX_set(mont, n, ctx);
+ BN_mod_mul_montgomery(c, a, b, mont, ctx);
+ BN_mod_mul_montgomery(d, b, a, mont, ctx);
+ if (BN_cmp(c, d)) {
+ fprintf(stderr, "Montgomery multiplication test failed:"
+ " a*b != b*a.\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_bntest_rand(a, 1024, 0, 0);
+ for (i = 0; i < num0; i++) {
+ BN_bntest_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();
+
+ BN_one(a);
+ BN_one(b);
+ BN_zero(c);
+ if (BN_mod_mul(e, a, b, c, ctx)) {
+ fprintf(stderr, "BN_mod_mul with zero modulus succeeded!\n");
+ return 0;
+ }
+
+ for (j = 0; j < 3; j++) {
+ BN_bntest_rand(c, 1024, 0, 0);
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 475 + i * 10, 0, 0);
+ BN_bntest_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));
+ EXIT(1);
+ }
+ 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_one(a);
+ BN_one(b);
+ BN_zero(c);
+ if (BN_mod_exp(d, a, b, c, ctx)) {
+ fprintf(stderr, "BN_mod_exp with zero modulus succeeded!\n");
+ return 0;
+ }
+
+ BN_bntest_rand(c, 30, 0, 1); /* must be odd for montgomery */
+ for (i = 0; i < num2; i++) {
+ BN_bntest_rand(a, 20 + i * 5, 0, 0);
+ BN_bntest_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;
+ }
+ }
+
+ /* Regression test for carry propagation bug in sqr8x_reduction */
+ BN_hex2bn(&a, "050505050505");
+ BN_hex2bn(&b, "02");
+ BN_hex2bn(&c,
+ "4141414141414141414141274141414141414141414141414141414141414141"
+ "4141414141414141414141414141414141414141414141414141414141414141"
+ "4141414141414141414141800000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000000000000000"
+ "0000000000000000000000000000000000000000000000000000000001");
+ BN_mod_exp(d, a, b, c, ctx);
+ BN_mul(e, a, a, ctx);
+ if (BN_cmp(d, e)) {
+ fprintf(stderr, "BN_mod_exp and BN_mul produce different results!\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_one(a);
+ BN_one(b);
+ BN_zero(c);
+ if (BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL)) {
+ fprintf(stderr, "BN_mod_exp_mont_consttime with zero modulus "
+ "succeeded\n");
+ return 0;
+ }
+
+ BN_set_word(c, 16);
+ if (BN_mod_exp_mont_consttime(d, a, b, c, ctx, NULL)) {
+ fprintf(stderr, "BN_mod_exp_mont_consttime with even modulus "
+ "succeeded\n");
+ return 0;
+ }
+
+ BN_bntest_rand(c, 30, 0, 1); /* must be odd for montgomery */
+ for (i = 0; i < num2; i++) {
+ BN_bntest_rand(a, 20 + i * 5, 0, 0);
+ BN_bntest_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_bntest_rand(m, 1024, 0, 1); /* must be odd for montgomery */
+ /* Zero exponent */
+ BN_bntest_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_bntest_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))
+ return 0;
+ if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
+ return 0;
+ if (!BN_mod_exp_simple(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_bntest_rand(e, 1024, 0, 0);
+ if (!BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
+ return 0;
+ if (!BN_mod_exp_simple(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_bntest_rand(a, 20 + i * 5, 0, 0);
+ BN_bntest_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);
+}
+
+#ifndef OPENSSL_NO_EC2M
+int test_gf2m_add(BIO *bp)
+{
+ BIGNUM *a, *b, *c;
+ int i, ret = 0;
+
+ a = BN_new();
+ b = BN_new();
+ c = BN_new();
+
+ for (i = 0; i < num0; i++) {
+ BN_rand(a, 512, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY);
+ BN_copy(b, BN_value_one());
+ a->neg = rand_neg();
+ b->neg = rand_neg();
+ BN_GF2m_add(c, a, b);
+ /* Test that two added values have the correct parity. */
+ if ((BN_is_odd(a) && BN_is_odd(c))
+ || (!BN_is_odd(a) && !BN_is_odd(c))) {
+ fprintf(stderr, "GF(2^m) addition test (a) failed!\n");
+ goto err;
+ }
+ BN_GF2m_add(c, c, c);
+ /* Test that c + c = 0. */
+ if (!BN_is_zero(c)) {
+ fprintf(stderr, "GF(2^m) addition test (b) failed!\n");
+ goto err;
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b);
+ BN_free(c);
+ return ret;
+}
+
+int test_gf2m_mod(BIO *bp)
+{
+ BIGNUM *a, *b[2], *c, *d, *e;
+ int i, j, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 1024, 0, 0);
+ for (j = 0; j < 2; j++) {
+ BN_GF2m_mod(c, a, b[j]);
+ BN_GF2m_add(d, a, c);
+ BN_GF2m_mod(e, d, b[j]);
+ /* Test that a + (a mod p) mod p == 0. */
+ if (!BN_is_zero(e)) {
+ fprintf(stderr, "GF(2^m) modulo test failed!\n");
+ goto err;
+ }
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ BN_free(e);
+ return ret;
+}
+
+int test_gf2m_mod_mul(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b[2], *c, *d, *e, *f, *g, *h;
+ int i, j, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+ f = BN_new();
+ g = BN_new();
+ h = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 1024, 0, 0);
+ BN_bntest_rand(c, 1024, 0, 0);
+ BN_bntest_rand(d, 1024, 0, 0);
+ for (j = 0; j < 2; j++) {
+ BN_GF2m_mod_mul(e, a, c, b[j], ctx);
+ BN_GF2m_add(f, a, d);
+ BN_GF2m_mod_mul(g, f, c, b[j], ctx);
+ BN_GF2m_mod_mul(h, d, c, b[j], ctx);
+ BN_GF2m_add(f, e, g);
+ BN_GF2m_add(f, f, h);
+ /* Test that (a+d)*c = a*c + d*c. */
+ if (!BN_is_zero(f)) {
+ fprintf(stderr,
+ "GF(2^m) modular multiplication test failed!\n");
+ goto err;
+ }
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ BN_free(e);
+ BN_free(f);
+ BN_free(g);
+ BN_free(h);
+ return ret;
+}
+
+int test_gf2m_mod_sqr(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b[2], *c, *d;
+ int i, j, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 1024, 0, 0);
+ for (j = 0; j < 2; j++) {
+ BN_GF2m_mod_sqr(c, a, b[j], ctx);
+ BN_copy(d, a);
+ BN_GF2m_mod_mul(d, a, d, b[j], ctx);
+ BN_GF2m_add(d, c, d);
+ /* Test that a*a = a^2. */
+ if (!BN_is_zero(d)) {
+ fprintf(stderr, "GF(2^m) modular squaring test failed!\n");
+ goto err;
+ }
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ return ret;
+}
+
+int test_gf2m_mod_inv(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b[2], *c, *d;
+ int i, j, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 512, 0, 0);
+ for (j = 0; j < 2; j++) {
+ BN_GF2m_mod_inv(c, a, b[j], ctx);
+ BN_GF2m_mod_mul(d, a, c, b[j], ctx);
+ /* Test that ((1/a)*a) = 1. */
+ if (!BN_is_one(d)) {
+ fprintf(stderr, "GF(2^m) modular inversion test failed!\n");
+ goto err;
+ }
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ return ret;
+}
+
+int test_gf2m_mod_div(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b[2], *c, *d, *e, *f;
+ int i, j, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+ f = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 512, 0, 0);
+ BN_bntest_rand(c, 512, 0, 0);
+ for (j = 0; j < 2; j++) {
+ BN_GF2m_mod_div(d, a, c, b[j], ctx);
+ BN_GF2m_mod_mul(e, d, c, b[j], ctx);
+ BN_GF2m_mod_div(f, a, e, b[j], ctx);
+ /* Test that ((a/c)*c)/a = 1. */
+ if (!BN_is_one(f)) {
+ fprintf(stderr, "GF(2^m) modular division test failed!\n");
+ goto err;
+ }
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ BN_free(e);
+ BN_free(f);
+ return ret;
+}
+
+int test_gf2m_mod_exp(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b[2], *c, *d, *e, *f;
+ int i, j, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+ f = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 512, 0, 0);
+ BN_bntest_rand(c, 512, 0, 0);
+ BN_bntest_rand(d, 512, 0, 0);
+ for (j = 0; j < 2; j++) {
+ BN_GF2m_mod_exp(e, a, c, b[j], ctx);
+ BN_GF2m_mod_exp(f, a, d, b[j], ctx);
+ BN_GF2m_mod_mul(e, e, f, b[j], ctx);
+ BN_add(f, c, d);
+ BN_GF2m_mod_exp(f, a, f, b[j], ctx);
+ BN_GF2m_add(f, e, f);
+ /* Test that a^(c+d)=a^c*a^d. */
+ if (!BN_is_zero(f)) {
+ fprintf(stderr,
+ "GF(2^m) modular exponentiation test failed!\n");
+ goto err;
+ }
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ BN_free(e);
+ BN_free(f);
+ return ret;
+}
+
+int test_gf2m_mod_sqrt(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b[2], *c, *d, *e, *f;
+ int i, j, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+ f = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 512, 0, 0);
+ for (j = 0; j < 2; j++) {
+ BN_GF2m_mod(c, a, b[j]);
+ BN_GF2m_mod_sqrt(d, a, b[j], ctx);
+ BN_GF2m_mod_sqr(e, d, b[j], ctx);
+ BN_GF2m_add(f, c, e);
+ /* Test that d^2 = a, where d = sqrt(a). */
+ if (!BN_is_zero(f)) {
+ fprintf(stderr, "GF(2^m) modular square root test failed!\n");
+ goto err;
+ }
+ }
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ BN_free(e);
+ BN_free(f);
+ return ret;
+}
+
+int test_gf2m_mod_solve_quad(BIO *bp, BN_CTX *ctx)
+{
+ BIGNUM *a, *b[2], *c, *d, *e;
+ int i, j, s = 0, t, ret = 0;
+ int p0[] = { 163, 7, 6, 3, 0, -1 };
+ int p1[] = { 193, 15, 0, -1 };
+
+ a = BN_new();
+ b[0] = BN_new();
+ b[1] = BN_new();
+ c = BN_new();
+ d = BN_new();
+ e = BN_new();
+
+ BN_GF2m_arr2poly(p0, b[0]);
+ BN_GF2m_arr2poly(p1, b[1]);
+
+ for (i = 0; i < num0; i++) {
+ BN_bntest_rand(a, 512, 0, 0);
+ for (j = 0; j < 2; j++) {
+ t = BN_GF2m_mod_solve_quad(c, a, b[j], ctx);
+ if (t) {
+ s++;
+ BN_GF2m_mod_sqr(d, c, b[j], ctx);
+ BN_GF2m_add(d, c, d);
+ BN_GF2m_mod(e, a, b[j]);
+ BN_GF2m_add(e, e, d);
+ /*
+ * Test that solution of quadratic c satisfies c^2 + c = a.
+ */
+ if (!BN_is_zero(e)) {
+ fprintf(stderr,
+ "GF(2^m) modular solve quadratic test failed!\n");
+ goto err;
+ }
+
+ }
+ }
+ }
+ if (s == 0) {
+ fprintf(stderr,
+ "All %i tests of GF(2^m) modular solve quadratic resulted in no roots;\n",
+ num0);
+ fprintf(stderr,
+ "this is very unlikely and probably indicates an error.\n");
+ goto err;
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b[0]);
+ BN_free(b[1]);
+ BN_free(c);
+ BN_free(d);
+ BN_free(e);
+ return ret;
+}
+#endif
+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, stderr);
+ fflush(stderr);
+ return 1;
+}
+
+int test_kron(BIO *bp, BN_CTX *ctx)
+{
+ BN_GENCB cb;
+ BIGNUM *a, *b, *r, *t;
+ int i;
+ int legendre, kronecker;
+ int ret = 0;
+
+ a = BN_new();
+ b = BN_new();
+ r = BN_new();
+ t = BN_new();
+ if (a == NULL || b == NULL || r == NULL || t == NULL)
+ goto err;
+
+ BN_GENCB_set(&cb, genprime_cb, NULL);
+
+ /*
+ * We test BN_kronecker(a, b, ctx) just for b odd (Jacobi symbol). In
+ * this case we know that if b is prime, then BN_kronecker(a, b, ctx) is
+ * congruent to $a^{(b-1)/2}$, modulo $b$ (Legendre symbol). So we
+ * generate a random prime b and compare these values for a number of
+ * random a's. (That is, we run the Solovay-Strassen primality test to
+ * confirm that b is prime, except that we don't want to test whether b
+ * is prime but whether BN_kronecker works.)
+ */
+
+ if (!BN_generate_prime_ex(b, 512, 0, NULL, NULL, &cb))
+ goto err;
+ b->neg = rand_neg();
+ putc('\n', stderr);
+
+ for (i = 0; i < num0; i++) {
+ if (!BN_bntest_rand(a, 512, 0, 0))
+ goto err;
+ a->neg = rand_neg();
+
+ /* t := (|b|-1)/2 (note that b is odd) */
+ if (!BN_copy(t, b))
+ goto err;
+ t->neg = 0;
+ if (!BN_sub_word(t, 1))
+ goto err;
+ if (!BN_rshift1(t, t))
+ goto err;
+ /* r := a^t mod b */
+ b->neg = 0;
+
+ if (!BN_mod_exp_recp(r, a, t, b, ctx))
+ goto err;
+ b->neg = 1;
+
+ if (BN_is_word(r, 1))
+ legendre = 1;
+ else if (BN_is_zero(r))
+ legendre = 0;
+ else {
+ if (!BN_add_word(r, 1))
+ goto err;
+ if (0 != BN_ucmp(r, b)) {
+ fprintf(stderr, "Legendre symbol computation failed\n");
+ goto err;
+ }
+ legendre = -1;
+ }
+
+ kronecker = BN_kronecker(a, b, ctx);
+ if (kronecker < -1)
+ goto err;
+ /* we actually need BN_kronecker(a, |b|) */
+ if (a->neg && b->neg)
+ kronecker = -kronecker;
+
+ if (legendre != kronecker) {
+ fprintf(stderr, "legendre != kronecker; a = ");
+ BN_print_fp(stderr, a);
+ fprintf(stderr, ", b = ");
+ BN_print_fp(stderr, b);
+ fprintf(stderr, "\n");
+ goto err;
+ }
+
+ putc('.', stderr);
+ fflush(stderr);
+ }
+
+ putc('\n', stderr);
+ fflush(stderr);
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(b);
+ BN_free(r);
+ BN_free(t);
+ return ret;
+}
+
+int test_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', stderr);
+ }
+ 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_bntest_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_bntest_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('.', stderr);
+ fflush(stderr);
+ }
+
+ putc('\n', stderr);
+ fflush(stderr);
+ }
+ ret = 1;
+ err:
+ BN_free(a);
+ BN_free(p);
+ BN_free(r);
+ return ret;
+}
+
+int test_small_prime(BIO *bp, BN_CTX *ctx)
+{
+ static const int bits = 10;
+ int ret = 0;
+ BIGNUM *r;
+
+ r = BN_new();
+ 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_clear_free(r);
+ return ret;
+}
+
+int test_bn2dec(BIO *bp)
+{
+ static const char *bn2dec_tests[] = {
+ "0",
+ "1",
+ "-1",
+ "100",
+ "-100",
+ "123456789012345678901234567890",
+ "-123456789012345678901234567890",
+ "123456789012345678901234567890123456789012345678901234567890",
+ "-123456789012345678901234567890123456789012345678901234567890",
+ };
+ int ret = 0;
+ size_t i;
+ BIGNUM *bn = NULL;
+ char *dec = NULL;
+
+ for (i = 0; i < OSSL_NELEM(bn2dec_tests); i++) {
+ if (!BN_dec2bn(&bn, bn2dec_tests[i]))
+ goto err;
+
+ dec = BN_bn2dec(bn);
+ if (dec == NULL) {
+ fprintf(stderr, "BN_bn2dec failed on %s.\n", bn2dec_tests[i]);
+ goto err;
+ }
+
+ if (strcmp(dec, bn2dec_tests[i]) != 0) {
+ fprintf(stderr, "BN_bn2dec gave %s, wanted %s.\n", dec,
+ bn2dec_tests[i]);
+ goto err;
+ }
+
+ OPENSSL_free(dec);
+ dec = NULL;
+ }
+
+ ret = 1;
+
+err:
+ BN_free(bn);
+ OPENSSL_free(dec);
+ return ret;
+}
+
+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_bntest_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_lshift1(BIO *bp)
+{
+ BIGNUM *a, *b, *c;
+ int i;
+
+ a = BN_new();
+ b = BN_new();
+ c = BN_new();
+
+ BN_bntest_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_bntest_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_bntest_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 rand_neg(void)
+{
+ static unsigned int neg = 0;
+ static int sign[8] = { 0, 0, 0, 1, 1, 0, 1, 1 };
+
+ return (sign[(neg++) % 8]);
+}
projects / cassiopeia.git / blobdiff