C++ BN_rshift函數代碼示例

int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
                       BN_CTX *ctx)
{
    int retn = 0;
#ifdef MONT_WORD
    BIGNUM *t;

    BN_CTX_start(ctx);
    if ((t = BN_CTX_get(ctx)) && BN_copy(t, a))
        retn = BN_from_montgomery_word(ret, t, mont);
    BN_CTX_end(ctx);
#else                           /* !MONT_WORD */
    BIGNUM *t1, *t2;

    BN_CTX_start(ctx);
    t1 = BN_CTX_get(ctx);
    t2 = BN_CTX_get(ctx);
    if (t1 == NULL || t2 == NULL)
        goto err;

    if (!BN_copy(t1, a))
        goto err;
    BN_mask_bits(t1, mont->ri);

    if (!BN_mul(t2, t1, &mont->Ni, ctx))
        goto err;
    BN_mask_bits(t2, mont->ri);

    if (!BN_mul(t1, t2, &mont->N, ctx))
        goto err;
    if (!BN_add(t2, a, t1))
        goto err;
    if (!BN_rshift(ret, t2, mont->ri))
        goto err;

#if !defined(BRANCH_FREE) || BRANCH_FREE==0
    if (BN_ucmp(ret, &(mont->N)) >= 0) {
        if (!BN_usub(ret, ret, &(mont->N)))
            goto err;
    }
#endif
    retn = 1;
    bn_check_top(ret);
 err:
    BN_CTX_end(ctx);
#endif                          /* MONT_WORD */
    return (retn);
}

static void
bsqrt(void)
{
	struct number	*n;
	struct number	*r;
	BIGNUM		*x, *y;
	u_int		scale, onecount;
	BN_CTX		*ctx;

	onecount = 0;
	n = pop_number();
	if (n == NULL) {
		return;
	}
	if (BN_is_zero(n->number)) {
		r = new_number();
		push_number(r);
	} else if (BN_is_negative(n->number))
		warnx("square root of negative number");
	else {
		scale = max(bmachine.scale, n->scale);
		normalize(n, 2*scale);
		x = BN_dup(n->number);
		bn_checkp(x);
		bn_check(BN_rshift(x, x, BN_num_bits(x)/2));
		y = BN_new();
		bn_checkp(y);
		ctx = BN_CTX_new();
		bn_checkp(ctx);
		for (;;) {
			bn_checkp(BN_copy(y, x));
			bn_check(BN_div(x, NULL, n->number, x, ctx));
			bn_check(BN_add(x, x, y));
			bn_check(BN_rshift1(x, x));
			if (bsqrt_stop(x, y, &onecount))
				break;
		}
		r = bmalloc(sizeof(*r));
		r->scale = scale;
		r->number = y;
		BN_free(x);
		BN_CTX_free(ctx);
		push_number(r);
	}

	free_number(n);
}

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);
	}

/*
 * rsa_get_exponent(): - Get the public exponent from an RSA key
 */
static int rsa_get_exponent(RSA *key, uint64_t *e)
{
	int ret;
	BIGNUM *bn_te;
	uint64_t te;

	ret = -EINVAL;
	bn_te = NULL;

	if (!e)
		goto cleanup;

	if (BN_num_bits(key->e) > 64)
		goto cleanup;

	*e = BN_get_word(key->e);

	if (BN_num_bits(key->e) < 33) {
		ret = 0;
		goto cleanup;
	}

	bn_te = BN_dup(key->e);
	if (!bn_te)
		goto cleanup;

	if (!BN_rshift(bn_te, bn_te, 32))
		goto cleanup;

	if (!BN_mask_bits(bn_te, 32))
		goto cleanup;

	te = BN_get_word(bn_te);
	te <<= 32;
	*e |= te;
	ret = 0;

cleanup:
	if (bn_te)
		BN_free(bn_te);

	return ret;
}

// digest_to_bn interprets |digest_len| bytes from |digest| as a big-endian
// number and sets |out| to that value. It then truncates |out| so that it's,
// at most, as long as |order|. It returns one on success and zero otherwise.
static int digest_to_bn(BIGNUM *out, const uint8_t *digest, size_t digest_len,
                        const BIGNUM *order) {
  size_t num_bits;

  num_bits = BN_num_bits(order);
  // Need to truncate digest if it is too long: first truncate whole
  // bytes.
  if (8 * digest_len > num_bits) {
    digest_len = (num_bits + 7) / 8;
  }
  if (!BN_bin2bn(digest, digest_len, out)) {
    OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB);
    return 0;
  }

  // If still too long truncate remaining bits with a shift
  if ((8 * digest_len > num_bits) &&
      !BN_rshift(out, out, 8 - (num_bits & 0x7))) {
    OPENSSL_PUT_ERROR(ECDSA, ERR_R_BN_LIB);
    return 0;
  }

  return 1;
}

static int get_key_bignum(BIGNUM *num, int num_bits, uint32_t *key_mod)
{
	BIGNUM *tmp, *big2, *big32, *big2_32;
	BN_CTX *ctx;
	int ret;

	tmp = BN_new();
	big2 = BN_new();
	big32 = BN_new();
	big2_32 = BN_new();
	if (!tmp || !big2 || !big32 || !big2_32) {
		fprintf(stderr, "Out of memory (bignum)\n");
		return -1;
	}
	ctx = BN_CTX_new();
	if (!tmp) {
		fprintf(stderr, "Out of memory (bignum context)\n");
		return -1;
	}
	BN_set_word(big2, 2L);
	BN_set_word(big32, 32L);
	BN_exp(big2_32, big2, big32, ctx); /* B = 2^32 */

	for (ret = 0; ret <= 63; ret++) {
		BN_mod(tmp, num, big2_32, ctx); /* n = N mod B */
		key_mod[ret] = htonl(BN_get_word(tmp));
		BN_rshift(num, num, 32); /*  N = N/B */
	}

	BN_free(tmp);
	BN_free(big2);
	BN_free(big32);
	BN_free(big2_32);

	return 0;
}

int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
                            int do_trial_division, BN_GENCB *cb)
{
    int i, j, ret = -1;
    int k;
    BN_CTX *ctx = NULL;
    BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
    BN_MONT_CTX *mont = NULL;

    if (BN_cmp(a, BN_value_one()) <= 0)
        return 0;

    if (checks == BN_prime_checks)
        checks = BN_prime_checks_for_size(BN_num_bits(a));

    /* first look for small factors */
    if (!BN_is_odd(a))
        /* a is even => a is prime if and only if a == 2 */
        return BN_is_word(a, 2);
    if (do_trial_division) {
        for (i = 1; i < NUMPRIMES; i++) {
            BN_ULONG mod = BN_mod_word(a, primes[i]);
            if (mod == (BN_ULONG)-1)
                goto err;
            if (mod == 0)
                return BN_is_word(a, primes[i]);
        }
        if (!BN_GENCB_call(cb, 1, -1))
            goto err;
    }

    if (ctx_passed != NULL)
        ctx = ctx_passed;
    else if ((ctx = BN_CTX_new()) == NULL)
        goto err;
    BN_CTX_start(ctx);

    A1 = BN_CTX_get(ctx);
    A1_odd = BN_CTX_get(ctx);
    check = BN_CTX_get(ctx);
    if (check == NULL)
        goto err;

    /* compute A1 := a - 1 */
    if (!BN_copy(A1, a))
        goto err;
    if (!BN_sub_word(A1, 1))
        goto err;
    if (BN_is_zero(A1)) {
        ret = 0;
        goto err;
    }

    /* write  A1  as  A1_odd * 2^k */
    k = 1;
    while (!BN_is_bit_set(A1, k))
        k++;
    if (!BN_rshift(A1_odd, A1, k))
        goto err;

    /* Montgomery setup for computations mod a */
    mont = BN_MONT_CTX_new();
    if (mont == NULL)
        goto err;
    if (!BN_MONT_CTX_set(mont, a, ctx))
        goto err;

    for (i = 0; i < checks; i++) {
        if (!BN_priv_rand_range(check, A1))
            goto err;
        if (!BN_add_word(check, 1))
            goto err;
        /* now 1 <= check < a */

        j = witness(check, a, A1, A1_odd, k, ctx, mont);
        if (j == -1)
            goto err;
        if (j) {
            ret = 0;
            goto err;
        }
        if (!BN_GENCB_call(cb, 1, i))
            goto err;
    }
    ret = 1;
 err:
    if (ctx != NULL) {
        BN_CTX_end(ctx);
        if (ctx_passed == NULL)
            BN_CTX_free(ctx);
    }
    BN_MONT_CTX_free(mont);

    return ret;
}

//.........這裏部分代碼省略.........
		n1 = wnump[-1];
		if(n0 == d0)
			{ q = BN_MASK2; }
		else            /* n0 < d0 */
		{
#ifdef BN_LLONG
			BN_ULLONG t2;

#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
			q = (BN_ULONG)(((((BN_ULLONG)n0) << BN_BITS2) | n1) / d0);
#else
			q = bn_div_words(n0, n1, d0);
#endif

#ifndef REMAINDER_IS_ALREADY_CALCULATED
			/*
			 * rem doesn't have to be BN_ULLONG. The least we
			 * know it's less that d0, isn't it?
			 */
			rem = (n1 - q * d0)&BN_MASK2;
#endif
			t2 = (BN_ULLONG)d1 * q;

			for(;;)
			{
				if(t2 <= ((((BN_ULLONG)rem) << BN_BITS2) | wnump[-2]))
					{ break; }
				q--;
				rem += d0;
				if(rem < d0) { break; }  /* don't let rem overflow */
				t2 -= d1;
			}
#else /* !BN_LLONG */
			BN_ULONG t2l, t2h, ql, qh;

			q = bn_div_words(n0, n1, d0);
#ifndef REMAINDER_IS_ALREADY_CALCULATED
			rem = (n1 - q * d0)&BN_MASK2;
#endif

#ifdef BN_UMULT_HIGH
			t2l = d1 * q;
			t2h = BN_UMULT_HIGH(d1, q);
#else
			t2l = LBITS(d1);
			t2h = HBITS(d1);
			ql = LBITS(q);
			qh = HBITS(q);
			mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
#endif

			for(;;)
			{
				if((t2h < rem) ||
						((t2h == rem) && (t2l <= wnump[-2])))
					{ break; }
				q--;
				rem += d0;
				if(rem < d0) { break; }  /* don't let rem overflow */
				if(t2l < d1) { t2h--; }
				t2l -= d1;
			}
#endif /* !BN_LLONG */
		}
#endif /* !BN_DIV3W */

		l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
		wnum.d--;
		wnum.top++;
		tmp->d[div_n] = l0;
		for(j = div_n + 1; j > 0; j--)
			if(tmp->d[j - 1]) { break; }
		tmp->top = j;

		j = wnum.top;
		BN_sub(&wnum, &wnum, tmp);

		snum->top = snum->top + wnum.top - j;

		if(wnum.neg)
		{
			q--;
			j = wnum.top;
			BN_add(&wnum, &wnum, sdiv);
			snum->top += wnum.top - j;
		}
		*(resp--) = q;
		wnump--;
	}
	if(rm != NULL)
	{
		BN_rshift(rm, snum, norm_shift);
		rm->neg = num->neg;
	}
	BN_CTX_end(ctx);
	return (1);
err:
	BN_CTX_end(ctx);
	return (0);
}

/* Returns -2 for errors because both -1 and 0 are valid results. */
int BN_kronecker (const BIGNUM * a, const BIGNUM * b, BN_CTX * ctx)
{
    int i;

    int ret = -2;                /* avoid 'uninitialized' warning */

    int err = 0;

    BIGNUM *A, *B, *tmp;

    /* In 'tab', only odd-indexed entries are relevant:
     * For any odd BIGNUM n,
     *     tab[BN_lsw(n) & 7]
     * is $(-1)^{(n^2-1)/8}$ (using TeX notation).
     * Note that the sign of n does not matter.
     */
    static const int tab[8] = { 0, 1, 0, -1, 0, -1, 0, 1 };

    bn_check_top (a);
    bn_check_top (b);

    BN_CTX_start (ctx);
    A = BN_CTX_get (ctx);
    B = BN_CTX_get (ctx);
    if (B == NULL)
        goto end;

    err = !BN_copy (A, a);
    if (err)
        goto end;
    err = !BN_copy (B, b);
    if (err)
        goto end;

    /*
     * Kronecker symbol, imlemented according to Henri Cohen,
     * "A Course in Computational Algebraic Number Theory"
     * (algorithm 1.4.10).
     */

    /* Cohen's step 1: */

    if (BN_is_zero (B))
    {
        ret = BN_abs_is_word (A, 1);
        goto end;
    }

    /* Cohen's step 2: */

    if (!BN_is_odd (A) && !BN_is_odd (B))
    {
        ret = 0;
        goto end;
    }

    /* now  B  is non-zero */
    i = 0;
    while (!BN_is_bit_set (B, i))
        i++;
    err = !BN_rshift (B, B, i);
    if (err)
        goto end;
    if (i & 1)
    {
        /* i is odd */
        /* (thus  B  was even, thus  A  must be odd!)  */

        /* set 'ret' to $(-1)^{(A^2-1)/8}$ */
        ret = tab[BN_lsw (A) & 7];
    }
    else
    {
        /* i is even */
        ret = 1;
    }

    if (B->neg)
    {
        B->neg = 0;
        if (A->neg)
            ret = -ret;
    }

    /* now  B  is positive and odd, so what remains to be done is
     * to compute the Jacobi symbol  (A/B)  and multiply it by 'ret' */

    while (1)
    {
        /* Cohen's step 3: */

        /*  B  is positive and odd */

        if (BN_is_zero (A))
        {
            ret = BN_is_one (B) ? ret : 0;
            goto end;
        }

//.........這裏部分代碼省略.........

int RSA_generate_key_ex(RSA *rsa, int bits, BIGNUM *e_value, BN_GENCB *cb) {
  // See FIPS 186-4 appendix B.3. This function implements a generalized version
  // of the FIPS algorithm. |RSA_generate_key_fips| performs additional checks
  // for FIPS-compliant key generation.

  // Always generate RSA keys which are a multiple of 128 bits. Round |bits|
  // down as needed.
  bits &= ~127;

  // Reject excessively small keys.
  if (bits < 256) {
    OPENSSL_PUT_ERROR(RSA, RSA_R_KEY_SIZE_TOO_SMALL);
    return 0;
  }

  // Reject excessively large public exponents. Windows CryptoAPI and Go don't
  // support values larger than 32 bits, so match their limits for generating
  // keys. (|check_modulus_and_exponent_sizes| uses a slightly more conservative
  // value, but we don't need to support generating such keys.)
  // https://github.com/golang/go/issues/3161
  // https://msdn.microsoft.com/en-us/library/aa387685(VS.85).aspx
  if (BN_num_bits(e_value) > 32) {
    OPENSSL_PUT_ERROR(RSA, RSA_R_BAD_E_VALUE);
    return 0;
  }

  int ret = 0;
  int prime_bits = bits / 2;
  BN_CTX *ctx = BN_CTX_new();
  if (ctx == NULL) {
    goto bn_err;
  }
  BN_CTX_start(ctx);
  BIGNUM *totient = BN_CTX_get(ctx);
  BIGNUM *pm1 = BN_CTX_get(ctx);
  BIGNUM *qm1 = BN_CTX_get(ctx);
  BIGNUM *sqrt2 = BN_CTX_get(ctx);
  BIGNUM *pow2_prime_bits_100 = BN_CTX_get(ctx);
  BIGNUM *pow2_prime_bits = BN_CTX_get(ctx);
  if (totient == NULL || pm1 == NULL || qm1 == NULL || sqrt2 == NULL ||
      pow2_prime_bits_100 == NULL || pow2_prime_bits == NULL ||
      !BN_set_bit(pow2_prime_bits_100, prime_bits - 100) ||
      !BN_set_bit(pow2_prime_bits, prime_bits)) {
    goto bn_err;
  }

  // We need the RSA components non-NULL.
  if (!ensure_bignum(&rsa->n) ||
      !ensure_bignum(&rsa->d) ||
      !ensure_bignum(&rsa->e) ||
      !ensure_bignum(&rsa->p) ||
      !ensure_bignum(&rsa->q) ||
      !ensure_bignum(&rsa->dmp1) ||
      !ensure_bignum(&rsa->dmq1)) {
    goto bn_err;
  }

  if (!BN_copy(rsa->e, e_value)) {
    goto bn_err;
  }

  // Compute sqrt2 >= ⌊2^(prime_bits-1)×√2⌋.
  if (!bn_set_words(sqrt2, kBoringSSLRSASqrtTwo, kBoringSSLRSASqrtTwoLen)) {
    goto bn_err;
  }
  int sqrt2_bits = kBoringSSLRSASqrtTwoLen * BN_BITS2;
  assert(sqrt2_bits == (int)BN_num_bits(sqrt2));
  if (sqrt2_bits > prime_bits) {
    // For key sizes up to 3072 (prime_bits = 1536), this is exactly
    // ⌊2^(prime_bits-1)×√2⌋.
    if (!BN_rshift(sqrt2, sqrt2, sqrt2_bits - prime_bits)) {
      goto bn_err;
    }
  } else if (prime_bits > sqrt2_bits) {
    // For key sizes beyond 3072, this is approximate. We err towards retrying
    // to ensure our key is the right size and round up.
    if (!BN_add_word(sqrt2, 1) ||
        !BN_lshift(sqrt2, sqrt2, prime_bits - sqrt2_bits)) {
      goto bn_err;
    }
  }
  assert(prime_bits == (int)BN_num_bits(sqrt2));

  do {
    // Generate p and q, each of size |prime_bits|, using the steps outlined in
    // appendix FIPS 186-4 appendix B.3.3.
    if (!generate_prime(rsa->p, prime_bits, rsa->e, NULL, sqrt2,
                        pow2_prime_bits_100, ctx, cb) ||
        !BN_GENCB_call(cb, 3, 0) ||
        !generate_prime(rsa->q, prime_bits, rsa->e, rsa->p, sqrt2,
                        pow2_prime_bits_100, ctx, cb) ||
        !BN_GENCB_call(cb, 3, 1)) {
      goto bn_err;
    }

    if (BN_cmp(rsa->p, rsa->q) < 0) {
      BIGNUM *tmp = rsa->p;
      rsa->p = rsa->q;
      rsa->q = tmp;
    }
//.........這裏部分代碼省略.........

static ECDSA_SIG *ecdsa_do_sign(const unsigned char *dgst, int dgst_len, 
		const BIGNUM *in_kinv, const BIGNUM *in_r, EC_KEY *eckey)
{
	int     ok = 0, i;
	BIGNUM *kinv=NULL, *s, *m=NULL,*tmp=NULL,*order=NULL;
	const BIGNUM *ckinv;
	BN_CTX     *ctx = NULL;
	const EC_GROUP   *group;
	ECDSA_SIG  *ret;
	ECDSA_DATA *ecdsa;
	const BIGNUM *priv_key;

	ecdsa    = ecdsa_check(eckey);
	group    = EC_KEY_get0_group(eckey);
	priv_key = EC_KEY_get0_private_key(eckey);
	
	if (group == NULL || priv_key == NULL || ecdsa == NULL)
	{
		ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_PASSED_NULL_PARAMETER);
		return NULL;
	}

#ifdef OPENSSL_FIPS
	if (!fips_check_ec_prng(eckey))
		return NULL;
#endif

	ret = ECDSA_SIG_new();
	if (!ret)
	{
		ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_MALLOC_FAILURE);
		return NULL;
	}
	s = ret->s;

	if ((ctx = BN_CTX_new()) == NULL || (order = BN_new()) == NULL ||
		(tmp = BN_new()) == NULL || (m = BN_new()) == NULL)
	{
		ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_MALLOC_FAILURE);
		goto err;
	}

	if (!EC_GROUP_get_order(group, order, ctx))
	{
		ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_EC_LIB);
		goto err;
	}
	i = BN_num_bits(order);
	/* Need to truncate digest if it is too long: first truncate whole
	 * bytes.
	 */
	if (8 * dgst_len > i)
		dgst_len = (i + 7)/8;
	if (!BN_bin2bn(dgst, dgst_len, m))
	{
		ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB);
		goto err;
	}
	/* If still too long truncate remaining bits with a shift */
	if ((8 * dgst_len > i) && !BN_rshift(m, m, 8 - (i & 0x7)))
	{
		ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB);
		goto err;
	}
	do
	{
		if (in_kinv == NULL || in_r == NULL)
		{
			if (!ecdsa->meth->ecdsa_sign_setup(eckey, ctx,
								&kinv, &ret->r))
			{
				ECDSAerr(ECDSA_F_ECDSA_DO_SIGN,ERR_R_ECDSA_LIB);
				goto err;
			}
			ckinv = kinv;
		}
		else
		{
			ckinv  = in_kinv;
			if (BN_copy(ret->r, in_r) == NULL)
			{
				ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_MALLOC_FAILURE);
				goto err;
			}
		}

		if (!BN_mod_mul(tmp, priv_key, ret->r, order, ctx))
		{
			ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB);
			goto err;
		}
		if (!BN_mod_add_quick(s, tmp, m, order))
		{
			ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB);
			goto err;
		}
		if (!BN_mod_mul(s, s, ckinv, order, ctx))
		{
			ECDSAerr(ECDSA_F_ECDSA_DO_SIGN, ERR_R_BN_LIB);
			goto err;
//.........這裏部分代碼省略.........

//.........這裏部分代碼省略.........
			/*
			 * rem doesn't have to be BN_ULLONG. The least we
			 * know it's less that d0, isn't it?
			 */
			rem=(n1-q*d0)&BN_MASK2;
#endif
			t2=(BN_ULLONG)d1*q;

			for (;;)
				{
				if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
					break;
				q--;
				rem += d0;
				if (rem < d0) break; /* don't let rem overflow */
				t2 -= d1;
				}
#else /* !BN_LLONG */
			BN_ULONG t2l,t2h;

			q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
			TINYCLR_SSL_FPRINTF(OPENSSL_TYPE__FILE_STDERR,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
				n0, n1, d0, q);
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
			rem=(n1-q*d0)&BN_MASK2;
#endif

#if defined(BN_UMULT_LOHI)
			BN_UMULT_LOHI(t2l,t2h,d1,q);
#elif defined(BN_UMULT_HIGH)
			t2l = d1 * q;
			t2h = BN_UMULT_HIGH(d1,q);
#else
			{
			BN_ULONG ql, qh;
			t2l=LBITS(d1); t2h=HBITS(d1);
			ql =LBITS(q);  qh =HBITS(q);
			mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
			}
#endif

			for (;;)
				{
				if ((t2h < rem) ||
					((t2h == rem) && (t2l <= wnump[-2])))
					break;
				q--;
				rem += d0;
				if (rem < d0) break; /* don't let rem overflow */
				if (t2l < d1) t2h--; t2l -= d1;
				}
#endif /* !BN_LLONG */
			}
#endif /* !BN_DIV3W */

		l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
		tmp->d[div_n]=l0;
		wnum.d--;
		/* ingore top values of the bignums just sub the two 
		 * BN_ULONG arrays with bn_sub_words */
		if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
			{
			/* Note: As we have considered only the leading
			 * two BN_ULONGs in the calculation of q, sdiv * q
			 * might be greater than wnum (but then (q-1) * sdiv
			 * is less or equal than wnum)
			 */
			q--;
			if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
				/* we can't have an overflow here (assuming
				 * that q != 0, but if q == 0 then tmp is
				 * zero anyway) */
				(*wnump)++;
			}
		/* store part of the result */
		*resp = q;
		}
	bn_correct_top(snum);
	if (rm != NULL)
		{
		/* Keep a copy of the neg flag in num because if rm==num
		 * BN_rshift() will overwrite it.
		 */
		int neg = num->neg;
		BN_rshift(rm,snum,norm_shift);
		if (!BN_is_zero(rm))
			rm->neg = neg;
		bn_check_top(rm);
		}
	bn_correct_top(res);
	BN_CTX_end(ctx);
	return(1);
err:
	bn_check_top(rm);
	BN_CTX_end(ctx);
	return(0);
	}

BIGNUM *BN_mod_inverse(BIGNUM *in,
	const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
	{
	BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;
	BIGNUM *ret=NULL;
	int sign;

	if ((BN_get_flags(a, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(n, BN_FLG_CONSTTIME) != 0))
		{
		return BN_mod_inverse_no_branch(in, a, n, ctx);
		}

	bn_check_top(a);
	bn_check_top(n);

	BN_CTX_start(ctx);
	A = BN_CTX_get(ctx);
	B = BN_CTX_get(ctx);
	X = BN_CTX_get(ctx);
	D = BN_CTX_get(ctx);
	M = BN_CTX_get(ctx);
	Y = BN_CTX_get(ctx);
	T = BN_CTX_get(ctx);
	if (T == NULL) goto err;

	if (in == NULL)
		R=BN_new();
	else
		R=in;
	if (R == NULL) goto err;

	BN_one(X);
	BN_zero(Y);
	if (BN_copy(B,a) == NULL) goto err;
	if (BN_copy(A,n) == NULL) goto err;
	A->neg = 0;
	if (B->neg || (BN_ucmp(B, A) >= 0))
		{
		if (!BN_nnmod(B, B, A, ctx)) goto err;
		}
	sign = -1;
	/* From  B = a mod |n|,  A = |n|  it follows that
	 *
	 *      0 <= B < A,
	 *     -sign*X*a  ==  B   (mod |n|),
	 *      sign*Y*a  ==  A   (mod |n|).
	 */

	if (BN_is_odd(n) && (BN_num_bits(n) <= (BN_BITS <= 32 ? 450 : 2048)))
		{
		/* Binary inversion algorithm; requires odd modulus.
		 * This is faster than the general algorithm if the modulus
		 * is sufficiently small (about 400 .. 500 bits on 32-bit
		 * sytems, but much more on 64-bit systems) */
		int shift;
		
		while (!BN_is_zero(B))
			{
			/*
			 *      0 < B < |n|,
			 *      0 < A <= |n|,
			 * (1) -sign*X*a  ==  B   (mod |n|),
			 * (2)  sign*Y*a  ==  A   (mod |n|)
			 */

			/* Now divide  B  by the maximum possible power of two in the integers,
			 * and divide  X  by the same value mod |n|.
			 * When we're done, (1) still holds. */
			shift = 0;
			while (!BN_is_bit_set(B, shift)) /* note that 0 < B */
				{
				shift++;
				
				if (BN_is_odd(X))
					{
					if (!BN_uadd(X, X, n)) goto err;
					}
				/* now X is even, so we can easily divide it by two */
				if (!BN_rshift1(X, X)) goto err;
				}
			if (shift > 0)
				{
				if (!BN_rshift(B, B, shift)) goto err;
				}


			/* Same for  A  and  Y.  Afterwards, (2) still holds. */
			shift = 0;
			while (!BN_is_bit_set(A, shift)) /* note that 0 < A */
				{
				shift++;
				
				if (BN_is_odd(Y))
					{
					if (!BN_uadd(Y, Y, n)) goto err;
					}
				/* now Y is even */
				if (!BN_rshift1(Y, Y)) goto err;
				}
			if (shift > 0)
//.........這裏部分代碼省略.........

//.........這裏部分代碼省略.........
	ret->neg=r->neg;

	rp=ret->d;
	ap=&(r->d[ri]);

	{
	size_t m1,m2;

	v=bn_sub_words(rp,ap,np,ri);
	/* this ----------------^^ works even in al<ri case
	 * thanks to zealous zeroing of top of the vector in the
	 * beginning. */

	/* if (al==ri && !v) || al>ri) nrp=rp; else nrp=ap; */
	/* in other words if subtraction result is real, then
	 * trick unconditional memcpy below to perform in-place
	 * "refresh" instead of actual copy. */
	m1=0-(size_t)(((al-ri)>>(sizeof(al)*8-1))&1);	/* al<ri */
	m2=0-(size_t)(((ri-al)>>(sizeof(al)*8-1))&1);	/* al>ri */
	m1|=m2;			/* (al!=ri) */
	m1|=(0-(size_t)v);	/* (al!=ri || v) */
	m1&=~m2;		/* (al!=ri || v) && !al>ri */
	nrp=(BN_ULONG *)(((size_t)rp&~m1)|((size_t)ap&m1));
	}

	/* 'i<ri' is chosen to eliminate dependency on input data, even
	 * though it results in redundant copy in al<ri case. */
	for (i=0,ri-=4; i<ri; i+=4)
		{
		BN_ULONG t1,t2,t3,t4;
		
		t1=nrp[i+0];
		t2=nrp[i+1];
		t3=nrp[i+2];	ap[i+0]=0;
		t4=nrp[i+3];	ap[i+1]=0;
		rp[i+0]=t1;	ap[i+2]=0;
		rp[i+1]=t2;	ap[i+3]=0;
		rp[i+2]=t3;
		rp[i+3]=t4;
		}
	for (ri+=4; i<ri; i++)
		rp[i]=nrp[i], ap[i]=0;
	bn_correct_top(r);
	bn_correct_top(ret);
# else
	if (bn_wexpand(ret,al) == NULL) goto err;
	ret->top=al;
	ret->neg=r->neg;

	rp=ret->d;
	ap=&(r->d[ri]);
	al-=4;
	for (i=0; i<al; i+=4)
		{
		BN_ULONG t1,t2,t3,t4;
		
		t1=ap[i+0];
		t2=ap[i+1];
		t3=ap[i+2];
		t4=ap[i+3];
		rp[i+0]=t1;
		rp[i+1]=t2;
		rp[i+2]=t3;
		rp[i+3]=t4;
		}
	al+=4;
	for (; i<al; i++)
		rp[i]=ap[i];
# endif
#else /* !MONT_WORD */ 
	BIGNUM *t1,*t2;

	BN_CTX_start(ctx);
	t1 = BN_CTX_get(ctx);
	t2 = BN_CTX_get(ctx);
	if (t1 == NULL || t2 == NULL) goto err;
	
	if (!BN_copy(t1,a)) goto err;
	BN_mask_bits(t1,mont->ri);

	if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
	BN_mask_bits(t2,mont->ri);

	if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
	if (!BN_add(t2,a,t1)) goto err;
	if (!BN_rshift(ret,t2,mont->ri)) goto err;
#endif /* MONT_WORD */

#if !defined(BRANCH_FREE) || BRANCH_FREE==0
	if (BN_ucmp(ret, &(mont->N)) >= 0)
		{
		if (!BN_usub(ret,ret,&(mont->N))) goto err;
		}
#endif
	retn=1;
	bn_check_top(ret);
 err:
	BN_CTX_end(ctx);
	return(retn);
	}

int BN_is_prime_fasttest(const BIGNUM *a, int checks,
		void (*callback)(int,int,void *),
		BN_CTX *ctx_passed, void *cb_arg,
		int do_trial_division)
	{
	int i, j, ret = -1;
	int k;
	BN_CTX *ctx = NULL;
	BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
	BN_MONT_CTX *mont = NULL;
	const BIGNUM *A = NULL;

	if (BN_cmp(a, BN_value_one()) <= 0)
		return 0;
	
	if (checks == BN_prime_checks)
		checks = BN_prime_checks_for_size(BN_num_bits(a));

	/* first look for small factors */
	if (!BN_is_odd(a))
		return 0;
	if (do_trial_division)
		{
		for (i = 1; i < NUMPRIMES; i++)
			if (BN_mod_word(a, primes[i]) == 0) 
				return 0;
		if (callback != NULL) callback(1, -1, cb_arg);
		}

	if (ctx_passed != NULL)
		ctx = ctx_passed;
	else
		if ((ctx=BN_CTX_new()) == NULL)
			goto err;
	BN_CTX_start(ctx);

	/* A := abs(a) */
	if (a->neg)
		{
		BIGNUM *t;
		if ((t = BN_CTX_get(ctx)) == NULL) goto err;
		BN_copy(t, a);
		t->neg = 0;
		A = t;
		}
	else
		A = a;
	A1 = BN_CTX_get(ctx);
	A1_odd = BN_CTX_get(ctx);
	check = BN_CTX_get(ctx);
	if (check == NULL) goto err;

	/* compute A1 := A - 1 */
	if (!BN_copy(A1, A))
		goto err;
	if (!BN_sub_word(A1, 1))
		goto err;
	if (BN_is_zero(A1))
		{
		ret = 0;
		goto err;
		}

	/* write  A1  as  A1_odd * 2^k */
	k = 1;
	while (!BN_is_bit_set(A1, k))
		k++;
	if (!BN_rshift(A1_odd, A1, k))
		goto err;

	/* Montgomery setup for computations mod A */
	mont = BN_MONT_CTX_new();
	if (mont == NULL)
		goto err;
	if (!BN_MONT_CTX_set(mont, A, ctx))
		goto err;
	
	for (i = 0; i < checks; i++)
		{
		if (!BN_pseudo_rand_range(check, A1))
			goto err;
		if (!BN_add_word(check, 1))
			goto err;
		/* now 1 <= check < A */

		j = witness(check, A, A1, A1_odd, k, ctx, mont);
		if (j == -1) goto err;
		if (j)
			{
			ret=0;
			goto err;
			}
		if (callback != NULL) callback(1,i,cb_arg);
		}
	ret=1;
err:
	if (ctx != NULL)
		{
		BN_CTX_end(ctx);
		if (ctx_passed == NULL)
//.........這裏部分代碼省略.........