/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)

 * All rights reserved.

 *

 * This package is an SSL implementation written

 * by Eric Young (eay@cryptsoft.com).

 * The implementation was written so as to conform with Netscapes SSL.

 *

 * This library is free for commercial and non-commercial use as long as

 * the following conditions are aheared to.  The following conditions

 * apply to all code found in this distribution, be it the RC4, RSA,

 * lhash, DES, etc., code; not just the SSL code.  The SSL documentation

 * included with this distribution is covered by the same copyright terms

 * except that the holder is Tim Hudson (tjh@cryptsoft.com).

 *

 * Copyright remains Eric Young's, and as such any Copyright notices in

 * the code are not to be removed.

 * If this package is used in a product, Eric Young should be given attribution

 * as the author of the parts of the library used.

 * This can be in the form of a textual message at program startup or

 * in documentation (online or textual) provided with the package.

 *

 * Redistribution and use in source and binary forms, with or without

 * modification, are permitted provided that the following conditions

 * are met:

 * 1. Redistributions of source code must retain the copyright

 *    notice, this list of conditions and the following disclaimer.

 * 2. Redistributions in binary form must reproduce the above copyright

 *    notice, this list of conditions and the following disclaimer in the

 *    documentation and/or other materials provided with the distribution.

 * 3. All advertising materials mentioning features or use of this software

 *    must display the following acknowledgement:

 *    "This product includes cryptographic software written by

 *     Eric Young (eay@cryptsoft.com)"

 *    The word 'cryptographic' can be left out if the rouines from the library

 *    being used are not cryptographic related :-).

 * 4. If you include any Windows specific code (or a derivative thereof) from

 *    the apps directory (application code) you must include an acknowledgement:

 *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"

 *

 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND

 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE

 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE

 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE

 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL

 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS

 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)

 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT

 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY

 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF

 * SUCH DAMAGE.

 *

 * The licence and distribution terms for any publically available version or

 * derivative of this code cannot be changed.  i.e. this code cannot simply be

 * copied and put under another distribution licence

 * [including the GNU Public Licence.]

 */

/* ====================================================================

 * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.

 *

 * Redistribution and use in source and binary forms, with or without

 * modification, are permitted provided that the following conditions

 * are met:

 *

 * 1. Redistributions of source code must retain the above copyright

 *    notice, this list of conditions and the following disclaimer.

 *

 * 2. Redistributions in binary form must reproduce the above copyright

 *    notice, this list of conditions and the following disclaimer in

 *    the documentation and/or other materials provided with the

 *    distribution.

 *

 * 3. All advertising materials mentioning features or use of this

 *    software must display the following acknowledgment:

 *    "This product includes software developed by the OpenSSL Project

 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"

 *

 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to

 *    endorse or promote products derived from this software without

 *    prior written permission. For written permission, please contact

 *    openssl-core@openssl.org.

 *

 * 5. Products derived from this software may not be called "OpenSSL"

 *    nor may "OpenSSL" appear in their names without prior written

 *    permission of the OpenSSL Project.

 *

 * 6. Redistributions of any form whatsoever must retain the following

 *    acknowledgment:

 *    "This product includes software developed by the OpenSSL Project

 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"

 *

 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY

 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE

 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR

 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR

 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,

 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT

 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;

 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)

 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,

 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)

 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED

 * OF THE POSSIBILITY OF SUCH DAMAGE.

 * ====================================================================

 *

 * This product includes cryptographic software written by Eric Young

 * (eay@cryptsoft.com).  This product includes software written by Tim

 * Hudson (tjh@cryptsoft.com). */

#include <openssl/bn.h>

#include <openssl/err.h>

#include "internal.h"

int BN_mod_inverse_odd(BIGNUM *out, int *out_no_inverse, const BIGNUM *a,

                       const BIGNUM *n, BN_CTX *ctx) {

  *out_no_inverse = 0;

  if (!BN_is_odd(n)) {

    OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);

    return 0;

  }

  if (BN_is_negative(a) || BN_cmp(a, n) >= 0) {

    OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED);

    return 0;

  }

  BIGNUM *A, *B, *X, *Y;

  int ret = 0;

  int sign;

  BN_CTX_start(ctx);

  A = BN_CTX_get(ctx);

  B = BN_CTX_get(ctx);

  X = BN_CTX_get(ctx);

  Y = BN_CTX_get(ctx);

  if (Y == NULL) {

    goto err;

  }

  BIGNUM *R = out;

  BN_zero(Y);

  if (!BN_one(X) || BN_copy(B, a) == NULL || BN_copy(A, n) == NULL) {

    goto err;

  }

  A->neg = 0;

  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|).

  // 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 systems, but much more on 64-bit systems)

  int shift;

  while (!BN_is_zero(B)) {

    //      0 < B < |n|,

    //      0 < A <= |n|,

    // (1) -sign*X*a  ==  B   (mod |n|),

    // (2)  sign*Y*a  ==  A   (mod |n|)

    // Now divide  B  by the maximum possible power of two in the integers,

    // and divide  X  by the same value mod |n|.

    // When we're done, (1) still holds.

    shift = 0;

    while (!BN_is_bit_set(B, shift)) {

      // note that 0 < B

      shift++;

      if (BN_is_odd(X)) {

        if (!BN_uadd(X, X, n)) {

          goto err;

        }

      }

      // now X is even, so we can easily divide it by two

      if (!BN_rshift1(X, X)) {

        goto err;

      }

    }

    if (shift > 0) {

      if (!BN_rshift(B, B, shift)) {

        goto err;

      }

    }

    // Same for A and Y. Afterwards, (2) still holds.

    shift = 0;

    while (!BN_is_bit_set(A, shift)) {

      // note that 0 < A

      shift++;

      if (BN_is_odd(Y)) {

        if (!BN_uadd(Y, Y, n)) {

          goto err;

        }

      }

      // now Y is even

      if (!BN_rshift1(Y, Y)) {

        goto err;

      }

    }

    if (shift > 0) {

      if (!BN_rshift(A, A, shift)) {

        goto err;

      }

    }

    // We still have (1) and (2).

    // Both  A  and  B  are odd.

    // The following computations ensure that

    //

    //     0 <= B < |n|,

    //      0 < A < |n|,

    // (1) -sign*X*a  ==  B   (mod |n|),

    // (2)  sign*Y*a  ==  A   (mod |n|),

    //

    // and that either  A  or  B  is even in the next iteration.

    if (BN_ucmp(B, A) >= 0) {

      // -sign*(X + Y)*a == B - A  (mod |n|)

      if (!BN_uadd(X, X, Y)) {

        goto err;

      }

      // NB: we could use BN_mod_add_quick(X, X, Y, n), but that

      // actually makes the algorithm slower

      if (!BN_usub(B, B, A)) {

        goto err;

      }

    } else {

      //  sign*(X + Y)*a == A - B  (mod |n|)

      if (!BN_uadd(Y, Y, X)) {

        goto err;

      }

      // as above, BN_mod_add_quick(Y, Y, X, n) would slow things down

      if (!BN_usub(A, A, B)) {

        goto err;

      }

    }

  }

  if (!BN_is_one(A)) {

    *out_no_inverse = 1;

    OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);

    goto err;

  }

  // The while loop (Euclid's algorithm) ends when

  //      A == gcd(a,n);

  // we have

  //       sign*Y*a  ==  A  (mod |n|),

  // where  Y  is non-negative.

  if (sign < 0) {

    if (!BN_sub(Y, n, Y)) {

      goto err;

    }

  }

  // Now  Y*a  ==  A  (mod |n|).

  // Y*a == 1  (mod |n|)

  if (Y->neg || BN_ucmp(Y, n) >= 0) {

    if (!BN_nnmod(Y, Y, n, ctx)) {

      goto err;

    }

  }

  if (!BN_copy(R, Y)) {

    goto err;

  }

  ret = 1;

err:

  BN_CTX_end(ctx);

  return ret;

}

BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a, const BIGNUM *n,

                       BN_CTX *ctx) {

  BIGNUM *new_out = NULL;

  if (out == NULL) {

    new_out = BN_new();

    if (new_out == NULL) {

      return NULL;

    }

    out = new_out;

  }

  int ok = 0;

  BIGNUM *a_reduced = NULL;

  if (a->neg || BN_ucmp(a, n) >= 0) {

    a_reduced = BN_dup(a);

    if (a_reduced == NULL) {

      goto err;

    }

    if (!BN_nnmod(a_reduced, a_reduced, n, ctx)) {

      goto err;

    }

    a = a_reduced;

  }

  int no_inverse;

  if (!BN_is_odd(n)) {

    if (!bn_mod_inverse_consttime(out, &no_inverse, a, n, ctx)) {

      goto err;

    }

  } else if (!BN_mod_inverse_odd(out, &no_inverse, a, n, ctx)) {

    goto err;

  }

  ok = 1;

err:

  if (!ok) {

    BN_free(new_out);

    out = NULL;

  }

  BN_free(a_reduced);

  return out;

}

int BN_mod_inverse_blinded(BIGNUM *out, int *out_no_inverse, const BIGNUM *a,

                           const BN_MONT_CTX *mont, BN_CTX *ctx) {

  *out_no_inverse = 0;

  // |a| is secret, but it is required to be in range, so these comparisons may

  // be leaked.

  if (BN_is_negative(a) ||

      constant_time_declassify_int(BN_cmp(a, &mont->N) >= 0)) {

    OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED);

    return 0;

  }

  int ret = 0;

  BIGNUM blinding_factor;

  BN_init(&blinding_factor);

  // |BN_mod_inverse_odd| is leaky, so generate a secret blinding factor and

  // blind |a|. This works because (ar)^-1 * r = a^-1, supposing r is

  // invertible. If r is not invertible, this function will fail. However, we

  // only use this in RSA, where stumbling on an uninvertible element means

  // stumbling on the key's factorization. That is, if this function fails, the

  // RSA key was not actually a product of two large primes.

  //

  // TODO(crbug.com/boringssl/677): When the PRNG output is marked secret by

  // default, the explicit |bn_secret| call can be removed.

  if (!BN_rand_range_ex(&blinding_factor, 1, &mont->N)) {

    goto err;

  }

  bn_secret(&blinding_factor);

  if (!BN_mod_mul_montgomery(out, &blinding_factor, a, mont, ctx)) {

    goto err;

  }

  // Once blinded, |out| is no longer secret, so it may be passed to a leaky

  // mod inverse function. Note |blinding_factor| is secret, so |out| will be

  // secret again after multiplying.

  bn_declassify(out);

  if (!BN_mod_inverse_odd(out, out_no_inverse, out, &mont->N, ctx) ||

      !BN_mod_mul_montgomery(out, &blinding_factor, out, mont, ctx)) {

    goto err;

  }

  ret = 1;

err:

  BN_free(&blinding_factor);

  return ret;

}

int bn_mod_inverse_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,

                         BN_CTX *ctx, const BN_MONT_CTX *mont_p) {

  BN_CTX_start(ctx);

  BIGNUM *p_minus_2 = BN_CTX_get(ctx);

  int ok = p_minus_2 != NULL &&

           BN_copy(p_minus_2, p) &&

           BN_sub_word(p_minus_2, 2) &&

           BN_mod_exp_mont(out, a, p_minus_2, p, ctx, mont_p);

  BN_CTX_end(ctx);

  return ok;

}

int bn_mod_inverse_secret_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,

                                BN_CTX *ctx, const BN_MONT_CTX *mont_p) {

  BN_CTX_start(ctx);

  BIGNUM *p_minus_2 = BN_CTX_get(ctx);

  int ok = p_minus_2 != NULL &&

           BN_copy(p_minus_2, p) &&

           BN_sub_word(p_minus_2, 2) &&

           BN_mod_exp_mont_consttime(out, a, p_minus_2, p, ctx, mont_p);

  BN_CTX_end(ctx);

  return ok;

}