/src/boringssl/crypto/fipsmodule/bn/gcd.cc.inc

Source
// Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

#include <openssl/bn.h>

#include <openssl/err.h>

#include "internal.h"


using namespace bssl;

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;
  }

  int sign;
  BN_CTXScope scope(ctx);
  BIGNUM *A = BN_CTX_get(ctx);
  BIGNUM *B = BN_CTX_get(ctx);
  BIGNUM *X = BN_CTX_get(ctx);
  BIGNUM *Y = BN_CTX_get(ctx);
  BIGNUM *R = out;
  if (Y == nullptr) {
    return 0;
  }

  BN_zero(Y);
  if (!BN_one(X) || BN_copy(B, a) == nullptr || BN_copy(A, n) == nullptr) {
    return 0;
  }
  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)) {
          return 0;
        }
      }
      // now X is even, so we can easily divide it by two
      if (!BN_rshift1(X, X)) {
        return 0;
      }
    }
    if (shift > 0) {
      if (!BN_rshift(B, B, shift)) {
        return 0;
      }
    }

    // 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)) {
          return 0;
        }
      }
      // now Y is even
      if (!BN_rshift1(Y, Y)) {
        return 0;
      }
    }
    if (shift > 0) {
      if (!BN_rshift(A, A, shift)) {
        return 0;
      }
    }

    // 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)) {
        return 0;
      }
      // 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)) {
        return 0;
      }
    } else {
      //  sign*(X + Y)*a == A - B  (mod |n|)
      if (!BN_uadd(Y, Y, X)) {
        return 0;
      }
      // as above, BN_mod_add_quick(Y, Y, X, n) would slow things down
      if (!BN_usub(A, A, B)) {
        return 0;
      }
    }
  }

  if (!BN_is_one(A)) {
    *out_no_inverse = 1;
    OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
    return 0;
  }

  // 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)) {
      return 0;
    }
  }
  // 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)) {
      return 0;
    }
  }
  if (!BN_copy(R, Y)) {
    return 0;
  }

  return 1;
}

BIGNUM *BN_mod_inverse(BIGNUM *out, const BIGNUM *a, const BIGNUM *n,
                       BN_CTX *ctx) {
  UniquePtr<BIGNUM> new_out;
  if (out == nullptr) {
    new_out.reset(BN_new());
    if (new_out == nullptr) {
      return nullptr;
    }
    out = new_out.get();
  }

  UniquePtr<BIGNUM> a_reduced;
  if (a->neg || BN_ucmp(a, n) >= 0) {
    a_reduced.reset(BN_dup(a));
    if (a_reduced == nullptr) {
      return nullptr;
    }
    if (!BN_nnmod(a_reduced.get(), a_reduced.get(), n, ctx)) {
      return nullptr;
    }
    a = a_reduced.get();
  }

  int no_inverse;
  if (!BN_is_odd(n)) {
    if (!bn_mod_inverse_consttime(out, &no_inverse, a, n, ctx)) {
      return nullptr;
    }
  } else if (!BN_mod_inverse_odd(out, &no_inverse, a, n, ctx)) {
    return nullptr;
  }

  new_out.release();  // Passed to the caller via |out|.
  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;
  }

  UniquePtr<BIGNUM> blinding_factor(BN_new());
  if (blinding_factor == nullptr) {
    return 0;
  }

  // |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.get(), 1, &mont->N)) {
    return 0;
  }
  bn_secret(blinding_factor.get());
  if (!BN_mod_mul_montgomery(out, blinding_factor.get(), a, mont, ctx)) {
    return 0;
  }

  // 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.get(), out, mont, ctx)) {
    return 0;
  }

  return 1;
}

int bssl::bn_mod_inverse_prime(BIGNUM *out, const BIGNUM *a, const BIGNUM *p,
                               BN_CTX *ctx, const BN_MONT_CTX *mont_p) {
  BN_CTXScope scope(ctx);
  BIGNUM *p_minus_2 = BN_CTX_get(ctx);
  return p_minus_2 != nullptr && 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);
}

int bssl::bn_mod_inverse_secret_prime(BIGNUM *out, const BIGNUM *a,
                                      const BIGNUM *p, BN_CTX *ctx,
                                      const BN_MONT_CTX *mont_p) {
  BN_CTXScope scope(ctx);
  BIGNUM *p_minus_2 = BN_CTX_get(ctx);
  return p_minus_2 != nullptr && 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);
}

Coverage Report

Created: 2026-04-30 06:12

Line	Count	Source
1		// Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
2		//
3		// Licensed under the Apache License, Version 2.0 (the "License");
4		// you may not use this file except in compliance with the License.
5		// You may obtain a copy of the License at
6		//
7		// https://www.apache.org/licenses/LICENSE-2.0
8		//
9		// Unless required by applicable law or agreed to in writing, software
10		// distributed under the License is distributed on an "AS IS" BASIS,
11		// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12		// See the License for the specific language governing permissions and
13		// limitations under the License.
14
15		#include <openssl/bn.h>
16
17		#include <openssl/err.h>
18
19		#include "internal.h"
20
21
22		using namespace bssl;
23
24		int BN_mod_inverse_odd(BIGNUM out, int out_no_inverse, const BIGNUM *a,
25	0	const BIGNUM n, BN_CTX ctx) {
26	0	*out_no_inverse = 0;
27
28	0	if (!BN_is_odd(n)) {
29	0	OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
30	0	return 0;
31	0	}
32
33	0	if (BN_is_negative(a) \|\| BN_cmp(a, n) >= 0) {
34	0	OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED);
35	0	return 0;
36	0	}
37
38	0	int sign;
39	0	BN_CTXScope scope(ctx);
40	0	BIGNUM *A = BN_CTX_get(ctx);
41	0	BIGNUM *B = BN_CTX_get(ctx);
42	0	BIGNUM *X = BN_CTX_get(ctx);
43	0	BIGNUM *Y = BN_CTX_get(ctx);
44	0	BIGNUM *R = out;
45	0	if (Y == nullptr) {
46	0	return 0;
47	0	}
48
49	0	BN_zero(Y);
50	0	if (!BN_one(X) \|\| BN_copy(B, a) == nullptr \|\| BN_copy(A, n) == nullptr) {
51	0	return 0;
52	0	}
53	0	A->neg = 0;
54	0	sign = -1;
55		// From B = a mod \|n\|, A = \|n\| it follows that
56		//
57		// 0 <= B < A,
58		// -signXa == B (mod \|n\|),
59		// signYa == A (mod \|n\|).
60
61		// Binary inversion algorithm; requires odd modulus. This is faster than the
62		// general algorithm if the modulus is sufficiently small (about 400 .. 500
63		// bits on 32-bit systems, but much more on 64-bit systems)
64	0	int shift;
65
66	0	while (!BN_is_zero(B)) {
67		// 0 < B < \|n\|,
68		// 0 < A <= \|n\|,
69		// (1) -signXa == B (mod \|n\|),
70		// (2) signYa == A (mod \|n\|)
71
72		// Now divide B by the maximum possible power of two in the integers,
73		// and divide X by the same value mod \|n\|.
74		// When we're done, (1) still holds.
75	0	shift = 0;
76	0	while (!BN_is_bit_set(B, shift)) {
77		// note that 0 < B
78	0	shift++;
79
80	0	if (BN_is_odd(X)) {
81	0	if (!BN_uadd(X, X, n)) {
82	0	return 0;
83	0	}
84	0	}
85		// now X is even, so we can easily divide it by two
86	0	if (!BN_rshift1(X, X)) {
87	0	return 0;
88	0	}
89	0	}
90	0	if (shift > 0) {
91	0	if (!BN_rshift(B, B, shift)) {
92	0	return 0;
93	0	}
94	0	}
95
96		// Same for A and Y. Afterwards, (2) still holds.
97	0	shift = 0;
98	0	while (!BN_is_bit_set(A, shift)) {
99		// note that 0 < A
100	0	shift++;
101
102	0	if (BN_is_odd(Y)) {
103	0	if (!BN_uadd(Y, Y, n)) {
104	0	return 0;
105	0	}
106	0	}
107		// now Y is even
108	0	if (!BN_rshift1(Y, Y)) {
109	0	return 0;
110	0	}
111	0	}
112	0	if (shift > 0) {
113	0	if (!BN_rshift(A, A, shift)) {
114	0	return 0;
115	0	}
116	0	}
117
118		// We still have (1) and (2).
119		// Both A and B are odd.
120		// The following computations ensure that
121		//
122		// 0 <= B < \|n\|,
123		// 0 < A < \|n\|,
124		// (1) -signXa == B (mod \|n\|),
125		// (2) signYa == A (mod \|n\|),
126		//
127		// and that either A or B is even in the next iteration.
128	0	if (BN_ucmp(B, A) >= 0) {
129		// -sign(X + Y)a == B - A (mod \|n\|)
130	0	if (!BN_uadd(X, X, Y)) {
131	0	return 0;
132	0	}
133		// NB: we could use BN_mod_add_quick(X, X, Y, n), but that
134		// actually makes the algorithm slower
135	0	if (!BN_usub(B, B, A)) {
136	0	return 0;
137	0	}
138	0	} else {
139		// sign(X + Y)a == A - B (mod \|n\|)
140	0	if (!BN_uadd(Y, Y, X)) {
141	0	return 0;
142	0	}
143		// as above, BN_mod_add_quick(Y, Y, X, n) would slow things down
144	0	if (!BN_usub(A, A, B)) {
145	0	return 0;
146	0	}
147	0	}
148	0	}
149
150	0	if (!BN_is_one(A)) {
151	0	*out_no_inverse = 1;
152	0	OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
153	0	return 0;
154	0	}
155
156		// The while loop (Euclid's algorithm) ends when
157		// A == gcd(a,n);
158		// we have
159		// signYa == A (mod \|n\|),
160		// where Y is non-negative.
161
162	0	if (sign < 0) {
163	0	if (!BN_sub(Y, n, Y)) {
164	0	return 0;
165	0	}
166	0	}
167		// Now Y*a == A (mod \|n\|).
168
169		// Y*a == 1 (mod \|n\|)
170	0	if (Y->neg \|\| BN_ucmp(Y, n) >= 0) {
171	0	if (!BN_nnmod(Y, Y, n, ctx)) {
172	0	return 0;
173	0	}
174	0	}
175	0	if (!BN_copy(R, Y)) {
176	0	return 0;
177	0	}
178
179	0	return 1;
180	0	}
181
182		BIGNUM BN_mod_inverse(BIGNUM out, const BIGNUM a, const BIGNUM n,
183	0	BN_CTX *ctx) {
184	0	UniquePtr<BIGNUM> new_out;
185	0	if (out == nullptr) {
186	0	new_out.reset(BN_new());
187	0	if (new_out == nullptr) {
188	0	return nullptr;
189	0	}
190	0	out = new_out.get();
191	0	}
192
193	0	UniquePtr<BIGNUM> a_reduced;
194	0	if (a->neg \|\| BN_ucmp(a, n) >= 0) {
195	0	a_reduced.reset(BN_dup(a));
196	0	if (a_reduced == nullptr) {
197	0	return nullptr;
198	0	}
199	0	if (!BN_nnmod(a_reduced.get(), a_reduced.get(), n, ctx)) {
200	0	return nullptr;
201	0	}
202	0	a = a_reduced.get();
203	0	}
204
205	0	int no_inverse;
206	0	if (!BN_is_odd(n)) {
207	0	if (!bn_mod_inverse_consttime(out, &no_inverse, a, n, ctx)) {
208	0	return nullptr;
209	0	}
210	0	} else if (!BN_mod_inverse_odd(out, &no_inverse, a, n, ctx)) {
211	0	return nullptr;
212	0	}
213
214	0	new_out.release(); // Passed to the caller via \|out\|.
215	0	return out;
216	0	}
217
218		int BN_mod_inverse_blinded(BIGNUM out, int out_no_inverse, const BIGNUM *a,
219	0	const BN_MONT_CTX mont, BN_CTX ctx) {
220	0	*out_no_inverse = 0;
221
222		// \|a\| is secret, but it is required to be in range, so these comparisons may
223		// be leaked.
224	0	if (BN_is_negative(a) \|\|
225	0	constant_time_declassify_int(BN_cmp(a, &mont->N) >= 0)) {
226	0	OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED);
227	0	return 0;
228	0	}
229
230	0	UniquePtr<BIGNUM> blinding_factor(BN_new());
231	0	if (blinding_factor == nullptr) {
232	0	return 0;
233	0	}
234
235		// \|BN_mod_inverse_odd\| is leaky, so generate a secret blinding factor and
236		// blind \|a\|. This works because (ar)^-1 * r = a^-1, supposing r is
237		// invertible. If r is not invertible, this function will fail. However, we
238		// only use this in RSA, where stumbling on an uninvertible element means
239		// stumbling on the key's factorization. That is, if this function fails, the
240		// RSA key was not actually a product of two large primes.
241		//
242		// TODO(crbug.com/boringssl/677): When the PRNG output is marked secret by
243		// default, the explicit \|bn_secret\| call can be removed.
244	0	if (!BN_rand_range_ex(blinding_factor.get(), 1, &mont->N)) {
245	0	return 0;
246	0	}
247	0	bn_secret(blinding_factor.get());
248	0	if (!BN_mod_mul_montgomery(out, blinding_factor.get(), a, mont, ctx)) {
249	0	return 0;
250	0	}
251
252		// Once blinded, \|out\| is no longer secret, so it may be passed to a leaky
253		// mod inverse function. Note \|blinding_factor\| is secret, so \|out\| will be
254		// secret again after multiplying.
255	0	bn_declassify(out);
256	0	if (!BN_mod_inverse_odd(out, out_no_inverse, out, &mont->N, ctx) \|\|
257	0	!BN_mod_mul_montgomery(out, blinding_factor.get(), out, mont, ctx)) {
258	0	return 0;
259	0	}
260
261	0	return 1;
262	0	}
263
264		int bssl::bn_mod_inverse_prime(BIGNUM out, const BIGNUM a, const BIGNUM *p,
265	0	BN_CTX ctx, const BN_MONT_CTX mont_p) {
266	0	BN_CTXScope scope(ctx);
267	0	BIGNUM *p_minus_2 = BN_CTX_get(ctx);
268	0	return p_minus_2 != nullptr && BN_copy(p_minus_2, p) &&
269	0	BN_sub_word(p_minus_2, 2) &&
270	0	BN_mod_exp_mont(out, a, p_minus_2, p, ctx, mont_p);
271	0	}
272
273		int bssl::bn_mod_inverse_secret_prime(BIGNUM out, const BIGNUM a,
274		const BIGNUM p, BN_CTX ctx,
275	0	const BN_MONT_CTX *mont_p) {
276	0	BN_CTXScope scope(ctx);
277	0	BIGNUM *p_minus_2 = BN_CTX_get(ctx);
278	0	return p_minus_2 != nullptr && BN_copy(p_minus_2, p) &&
279	0	BN_sub_word(p_minus_2, 2) &&
280	0	BN_mod_exp_mont_consttime(out, a, p_minus_2, p, ctx, mont_p);
281	0	}