openssl/test/bntest.c

/*
 * Copyright 1995-2017 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
 */
#include <assert.h>
#include <errno.h>
#include <stdio.h>
#include <string.h>
#include <ctype.h>

#include "e_os.h"
#include <internal/numbers.h>
#include <openssl/bn.h>
#include <openssl/crypto.h>
#include <openssl/err.h>
#include <openssl/rand.h>
#include "testutil.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 references 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"

/*
 * Things in boring, not in openssl.  TODO we should add them.
 */
#define HAVE_BN_PADDED 0
#define HAVE_BN_SQRT 0

typedef struct filetest_st {
    const char *name;
    int (*func)(STANZA *s);
} FILETEST;

typedef struct mpitest_st {
    const char *base10;
    const char *mpi;
    size_t mpi_len;
} MPITEST;

static const int NUM0 = 100;           /* number of tests */
static const int NUM1 = 50;            /* additional tests for some functions */
static BN_CTX *ctx;

/*
 * Polynomial coefficients used in GFM tests.
 */
static int p0[] = { 163, 7, 6, 3, 0, -1 };
static int p1[] = { 193, 15, 0, -1 };


/*
 * Look for |key| in the stanza and return it or NULL if not found.
 */
static const char *findattr(STANZA *s, const char *key)
{
    int i = s->numpairs;
    PAIR *pp = s->pairs;

    for ( ; --i >= 0; pp++)
        if (strcasecmp(pp->key, key) == 0)
            return pp->value;
    return NULL;
}

/*
 * Parse BIGNUM, return number of bytes parsed.
 */
static int parseBN(BIGNUM **out, const char *in)
{
    *out = NULL;
    return BN_hex2bn(out, in);
}

static int parsedecBN(BIGNUM **out, const char *in)
{
    *out = NULL;
    return BN_dec2bn(out, in);
}

static BIGNUM *getBN(STANZA *s, const char *attribute)
{
    const char *hex;
    BIGNUM *ret = NULL;

    if ((hex = findattr(s, attribute)) == NULL) {
        TEST_error("%s:%d: Can't find %s", s->test_file, s->start, attribute);
        return NULL;
    }

    if (parseBN(&ret, hex) != (int)strlen(hex)) {
        TEST_error("Could not decode '%s'", hex);
        return NULL;
    }
    return ret;
}

static int getint(STANZA *s, int *out, const char *attribute)
{
    BIGNUM *ret;
    BN_ULONG word;
    int st = 0;

    if (!TEST_ptr(ret = getBN(s, attribute))
            || !TEST_ulong_le(word = BN_get_word(ret), INT_MAX))
        goto err;

    *out = (int)word;
    st = 1;
err:
    BN_free(ret);
    return st;
}

static int equalBN(const char *op, const BIGNUM *expected, const BIGNUM *actual)
{
    if (BN_cmp(expected, actual) == 0)
        return 1;

    TEST_error("unexpected %s value", op);
    TEST_BN_eq(expected, actual);
    return 0;
}


/*
 * Return a "random" flag for if a BN should be negated.
 */
static 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 int test_sub()
{
    BIGNUM *a = NULL, *b = NULL, *c = NULL;
    int i, st = 0;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b = BN_new())
            || !TEST_ptr(c = BN_new()))
        goto err;

    for (i = 0; i < NUM0 + NUM1; i++) {
        if (i < NUM1) {
            BN_bntest_rand(a, 512, 0, 0);
            BN_copy(b, a);
            if (!TEST_int_ne(BN_set_bit(a, i), 0))
                goto err;
            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);
        BN_add(c, c, b);
        BN_sub(c, c, a);
        if (!TEST_BN_eq_zero(c))
            goto err;
    }
    st = 1;
err:
    BN_free(a);
    BN_free(b);
    BN_free(c);
    return st;
}


static int test_div_recip()
{
    BIGNUM *a = NULL, *b = NULL, *c = NULL, *d = NULL, *e = NULL;
    BN_RECP_CTX *recp = NULL;
    int st = 0, i;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b = BN_new())
            || !TEST_ptr(c = BN_new())
            || !TEST_ptr(d = BN_new())
            || !TEST_ptr(e = BN_new())
            || !TEST_ptr(recp = BN_RECP_CTX_new()))
        goto err;

    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);
        BN_mul(e, d, b, ctx);
        BN_add(d, e, c);
        BN_sub(d, d, a);
        if (!TEST_BN_eq_zero(d))
            goto err;
    }
    st = 1;
err:
    BN_free(a);
    BN_free(b);
    BN_free(c);
    BN_free(d);
    BN_free(e);
    BN_RECP_CTX_free(recp);
    return st;
}


static int test_mod()
{
    BIGNUM *a = NULL, *b = NULL, *c = NULL, *d = NULL, *e = NULL;
    int st = 0, i;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b = BN_new())
            || !TEST_ptr(c = BN_new())
            || !TEST_ptr(d = BN_new())
            || !TEST_ptr(e = BN_new()))
        goto err;

    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);
        BN_div(d, e, a, b, ctx);
        BN_sub(e, e, c);
        if (!TEST_BN_eq_zero(e))
            goto err;
    }
    st = 1;
err:
    BN_free(a);
    BN_free(b);
    BN_free(c);
    BN_free(d);
    BN_free(e);
    return st;
}

static const char *bn1strings[] = {
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000000000FFFFFFFF00",
    "0000000000000000000000000000000000000000000000000000000000000000",
    "0000000000000000000000000000000000000000000000000000000000000000",
    "0000000000000000000000000000000000000000000000000000000000000000",
    "0000000000000000000000000000000000000000000000000000000000000000",
    "0000000000000000000000000000000000000000000000000000000000000000",
    "0000000000000000000000000000000000000000000000000000000000000000",
    "0000000000000000000000000000000000000000000000000000000000000000",
    "00000000000000000000000000000000000000000000000000FFFFFFFFFFFFFF",
    NULL
};

static const char *bn2strings[] = {
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
    "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000000000FFFFFFFF0000000000",
    "0000000000000000000000000000000000000000000000000000000000000000",
    "0000000000000000000000000000000000000000000000000000000000000000",
    "0000000000000000000000000000000000000000000000000000000000000000",
    "0000000000000000000000000000000000000000000000000000000000000000",
    "0000000000000000000000000000000000000000000000000000000000000000",
    "0000000000000000000000000000000000000000000000000000000000000000",
    "0000000000000000000000000000000000000000000000000000000000000000",
    "000000000000000000000000000000000000000000FFFFFFFFFFFFFF00000000",
    NULL
};

static char *glue(const char *list[])
{
    size_t len = 0;
    char *p, *save;
    int i;

    for (i = 0; list[i] != NULL; i++)
        len += strlen(list[i]);
    if (!TEST_ptr(p = save = OPENSSL_malloc(len + 1)))
            return NULL;
    for (i = 0; list[i] != NULL; i++)
        p += strlen(strcpy(p, list[i]));
    return save;
}

/*
 * Test constant-time modular exponentiation with 1024-bit inputs, which on
 * x86_64 cause a different code branch to be taken.
 */
static int test_modexp_mont5()
{
    BIGNUM *a = NULL, *p = NULL, *m = NULL, *d = NULL, *e = NULL;
    BIGNUM *b = NULL, *n = NULL, *c = NULL;
    BN_MONT_CTX *mont = NULL;
    char *bigstring;
    int st = 0;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(p = BN_new())
            || !TEST_ptr(m = BN_new())
            || !TEST_ptr(d = BN_new())
            || !TEST_ptr(e = BN_new())
            || !TEST_ptr(b = BN_new())
            || !TEST_ptr(n = BN_new())
            || !TEST_ptr(c = BN_new())
            || !TEST_ptr(mont = BN_MONT_CTX_new()))
        goto err;

    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 (!TEST_true(BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL)))
        goto err;
    if (!TEST_BN_eq_one(d))
        goto err;

    /* 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 (!TEST_BN_eq(c, d))
        goto err;

    /* Regression test for carry bug in sqr[x]8x_mont */
    bigstring = glue(bn1strings);
    BN_hex2bn(&n, bigstring);
    OPENSSL_free(bigstring);
    bigstring = glue(bn2strings);
    BN_hex2bn(&a, bigstring);
    OPENSSL_free(bigstring);
    BN_free(b);
    b = BN_dup(a);
    BN_MONT_CTX_set(mont, n, ctx);
    BN_mod_mul_montgomery(c, a, a, mont, ctx);
    BN_mod_mul_montgomery(d, a, b, mont, ctx);
    if (!TEST_BN_eq(c, d))
        goto err;

    /* Zero input */
    BN_bntest_rand(p, 1024, 0, 0);
    BN_zero(a);
    if (!TEST_true(BN_mod_exp_mont_consttime(d, a, p, m, ctx, NULL))
            || !TEST_BN_eq_zero(d))
        goto err;

    /*
     * 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 (!TEST_true(BN_from_montgomery(e, a, mont, ctx))
            || !TEST_true(BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
            || !TEST_true(BN_mod_exp_simple(a, e, p, m, ctx))
            || !TEST_BN_eq(a, d))
        goto err;

    /* Finally, some regular test vectors. */
    BN_bntest_rand(e, 1024, 0, 0);
    if (!TEST_true(BN_mod_exp_mont_consttime(d, e, p, m, ctx, NULL))
            || !TEST_true(BN_mod_exp_simple(a, e, p, m, ctx))
            || !TEST_BN_eq(a, d))
        goto err;

    st = 1;

err:
    BN_MONT_CTX_free(mont);
    BN_free(a);
    BN_free(p);
    BN_free(m);
    BN_free(d);
    BN_free(e);
    BN_free(b);
    BN_free(n);
    BN_free(c);
    return st;
}

#ifndef OPENSSL_NO_EC2M
static int test_gf2m_add()
{
    BIGNUM *a = NULL, *b = NULL, *c = NULL;
    int i, st = 0;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b = BN_new())
            || !TEST_ptr(c = BN_new()))
        goto err;

    for (i = 0; i < NUM0; i++) {
        BN_rand(a, 512, 0, 0);
        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 (!TEST_false((BN_is_odd(a) && BN_is_odd(c))
                        || (!BN_is_odd(a) && !BN_is_odd(c))))
            goto err;
        BN_GF2m_add(c, c, c);
        /* Test that c + c = 0. */
        if (!TEST_BN_eq_zero(c))
            goto err;
    }
    st = 1;
 err:
    BN_free(a);
    BN_free(b);
    BN_free(c);
    return st;
}

static int test_gf2m_mod()
{
    BIGNUM *a = NULL, *b[2] = {NULL,NULL}, *c = NULL, *d = NULL, *e = NULL;
    int i, j, st = 0;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b[0] = BN_new())
            || !TEST_ptr(b[1] = BN_new())
            || !TEST_ptr(c = BN_new())
            || !TEST_ptr(d = BN_new())
            || !TEST_ptr(e = BN_new()))
        goto err;

    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 (!TEST_BN_eq_zero(e))
                goto err;
        }
    }
    st = 1;
 err:
    BN_free(a);
    BN_free(b[0]);
    BN_free(b[1]);
    BN_free(c);
    BN_free(d);
    BN_free(e);
    return st;
}

static int test_gf2m_mul()
{
    BIGNUM *a, *b[2] = {NULL, NULL}, *c = NULL, *d = NULL;
    BIGNUM *e = NULL, *f = NULL, *g = NULL, *h = NULL;
    int i, j, st = 0;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b[0] = BN_new())
            || !TEST_ptr(b[1] = BN_new())
            || !TEST_ptr(c = BN_new())
            || !TEST_ptr(d = BN_new())
            || !TEST_ptr(e = BN_new())
            || !TEST_ptr(f = BN_new())
            || !TEST_ptr(g = BN_new())
            || !TEST_ptr(h = BN_new()))
        goto err;

    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 (!TEST_BN_eq_zero(f))
                goto err;
        }
    }
    st = 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 st;
}

static int test_gf2m_sqr()
{
    BIGNUM *a = NULL, *b[2] = {NULL,NULL}, *c = NULL, *d = NULL;
    int i, j, st = 0;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b[0] = BN_new())
            || !TEST_ptr(b[1] = BN_new())
            || !TEST_ptr(c = BN_new())
            || !TEST_ptr(d = BN_new()))
        goto err;

    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 (!TEST_BN_eq_zero(d))
                goto err;
        }
    }
    st = 1;
 err:
    BN_free(a);
    BN_free(b[0]);
    BN_free(b[1]);
    BN_free(c);
    BN_free(d);
    return st;
}

static int test_gf2m_modinv()
{
    BIGNUM *a = NULL, *b[2] = {NULL,NULL}, *c = NULL, *d = NULL;
    int i, j, st = 0;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b[0] = BN_new())
            || !TEST_ptr(b[1] = BN_new())
            || !TEST_ptr(c = BN_new())
            || !TEST_ptr(d = BN_new()))
        goto err;

    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 (!TEST_BN_eq_one(d))
                goto err;
        }
    }
    st = 1;
 err:
    BN_free(a);
    BN_free(b[0]);
    BN_free(b[1]);
    BN_free(c);
    BN_free(d);
    return st;
}

static int test_gf2m_moddiv()
{
    BIGNUM *a = NULL, *b[2] = {NULL,NULL}, *c = NULL, *d = NULL;
    BIGNUM *e = NULL, *f = NULL;
    int i, j, st = 0;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b[0] = BN_new())
            || !TEST_ptr(b[1] = BN_new())
            || !TEST_ptr(c = BN_new())
            || !TEST_ptr(d = BN_new())
            || !TEST_ptr(e = BN_new())
            || !TEST_ptr(f = BN_new()))
        goto err;

    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 (!TEST_BN_eq_one(f))
                goto err;
        }
    }
    st = 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 st;
}

static int test_gf2m_modexp()
{
    BIGNUM *a = NULL, *b[2] = {NULL,NULL}, *c = NULL, *d = NULL;
    BIGNUM *e = NULL, *f = NULL;
    int i, j, st = 0;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b[0] = BN_new())
            || !TEST_ptr(b[1] = BN_new())
            || !TEST_ptr(c = BN_new())
            || !TEST_ptr(d = BN_new())
            || !TEST_ptr(e = BN_new())
            || !TEST_ptr(f = BN_new()))
        goto err;

    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 (!TEST_BN_eq_zero(f))
                goto err;
        }
    }
    st = 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 st;
}

static int test_gf2m_modsqrt()
{
    BIGNUM *a = NULL, *b[2] = {NULL,NULL}, *c = NULL, *d = NULL;
    BIGNUM *e = NULL, *f = NULL;
    int i, j, st = 0;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b[0] = BN_new())
            || !TEST_ptr(b[1] = BN_new())
            || !TEST_ptr(c = BN_new())
            || !TEST_ptr(d = BN_new())
            || !TEST_ptr(e = BN_new())
            || !TEST_ptr(f = BN_new()))
        goto err;

    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 (!TEST_BN_eq_zero(f))
                goto err;
        }
    }
    st = 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 st;
}

static int test_gf2m_modsolvequad()
{
    BIGNUM *a = NULL, *b[2] = {NULL,NULL}, *c = NULL, *d = NULL;
    BIGNUM *e = NULL;
    int i, j, s = 0, t, st = 0;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b[0] = BN_new())
            || !TEST_ptr(b[1] = BN_new())
            || !TEST_ptr(c = BN_new())
            || !TEST_ptr(d = BN_new())
            || !TEST_ptr(e = BN_new()))
        goto err;

    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 (!TEST_BN_eq_zero(e))
                    goto err;
            }
        }
    }
    if (!TEST_int_ge(s, 0)) {
        TEST_info("%d tests found no roots; probably an error", NUM0);
        goto err;
    }
    st = 1;
 err:
    BN_free(a);
    BN_free(b[0]);
    BN_free(b[1]);
    BN_free(c);
    BN_free(d);
    BN_free(e);
    return st;
}
#endif

static int test_kronecker()
{
    BIGNUM *a = NULL, *b = NULL, *r = NULL, *t = NULL;
    int i, legendre, kronecker, st = 0;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b = BN_new())
            || !TEST_ptr(r = BN_new())
            || !TEST_ptr(t = BN_new()))
        goto err;

    /*
     * 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 (!TEST_true(BN_generate_prime_ex(b, 512, 0, NULL, NULL, NULL)))
        goto err;
    b->neg = rand_neg();

    for (i = 0; i < NUM0; i++) {
        if (!TEST_true(BN_bntest_rand(a, 512, 0, 0)))
            goto err;
        a->neg = rand_neg();

        /* t := (|b|-1)/2  (note that b is odd) */
        if (!TEST_true(BN_copy(t, b)))
            goto err;
        t->neg = 0;
        if (!TEST_true(BN_sub_word(t, 1)))
            goto err;
        if (!TEST_true(BN_rshift1(t, t)))
            goto err;
        /* r := a^t mod b */
        b->neg = 0;

        if (!TEST_true(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 (!TEST_true(BN_add_word(r, 1)))
                goto err;
            if (!TEST_int_eq(BN_ucmp(r, b), 0)) {
                TEST_info("Legendre symbol computation failed");
                goto err;
            }
            legendre = -1;
        }

        if (!TEST_int_ge(kronecker = BN_kronecker(a, b, ctx), -1))
            goto err;
        /* we actually need BN_kronecker(a, |b|) */
        if (a->neg && b->neg)
            kronecker = -kronecker;

        if (!TEST_int_eq(legendre, kronecker))
            goto err;
    }

    st = 1;
 err:
    BN_free(a);
    BN_free(b);
    BN_free(r);
    BN_free(t);
    return st;
}

static int file_sum(STANZA *s)
{
    BIGNUM *a = NULL, *b = NULL, *sum = NULL, *ret = NULL;
    BN_ULONG b_word;
    int st = 0;

    if (!TEST_ptr(a = getBN(s, "A"))
            || !TEST_ptr(b = getBN(s, "B"))
            || !TEST_ptr(sum = getBN(s, "Sum"))
            || !TEST_ptr(ret = BN_new()))
        goto err;

    if (!TEST_true(BN_add(ret, a, b))
            || !equalBN("A + B", sum, ret)
            || !TEST_true(BN_sub(ret, sum, a))
            || !equalBN("Sum - A", b, ret)
            || !TEST_true(BN_sub(ret, sum, b))
            || !equalBN("Sum - B", a, ret))
        goto err;

    /*
     * Test that the functions work when |r| and |a| point to the same BIGNUM,
     * or when |r| and |b| point to the same BIGNUM.
     * TODO: Test where all of |r|, |a|, and |b| point to the same BIGNUM.
     */
    if (!TEST_true(BN_copy(ret, a))
            || !TEST_true(BN_add(ret, ret, b))
            || !equalBN("A + B (r is a)", sum, ret)
            || !TEST_true(BN_copy(ret, b))
            || !TEST_true(BN_add(ret, a, ret))
            || !equalBN("A + B (r is b)", sum, ret)
            || !TEST_true(BN_copy(ret, sum))
            || !TEST_true(BN_sub(ret, ret, a))
            || !equalBN("Sum - A (r is a)", b, ret)
            || !TEST_true(BN_copy(ret, a))
            || !TEST_true(BN_sub(ret, sum, ret))
            || !equalBN("Sum - A (r is b)", b, ret)
            || !TEST_true(BN_copy(ret, sum))
            || !TEST_true(BN_sub(ret, ret, b))
            || !equalBN("Sum - B (r is a)", a, ret)
            || !TEST_true(BN_copy(ret, b))
            || !TEST_true(BN_sub(ret, sum, ret))
            || !equalBN("Sum - B (r is b)", a, ret))
        goto err;

    /*
     * Test BN_uadd() and BN_usub() with the prerequisites they are
     * documented as having. Note that these functions are frequently used
     * when the prerequisites don't hold. In those cases, they are supposed
     * to work as if the prerequisite hold, but we don't test that yet.
     * TODO: test that.
     */
    if (!BN_is_negative(a) && !BN_is_negative(b) && BN_cmp(a, b) >= 0) {
        if (!TEST_true(BN_uadd(ret, a, b))
                || !equalBN("A +u B", sum, ret)
                || !TEST_true(BN_usub(ret, sum, a))
                || !equalBN("Sum -u A", b, ret)
                || !TEST_true(BN_usub(ret, sum, b))
                || !equalBN("Sum -u B", a, ret))
            goto err;
        /*
         * Test that the functions work when |r| and |a| point to the same
         * BIGNUM, or when |r| and |b| point to the same BIGNUM.
         * TODO: Test where all of |r|, |a|, and |b| point to the same BIGNUM.
         */
        if (!TEST_true(BN_copy(ret, a))
                || !TEST_true(BN_uadd(ret, ret, b))
                || !equalBN("A +u B (r is a)", sum, ret)
                || !TEST_true(BN_copy(ret, b))
                || !TEST_true(BN_uadd(ret, a, ret))
                || !equalBN("A +u B (r is b)", sum, ret)
                || !TEST_true(BN_copy(ret, sum))
                || !TEST_true(BN_usub(ret, ret, a))
                || !equalBN("Sum -u A (r is a)", b, ret)
                || !TEST_true(BN_copy(ret, a))
                || !TEST_true(BN_usub(ret, sum, ret))
                || !equalBN("Sum -u A (r is b)", b, ret)
                || !TEST_true(BN_copy(ret, sum))
                || !TEST_true(BN_usub(ret, ret, b))
                || !equalBN("Sum -u B (r is a)", a, ret)
                || !TEST_true(BN_copy(ret, b))
                || !TEST_true(BN_usub(ret, sum, ret))
                || !equalBN("Sum -u B (r is b)", a, ret))
            goto err;
    }

    /*
     * Test with BN_add_word() and BN_sub_word() if |b| is small enough.
     */
    b_word = BN_get_word(b);
    if (!BN_is_negative(b) && b_word != (BN_ULONG)-1) {
        if (!TEST_true(BN_copy(ret, a))
                || !TEST_true(BN_add_word(ret, b_word))
                || !equalBN("A + B (word)", sum, ret)
                || !TEST_true(BN_copy(ret, sum))
                || !TEST_true(BN_sub_word(ret, b_word))
                || !equalBN("Sum - B (word)", a, ret))
            goto err;
    }
    st = 1;

err:
    BN_free(a);
    BN_free(b);
    BN_free(sum);
    BN_free(ret);
    return st;
}

static int file_lshift1(STANZA *s)
{
    BIGNUM *a = NULL, *lshift1 = NULL, *zero = NULL, *ret = NULL;
    BIGNUM *two = NULL, *remainder = NULL;
    int st = 0;

    if (!TEST_ptr(a = getBN(s, "A"))
            || !TEST_ptr(lshift1 = getBN(s, "LShift1"))
            || !TEST_ptr(zero = BN_new())
            || !TEST_ptr(ret = BN_new())
            || !TEST_ptr(two = BN_new())
            || !TEST_ptr(remainder = BN_new()))
        goto err;

    BN_zero(zero);

    if (!TEST_true(BN_set_word(two, 2))
            || !TEST_true(BN_add(ret, a, a))
            || !equalBN("A + A", lshift1, ret)
            || !TEST_true(BN_mul(ret, a, two, ctx))
            || !equalBN("A * 2", lshift1, ret)
            || !TEST_true(BN_div(ret, remainder, lshift1, two, ctx))
            || !equalBN("LShift1 / 2", a, ret)
            || !equalBN("LShift1 % 2", zero, remainder)
            || !TEST_true(BN_lshift1(ret, a))
            || !equalBN("A << 1", lshift1, ret)
            || !TEST_true(BN_rshift1(ret, lshift1))
            || !equalBN("LShift >> 1", a, ret)
            || !TEST_true(BN_rshift1(ret, lshift1))
            || !equalBN("LShift >> 1", a, ret))
        goto err;

    /* Set the LSB to 1 and test rshift1 again. */
    if (!TEST_true(BN_set_bit(lshift1, 0))
            || !TEST_true(BN_div(ret, NULL /* rem */ , lshift1, two, ctx))
            || !equalBN("(LShift1 | 1) / 2", a, ret)
            || !TEST_true(BN_rshift1(ret, lshift1))
            || !equalBN("(LShift | 1) >> 1", a, ret))
        goto err;

    st = 1;
err:
    BN_free(a);
    BN_free(lshift1);
    BN_free(zero);
    BN_free(ret);
    BN_free(two);
    BN_free(remainder);

    return st;
}

static int file_lshift(STANZA *s)
{
    BIGNUM *a = NULL, *lshift = NULL, *ret = NULL;
    int n = 0, st = 0;

    if (!TEST_ptr(a = getBN(s, "A"))
            || !TEST_ptr(lshift = getBN(s, "LShift"))
            || !TEST_ptr(ret = BN_new()))

    if (!TEST_true(BN_lshift(ret, a, n))
            || !equalBN("A << N", lshift, ret)
            || !TEST_true(BN_rshift(ret, lshift, n))
            || !equalBN("A >> N", a, ret))
        goto err;

    st = 1;
err:
    BN_free(a);
    BN_free(lshift);
    BN_free(ret);
    return st;
}

static int file_rshift(STANZA *s)
{
    BIGNUM *a = NULL, *rshift = NULL, *ret = NULL;
    int n = 0, st = 0;

    if (!TEST_ptr(a = getBN(s, "A"))
            || !TEST_ptr(rshift = getBN(s, "RShift"))
            || !TEST_ptr(ret = BN_new())
            || !getint(s, &n, "N"))
        goto err;

    if (!TEST_true(BN_rshift(ret, a, n))
            || !equalBN("A >> N", rshift, ret))
        goto err;

    /* If N == 1, try with rshift1 as well */
    if (n == 1) {
        if (!TEST_true(BN_rshift1(ret, a))
                || !equalBN("A >> 1 (rshift1)", rshift, ret))
            goto err;
    }
    st = 1;

err:
    BN_free(a);
    BN_free(rshift);
    BN_free(ret);
    return st;
}

static int file_square(STANZA *s)
{
    BIGNUM *a = NULL, *square = NULL, *zero = NULL, *ret = NULL;
    BIGNUM *remainder = NULL, *tmp = NULL;
    int st = 0;

    if (!TEST_ptr(a = getBN(s, "A"))
            || !TEST_ptr(square = getBN(s, "Square"))
            || !TEST_ptr(zero = BN_new())
            || !TEST_ptr(ret = BN_new())
            || !TEST_ptr(remainder = BN_new()))
        goto err;

    BN_zero(zero);
    if (!TEST_true(BN_sqr(ret, a, ctx))
            || !equalBN("A^2", square, ret)
            || !TEST_true(BN_mul(ret, a, a, ctx))
            || !equalBN("A * A", square, ret)
            || !TEST_true(BN_div(ret, remainder, square, a, ctx))
            || !equalBN("Square / A", a, ret)
            || !equalBN("Square % A", zero, remainder))
        goto err;

#if HAVE_BN_SQRT
    BN_set_negative(a, 0);
    if (!TEST_true(BN_sqrt(ret, square, ctx))
            || !equalBN("sqrt(Square)", a, ret))
        goto err;

    /* BN_sqrt should fail on non-squares and negative numbers. */
    if (!TEST_BN_eq_zero(square)) {
        if (!TEST_ptr(tmp = BN_new())
                || !TEST_true(BN_copy(tmp, square)))
            goto err;
        BN_set_negative(tmp, 1);

        if (!TEST_int_eq(BN_sqrt(ret, tmp, ctx), 0))
            goto err;
        ERR_clear_error();

        BN_set_negative(tmp, 0);
        if (BN_add(tmp, tmp, BN_value_one()))
            goto err;
        if (!TEST_int_eq(BN_sqrt(ret, tmp, ctx)))
            goto err;
        ERR_clear_error();
    }
#endif

    st = 1;
err:
    BN_free(a);
    BN_free(square);
    BN_free(zero);
    BN_free(ret);
    BN_free(remainder);
    BN_free(tmp);
    return st;
}

static int file_product(STANZA *s)
{
    BIGNUM *a = NULL, *b = NULL, *product = NULL, *ret = NULL;
    BIGNUM *remainder = NULL, *zero = NULL;
    int st = 0;

    if (!TEST_ptr(a = getBN(s, "A"))
            || !TEST_ptr(b = getBN(s, "B"))
            || !TEST_ptr(product = getBN(s, "Product"))
            || !TEST_ptr(ret = BN_new())
            || !TEST_ptr(remainder = BN_new())
            || !TEST_ptr(zero = BN_new()))
        goto err;

    BN_zero(zero);

    if (!TEST_true(BN_mul(ret, a, b, ctx))
            || !equalBN("A * B", product, ret)
            || !TEST_true(BN_div(ret, remainder, product, a, ctx))
            || !equalBN("Product / A", b, ret)
            || !equalBN("Product % A", zero, remainder)
            || !TEST_true(BN_div(ret, remainder, product, b, ctx))
            || !equalBN("Product / B", a, ret)
            || !equalBN("Product % B", zero, remainder))
        goto err;

    st = 1;
err:
    BN_free(a);
    BN_free(b);
    BN_free(product);
    BN_free(ret);
    BN_free(remainder);
    BN_free(zero);
    return st;
}

static int file_quotient(STANZA *s)
{
    BIGNUM *a = NULL, *b = NULL, *quotient = NULL, *remainder = NULL;
    BIGNUM *ret = NULL, *ret2 = NULL, *nnmod = NULL;
    BN_ULONG b_word, ret_word;
    int st = 0;

    if (!TEST_ptr(a = getBN(s, "A"))
            || !TEST_ptr(b = getBN(s, "B"))
            || !TEST_ptr(quotient = getBN(s, "Quotient"))
            || !TEST_ptr(remainder = getBN(s, "Remainder"))
            || !TEST_ptr(ret = BN_new())
            || !TEST_ptr(ret2 = BN_new())
            || !TEST_ptr(nnmod = BN_new()))
        goto err;

    if (!TEST_true(BN_div(ret, ret2, a, b, ctx))
            || !equalBN("A / B", quotient, ret)
            || !equalBN("A % B", remainder, ret2)
            || !TEST_true(BN_mul(ret, quotient, b, ctx))
            || !TEST_true(BN_add(ret, ret, remainder))
            || !equalBN("Quotient * B + Remainder", a, ret))
        goto err;

    /*
     * Test with BN_mod_word() and BN_div_word() if the divisor is
     * small enough.
     */
    b_word = BN_get_word(b);
    if (!BN_is_negative(b) && b_word != (BN_ULONG)-1) {
        BN_ULONG remainder_word = BN_get_word(remainder);

        assert(remainder_word != (BN_ULONG)-1);
        if (!TEST_ptr(BN_copy(ret, a)))
            goto err;
        ret_word = BN_div_word(ret, b_word);
        if (ret_word != remainder_word) {
#ifdef BN_DEC_FMT1
            TEST_error(
                    "Got A %% B (word) = " BN_DEC_FMT1 ", wanted " BN_DEC_FMT1,
                    ret_word, remainder_word);
#else
            TEST_error("Got A %% B (word) mismatch");
#endif
            goto err;
        }
        if (!equalBN ("A / B (word)", quotient, ret))
            goto err;

        ret_word = BN_mod_word(a, b_word);
        if (ret_word != remainder_word) {
#ifdef BN_DEC_FMT1
            TEST_error(
                    "Got A %% B (word) = " BN_DEC_FMT1 ", wanted " BN_DEC_FMT1 "",
                    ret_word, remainder_word);
#else
            TEST_error("Got A %% B (word) mismatch");
#endif
            goto err;
        }
    }

    /* Test BN_nnmod. */
    if (!BN_is_negative(b)) {
        if (!TEST_true(BN_copy(nnmod, remainder))
                || (BN_is_negative(nnmod)
                        && !TEST_true(BN_add(nnmod, nnmod, b)))
                || !TEST_true(BN_nnmod(ret, a, b, ctx))
                || !equalBN("A % B (non-negative)", nnmod, ret))
            goto err;
    }

    st = 1;
err:
    BN_free(a);
    BN_free(b);
    BN_free(quotient);
    BN_free(remainder);
    BN_free(ret);
    BN_free(ret2);
    BN_free(nnmod);
    return st;
}

static int file_modmul(STANZA *s)
{
    BIGNUM *a = NULL, *b = NULL, *m = NULL, *mod_mul = NULL, *ret = NULL;
    int st = 0;

    if (!TEST_ptr(a = getBN(s, "A"))
            || !TEST_ptr(b = getBN(s, "B"))
            || !TEST_ptr(m = getBN(s, "M"))
            || !TEST_ptr(mod_mul = getBN(s, "ModMul"))
            || !TEST_ptr(ret = BN_new()))
        goto err;

    if (!TEST_true(BN_mod_mul(ret, a, b, m, ctx))
            || !equalBN("A * B (mod M)", mod_mul, ret))
        goto err;

    if (BN_is_odd(m)) {
        /* Reduce |a| and |b| and test the Montgomery version. */
        BN_MONT_CTX *mont = BN_MONT_CTX_new();
        BIGNUM *a_tmp = BN_new();
        BIGNUM *b_tmp = BN_new();

        if (mont == NULL || a_tmp == NULL || b_tmp == NULL
                || !TEST_true(BN_MONT_CTX_set(mont, m, ctx))
                || !TEST_true(BN_nnmod(a_tmp, a, m, ctx))
                || !TEST_true(BN_nnmod(b_tmp, b, m, ctx))
                || !TEST_true(BN_to_montgomery(a_tmp, a_tmp, mont, ctx))
                || !TEST_true(BN_to_montgomery(b_tmp, b_tmp, mont, ctx))
                || !TEST_true(BN_mod_mul_montgomery(ret, a_tmp, b_tmp,
                                                    mont, ctx))
                || !TEST_true(BN_from_montgomery(ret, ret, mont, ctx))
                || !equalBN("A * B (mod M) (mont)", mod_mul, ret))
            st = 0;
        else
            st = 1;
        BN_MONT_CTX_free(mont);
        BN_free(a_tmp);
        BN_free(b_tmp);
        if (st == 0)
            goto err;
    }

    st = 1;
err:
    BN_free(a);
    BN_free(b);
    BN_free(m);
    BN_free(mod_mul);
    BN_free(ret);
    return st;
}

static int file_modexp(STANZA *s)
{
    BIGNUM *a = NULL, *e = NULL, *m = NULL, *mod_exp = NULL, *ret = NULL;
    BIGNUM *b = NULL, *c = NULL, *d = NULL;
    int st = 0;

    if (!TEST_ptr(a = getBN(s, "A"))
            || !TEST_ptr(e = getBN(s, "E"))
            || !TEST_ptr(m = getBN(s, "M"))
            || !TEST_ptr(mod_exp = getBN(s, "ModExp"))
            || !TEST_ptr(ret = BN_new())
            || !TEST_ptr(d = BN_new()))
        goto err;

    if (!TEST_true(BN_mod_exp(ret, a, e, m, ctx))
            || !equalBN("A ^ E (mod M)", mod_exp, ret))
        goto err;

    if (BN_is_odd(m)) {
        if (!TEST_true(BN_mod_exp_mont(ret, a, e, m, ctx, NULL))
                || !equalBN("A ^ E (mod M) (mont)", mod_exp, ret)
                || !TEST_true(BN_mod_exp_mont_consttime(ret, a, e, m,
                                                        ctx, NULL))
                || !equalBN("A ^ E (mod M) (mont const", mod_exp, ret))
            goto err;
    }

    /* 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");
    if (!TEST_true(BN_mod_exp(d, a, b, c, ctx))
        || !TEST_true(BN_mul(e, a, a, ctx))
        || !TEST_BN_eq(d, e))
        goto err;

    st = 1;
err:
    BN_free(a);
    BN_free(b);
    BN_free(c);
    BN_free(d);
    BN_free(e);
    BN_free(m);
    BN_free(mod_exp);
    BN_free(ret);
    return st;
}

static int file_exp(STANZA *s)
{
    BIGNUM *a = NULL, *e = NULL, *exp = NULL, *ret = NULL;
    int st = 0;

    if (!TEST_ptr(a = getBN(s, "A"))
            || !TEST_ptr(e = getBN(s, "E"))
            || !TEST_ptr(exp = getBN(s, "Exp"))
            || !TEST_ptr(ret = BN_new()))
        goto err;

    if (!TEST_true(BN_exp(ret, a, e, ctx))
            || !equalBN("A ^ E", exp, ret))
        goto err;

    st = 1;
err:
    BN_free(a);
    BN_free(e);
    BN_free(exp);
    BN_free(ret);
    return st;
}

static int file_modsqrt(STANZA *s)
{
    BIGNUM *a = NULL, *p = NULL, *mod_sqrt = NULL, *ret = NULL, *ret2 = NULL;
    int st = 0;

    if (!TEST_ptr(a = getBN(s, "A"))
            || !TEST_ptr(p = getBN(s, "P"))
            || !TEST_ptr(mod_sqrt = getBN(s, "ModSqrt"))
            || !TEST_ptr(ret = BN_new())
            || !TEST_ptr(ret2 = BN_new()))
        goto err;

    /* There are two possible answers. */
    if (!TEST_true(BN_mod_sqrt(ret, a, p, ctx))
            || !TEST_true(BN_sub(ret2, p, ret)))
        goto err;

    /* The first condition should NOT be a test. */
    if (BN_cmp(ret2, mod_sqrt) != 0
            && !equalBN("sqrt(A) (mod P)", mod_sqrt, ret))
        goto err;

    st = 1;
err:
    BN_free(a);
    BN_free(p);
    BN_free(mod_sqrt);
    BN_free(ret);
    BN_free(ret2);
    return st;
}

static int test_bn2padded()
{
#if HAVE_BN_PADDED
    uint8_t zeros[256], out[256], reference[128];
    BIGNUM *n = BN_new();
    int st = 0;

    /* Test edge case at 0. */
    if (n == NULL)
        goto err;
    if (!TEST_true(BN_bn2bin_padded(NULL, 0, n)))
        goto err;
    memset(out, -1, sizeof(out));
    if (!TEST_true(BN_bn2bin_padded(out, sizeof(out)), n))
        goto err;
    memset(zeros, 0, sizeof(zeros));
    if (!TEST_mem_eq(zeros, sizeof(zeros), out, sizeof(out)))
        goto err;

    /* Test a random numbers at various byte lengths. */
    for (size_t bytes = 128 - 7; bytes <= 128; bytes++) {
#define TOP_BIT_ON 0
#define BOTTOM_BIT_NOTOUCH 0
        if (!TEST_true(BN_rand(n, bytes * 8, TOP_BIT_ON, BOTTOM_BIT_NOTOUCH)))
            goto err;
        if (!TEST_int_eq(BN_num_bytes(n),A) bytes
                || TEST_int_eq(BN_bn2bin(n, reference), bytes))
            goto err;
        /* Empty buffer should fail. */
        if (!TEST_int_eq(BN_bn2bin_padded(NULL, 0, n)), 0)
            goto err;
        /* One byte short should fail. */
        if (BN_bn2bin_padded(out, bytes - 1, n))
            goto err;
        /* Exactly right size should encode. */
        if (!TEST_true(BN_bn2bin_padded(out, bytes, n))
                || TEST_mem_eq(out, bytes, reference, bytes))
            goto err;
        /* Pad up one byte extra. */
        if (!TEST_true(BN_bn2bin_padded(out, bytes + 1, n))
                || !TEST_mem_eq(out + 1, bytes, reference, bytes)
                || !TEST_mem_eq(out, 1, zeros, 1))
            goto err;
        /* Pad up to 256. */
        if (!TEST_true(BN_bn2bin_padded(out, sizeof(out)), n)
                || !TEST_mem_eq(out + sizeof(out) - bytes, bytes,
                                reference, bytes)
                || !TEST_mem_eq(out, sizseof(out) - bytes,
                                zeros, sizeof(out) - bytes))
            goto err;
    }

    st = 1;
err:
    BN_free(n);
    return st;
#else
    return ctx != NULL;
#endif
}

static int test_dec2bn()
{
    BIGNUM *bn = NULL;
    int st = 0;

    if (!TEST_int_eq(parsedecBN(&bn, "0"), 1)
            || !TEST_BN_eq_word(bn, 0)
            || !TEST_BN_eq_zero(bn)
            || !TEST_BN_le_zero(bn)
            || !TEST_BN_ge_zero(bn)
            || !TEST_BN_even(bn))
        goto err;
    BN_free(bn);
    bn = NULL;

    if (!TEST_int_eq(parsedecBN(&bn, "256"), 3)
            || !TEST_BN_eq_word(bn, 256)
            || !TEST_BN_ge_zero(bn)
            || !TEST_BN_gt_zero(bn)
            || !TEST_BN_ne_zero(bn)
            || !TEST_BN_even(bn))
        goto err;
    BN_free(bn);
    bn = NULL;

    if (!TEST_int_eq(parsedecBN(&bn, "-42"), 3)
            || !TEST_BN_abs_eq_word(bn, 42)
            || !TEST_BN_lt_zero(bn)
            || !TEST_BN_le_zero(bn)
            || !TEST_BN_ne_zero(bn)
            || !TEST_BN_even(bn))
        goto err;
    BN_free(bn);
    bn = NULL;

    if (!TEST_int_eq(parsedecBN(&bn, "1"), 1)
            || !TEST_BN_eq_word(bn, 1)
            || !TEST_BN_ne_zero(bn)
            || !TEST_BN_gt_zero(bn)
            || !TEST_BN_ge_zero(bn)
            || !TEST_BN_eq_one(bn)
            || !TEST_BN_odd(bn))
        goto err;
    BN_free(bn);
    bn = NULL;

    if (!TEST_int_eq(parsedecBN(&bn, "-0"), 2)
            || !TEST_BN_eq_zero(bn)
            || !TEST_BN_ge_zero(bn)
            || !TEST_BN_le_zero(bn)
            || !TEST_BN_even(bn))
        goto err;
    BN_free(bn);
    bn = NULL;

    if (!TEST_int_eq(parsedecBN(&bn, "42trailing garbage is ignored"), 2)
            || !TEST_BN_abs_eq_word(bn, 42)
            || !TEST_BN_ge_zero(bn)
            || !TEST_BN_gt_zero(bn)
            || !TEST_BN_ne_zero(bn)
            || !TEST_BN_even(bn))
        goto err;

    st = 1;
err:
    BN_free(bn);
    return st;
}

static int test_hex2bn()
{
    BIGNUM *bn = NULL;
    int st = 0;

    if (!TEST_int_eq(parseBN(&bn, "0"), 1)
            || !TEST_BN_eq_zero(bn)
            || !TEST_BN_ge_zero(bn)
            || !TEST_BN_even(bn))
        goto err;
    BN_free(bn);
    bn = NULL;

    if (!TEST_int_eq(parseBN(&bn, "256"), 3)
            || !TEST_BN_eq_word(bn, 0x256)
            || !TEST_BN_ge_zero(bn)
            || !TEST_BN_gt_zero(bn)
            || !TEST_BN_ne_zero(bn)
            || !TEST_BN_even(bn))
        goto err;
    BN_free(bn);
    bn = NULL;

    if (!TEST_int_eq(parseBN(&bn, "-42"), 3)
            || !TEST_BN_abs_eq_word(bn, 0x42)
            || !TEST_BN_lt_zero(bn)
            || !TEST_BN_le_zero(bn)
            || !TEST_BN_ne_zero(bn)
            || !TEST_BN_even(bn))
        goto err;
    BN_free(bn);
    bn = NULL;

    if (!TEST_int_eq(parseBN(&bn, "cb"), 2)
            || !TEST_BN_eq_word(bn, 0xCB)
            || !TEST_BN_ge_zero(bn)
            || !TEST_BN_gt_zero(bn)
            || !TEST_BN_ne_zero(bn)
            || !TEST_BN_odd(bn))
        goto err;
    BN_free(bn);
    bn = NULL;

    if (!TEST_int_eq(parseBN(&bn, "-0"), 2)
            || !TEST_BN_eq_zero(bn)
            || !TEST_BN_ge_zero(bn)
            || !TEST_BN_le_zero(bn)
            || !TEST_BN_even(bn))
        goto err;
    BN_free(bn);
    bn = NULL;

    if (!TEST_int_eq(parseBN(&bn, "abctrailing garbage is ignored"), 3)
            || !TEST_BN_eq_word(bn, 0xabc)
            || !TEST_BN_ge_zero(bn)
            || !TEST_BN_gt_zero(bn)
            || !TEST_BN_ne_zero(bn)
            || !TEST_BN_even(bn))
        goto err;
    st = 1;

err:
    BN_free(bn);
    return st;
}

static int test_asc2bn()
{
    BIGNUM *bn = NULL;
    int st = 0;

    if (!TEST_ptr(bn = BN_new()))
        goto err;

    if (!TEST_true(BN_asc2bn(&bn, "0"))
            || !TEST_BN_eq_zero(bn)
            || !TEST_BN_ge_zero(bn))
        goto err;

    if (!TEST_true(BN_asc2bn(&bn, "256"))
            || !TEST_BN_eq_word(bn, 256)
            || !TEST_BN_ge_zero(bn))
        goto err;

    if (!TEST_true(BN_asc2bn(&bn, "-42"))
            || !TEST_BN_abs_eq_word(bn, 42)
            || !TEST_BN_lt_zero(bn))
        goto err;

    if (!TEST_true(BN_asc2bn(&bn, "0x1234"))
            || !TEST_BN_eq_word(bn, 0x1234)
            || !TEST_BN_ge_zero(bn))
        goto err;

    if (!TEST_true(BN_asc2bn(&bn, "0X1234"))
            || !TEST_BN_eq_word(bn, 0x1234)
            || !TEST_BN_ge_zero(bn))
        goto err;

    if (!TEST_true(BN_asc2bn(&bn, "-0xabcd"))
            || !TEST_BN_abs_eq_word(bn, 0xabcd)
            || !TEST_BN_lt_zero(bn))
        goto err;

    if (!TEST_true(BN_asc2bn(&bn, "-0"))
            || !TEST_BN_eq_zero(bn)
            || !TEST_BN_ge_zero(bn))
        goto err;

    if (!TEST_true(BN_asc2bn(&bn, "123trailing garbage is ignored"))
            || !TEST_BN_eq_word(bn, 123)
            || !TEST_BN_ge_zero(bn))
        goto err;

    st = 1;
err:
    BN_free(bn);
    return st;
}

static const MPITEST kMPITests[] = {
    {"0", "\x00\x00\x00\x00", 4},
    {"1", "\x00\x00\x00\x01\x01", 5},
    {"-1", "\x00\x00\x00\x01\x81", 5},
    {"128", "\x00\x00\x00\x02\x00\x80", 6},
    {"256", "\x00\x00\x00\x02\x01\x00", 6},
    {"-256", "\x00\x00\x00\x02\x81\x00", 6},
};

static int test_mpi(int i)
{
    uint8_t scratch[8];
    const MPITEST *test = &kMPITests[i];
    size_t mpi_len, mpi_len2;
    BIGNUM *bn = NULL;
    BIGNUM *bn2 = NULL;
    int st = 0;

    if (!TEST_ptr(bn = BN_new())
            || !TEST_true(BN_asc2bn(&bn, test->base10)))
        goto err;
    mpi_len = BN_bn2mpi(bn, NULL);
    if (!TEST_size_t_le(mpi_len, sizeof(scratch)))
        goto err;

    if (!TEST_size_t_eq(mpi_len2 = BN_bn2mpi(bn, scratch), mpi_len)
            || !TEST_mem_eq(test->mpi, test->mpi_len, scratch, mpi_len))
        goto err;

    if (!TEST_ptr(bn2 = BN_mpi2bn(scratch, mpi_len, NULL)))
        goto err;

    if (!TEST_BN_eq(bn, bn2)) {
        BN_free(bn2);
        goto err;
    }
    BN_free(bn2);

    st = 1;
err:
    BN_free(bn);
    return st;
}

static int test_rand()
{
    BIGNUM *bn = NULL;
    int st = 0;

    if (!TEST_ptr(bn = BN_new()))
        return 0;

    /* Test BN_rand for degenerate cases with |top| and |bottom| parameters. */
    if (!TEST_false(BN_rand(bn, 0, 0 /* top */ , 0 /* bottom */ ))
            || !TEST_false(BN_rand(bn, 0, 1 /* top */ , 1 /* bottom */ ))
            || !TEST_true(BN_rand(bn, 1, 0 /* top */ , 0 /* bottom */ ))
            || !TEST_BN_eq_one(bn)
            || !TEST_false(BN_rand(bn, 1, 1 /* top */ , 0 /* bottom */ ))
            || !TEST_true(BN_rand(bn, 1, -1 /* top */ , 1 /* bottom */ ))
            || !TEST_BN_eq_one(bn)
            || !TEST_true(BN_rand(bn, 2, 1 /* top */ , 0 /* bottom */ ))
            || !TEST_BN_eq_word(bn, 3))
        goto err;

    st = 1;
err:
    BN_free(bn);
    return st;
}

static int test_negzero()
{
    BIGNUM *a = NULL, *b = NULL, *c = NULL, *d = NULL;
    BIGNUM *numerator = NULL, *denominator = NULL;
    int consttime, st = 0;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b = BN_new())
            || !TEST_ptr(c = BN_new())
            || !TEST_ptr(d = BN_new()))
        goto err;

    /* Test that BN_mul never gives negative zero. */
    if (!TEST_true(BN_set_word(a, 1)))
        goto err;
    BN_set_negative(a, 1);
    BN_zero(b);
    if (!TEST_true(BN_mul(c, a, b, ctx)))
        goto err;
    if (!TEST_BN_eq_zero(c)
            || !TEST_BN_ge_zero(c))
        goto err;

    for (consttime = 0; consttime < 2; consttime++) {
        if (!TEST_ptr(numerator = BN_new())
                || !TEST_ptr(denominator = BN_new()))
            goto err;
        if (consttime) {
            BN_set_flags(numerator, BN_FLG_CONSTTIME);
            BN_set_flags(denominator, BN_FLG_CONSTTIME);
        }
        /* Test that BN_div never gives negative zero in the quotient. */
        if (!TEST_true(BN_set_word(numerator, 1))
                || !TEST_true(BN_set_word(denominator, 2)))
            goto err;
        BN_set_negative(numerator, 1);
        if (!TEST_true(BN_div(a, b, numerator, denominator, ctx))
                || !TEST_BN_eq_zero(a)
                || !TEST_BN_ge_zero(a))
            goto err;

        /* Test that BN_div never gives negative zero in the remainder. */
        if (!TEST_true(BN_set_word(denominator, 1))
                || !TEST_true(BN_div(a, b, numerator, denominator, ctx))
                || !TEST_BN_eq_zero(b)
                || !TEST_BN_ge_zero(b))
            goto err;
        BN_free(numerator);
        BN_free(denominator);
        numerator = denominator = NULL;
    }

    /* Test that BN_set_negative will not produce a negative zero. */
    BN_zero(a);
    BN_set_negative(a, 1);
    if (BN_is_negative(a))
        goto err;
    st = 1;

err:
    BN_free(a);
    BN_free(b);
    BN_free(c);
    BN_free(d);
    BN_free(numerator);
    BN_free(denominator);
    return st;
}

static int test_badmod()
{
    BIGNUM *a = NULL, *b = NULL, *zero = NULL;
    BN_MONT_CTX *mont = NULL;
    int st = 0;

    if (!TEST_ptr(a = BN_new())
            || !TEST_ptr(b = BN_new())
            || !TEST_ptr(zero = BN_new())
            || !TEST_ptr(mont = BN_MONT_CTX_new()))
        goto err;
    BN_zero(zero);

    if (!TEST_false(BN_div(a, b, BN_value_one(), zero, ctx)))
        goto err;
    ERR_clear_error();

    if (!TEST_false(BN_mod_mul(a, BN_value_one(), BN_value_one(), zero, ctx)))
        goto err;
    ERR_clear_error();

    if (!TEST_false(BN_mod_exp(a, BN_value_one(), BN_value_one(), zero, ctx)))
        goto err;
    ERR_clear_error();

    if (!TEST_false(BN_mod_exp_mont(a, BN_value_one(), BN_value_one(),
                                    zero, ctx, NULL)))
        goto err;
    ERR_clear_error();

    if (!TEST_false(BN_mod_exp_mont_consttime(a, BN_value_one(), BN_value_one(),
                                             zero, ctx, NULL)))
        goto err;
    ERR_clear_error();

    if (!TEST_false(BN_MONT_CTX_set(mont, zero, ctx)))
        goto err;
    ERR_clear_error();

    /* Some operations also may not be used with an even modulus. */
    if (!TEST_true(BN_set_word(b, 16)))
        goto err;

    if (!TEST_false(BN_MONT_CTX_set(mont, b, ctx)))
        goto err;
    ERR_clear_error();

    if (!TEST_false(BN_mod_exp_mont(a, BN_value_one(), BN_value_one(),
                                    b, ctx, NULL)))
        goto err;
    ERR_clear_error();

    if (!TEST_false(BN_mod_exp_mont_consttime(a, BN_value_one(), BN_value_one(),
                                  b, ctx, NULL)))
        goto err;
    ERR_clear_error();

    st = 1;
err:
    BN_free(a);
    BN_free(b);
    BN_free(zero);
    BN_MONT_CTX_free(mont);
    return st;
}

static int test_expmodzero()
{
    BIGNUM *a = NULL, *r = NULL, *zero = NULL;
    int st = 0;

    if (!TEST_ptr(zero = BN_new())
            || !TEST_ptr(a = BN_new())
            || !TEST_ptr(r = BN_new()))
        goto err;
    BN_zero(zero);

    if (!TEST_true(BN_mod_exp(r, a, zero, BN_value_one(), NULL))
            || !TEST_BN_eq_zero(r)
            || !TEST_true(BN_mod_exp_mont(r, a, zero, BN_value_one(),
                                          NULL, NULL))
            || !TEST_BN_eq_zero(r)
            || !TEST_true(BN_mod_exp_mont_consttime(r, a, zero,
                                                    BN_value_one(),
                                                    NULL, NULL))
            || !TEST_BN_eq_zero(r)
            || !TEST_true(BN_mod_exp_mont_word(r, 42, zero,
                                               BN_value_one(), NULL, NULL))
            || !TEST_BN_eq_zero(r))
        goto err;

    st = 1;
err:
    BN_free(zero);
    BN_free(a);
    BN_free(r);
    return st;
}

static int test_smallprime()
{
    static const int kBits = 10;
    BIGNUM *r;
    int st = 0;

    if (!TEST_ptr(r = BN_new())
            || !TEST_true(BN_generate_prime_ex(r, (int)kBits, 0,
                                               NULL, NULL, NULL))
            || !TEST_int_eq(BN_num_bits(r), kBits))
        goto err;

    st = 1;
err:
    BN_free(r);
    return st;
}

static int test_3_is_prime()
{
    int ret = 0;
    BIGNUM *r = NULL;

    /*
     * For a long time, small primes were not considered prime when
     * do_trial_division was set.
     */
    if (!TEST_ptr(r = BN_new())
            || !TEST_true(BN_set_word(r, 3))
            || !TEST_int_eq(BN_is_prime_fasttest_ex(r, 3 /* nchecks */, ctx,
                                0 /* do_trial_division */, NULL), 1)
            || !TEST_int_eq(BN_is_prime_fasttest_ex(r, 3 /* nchecks */, ctx,
                                1 /* do_trial_division */, NULL), 1))
        goto err;

    ret = 1;

err:
    BN_free(r);
    return ret;
}

static int file_test_run(STANZA *s)
{
    static const FILETEST filetests[] = {
        {"Sum", file_sum},
        {"LShift1", file_lshift1},
        {"LShift", file_lshift},
        {"RShift", file_rshift},
        {"Square", file_square},
        {"Product", file_product},
        {"Quotient", file_quotient},
        {"ModMul", file_modmul},
        {"ModExp", file_modexp},
        {"Exp", file_exp},
        {"ModSqrt", file_modsqrt},
    };
    int numtests = OSSL_NELEM(filetests);
    const FILETEST *tp = filetests;

    for ( ; --numtests >= 0; tp++) {
        if (findattr(s, tp->name) != NULL) {
            if (!tp->func(s)) {
                TEST_info("%s:%d: Failed %s test",
                          s->test_file, s->start, tp->name);
                return 0;
            }
            return 1;
        }
    }
    TEST_info("%s:%d: Unknown test", s->test_file, s->start);
    return 0;
}

static int run_file_tests(int i)
{
    STANZA *s = NULL;
    char *testfile = test_get_argument(i);
    int c;

    if (!TEST_ptr(s = OPENSSL_zalloc(sizeof(*s))))
        return 0;
    if (!test_start_file(s, testfile)) {
        OPENSSL_free(s);
        return 0;
    }

    /* Read test file. */
    while (!BIO_eof(s->fp) && test_readstanza(s)) {
        if (s->numpairs == 0)
            continue;
        if (!file_test_run(s))
            s->errors++;
        s->numtests++;
        test_clearstanza(s);
    }
    test_end_file(s);
    c = s->errors;
    OPENSSL_free(s);

    return c == 0;
}


int setup_tests(void)
{
    static const char rnd_seed[] =
        "If not seeded, BN_generate_prime might fail";
    int n = test_get_argument_count();

    RAND_seed(rnd_seed, sizeof(rnd_seed));
    if (!TEST_ptr(ctx = BN_CTX_new()))
        return 0;

    if (n == 0) {
        ADD_TEST(test_sub);
        ADD_TEST(test_div_recip);
        ADD_TEST(test_mod);
        ADD_TEST(test_modexp_mont5);
        ADD_TEST(test_kronecker);
        ADD_TEST(test_rand);
        ADD_TEST(test_bn2padded);
        ADD_TEST(test_dec2bn);
        ADD_TEST(test_hex2bn);
        ADD_TEST(test_asc2bn);
        ADD_ALL_TESTS(test_mpi, (int)OSSL_NELEM(kMPITests));
        ADD_TEST(test_negzero);
        ADD_TEST(test_badmod);
        ADD_TEST(test_expmodzero);
        ADD_TEST(test_smallprime);
#ifndef OPENSSL_NO_EC2M
        ADD_TEST(test_gf2m_add);
        ADD_TEST(test_gf2m_mod);
        ADD_TEST(test_gf2m_mul);
        ADD_TEST(test_gf2m_sqr);
        ADD_TEST(test_gf2m_modinv);
        ADD_TEST(test_gf2m_moddiv);
        ADD_TEST(test_gf2m_modexp);
        ADD_TEST(test_gf2m_modsqrt);
        ADD_TEST(test_gf2m_modsolvequad);
#endif
        ADD_TEST(test_3_is_prime);
    } else {
        ADD_ALL_TESTS(run_file_tests, n);
    }
    return 1;
}

void cleanup_tests(void)
{
    BN_CTX_free(ctx);
}