2 * Copyright 2018-2019 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2018-2019, Oracle and/or its affiliates. All rights reserved.
5 * Licensed under the OpenSSL license (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
12 * According to NIST SP800-131A "Transitioning the use of cryptographic
13 * algorithms and key lengths" Generation of 1024 bit RSA keys are no longer
14 * allowed for signatures (Table 2) or key transport (Table 5). In the code
15 * below any attempt to generate 1024 bit RSA keys will result in an error (Note
16 * that digital signature verification can still use deprecated 1024 bit keys).
18 * Also see FIPS1402IG A.14
19 * FIPS 186-4 relies on the use of the auxiliary primes p1, p2, q1 and q2 that
20 * must be generated before the module generates the RSA primes p and q.
21 * Table B.1 in FIPS 186-4 specifies, for RSA modulus lengths of 2048 and
22 * 3072 bits only, the min/max total length of the auxiliary primes.
23 * When implementing the RSA signature generation algorithm
24 * with other approved RSA modulus sizes, the vendor shall use the limitations
25 * from Table B.1 that apply to the longest RSA modulus shown in Table B.1 of
26 * FIPS 186-4 whose length does not exceed that of the implementation's RSA
27 * modulus. In particular, when generating the primes for the 4096-bit RSA
28 * modulus the limitations stated for the 3072-bit modulus shall apply.
31 #include <openssl/bn.h>
33 #include "crypto/bn.h"
36 * FIPS 186-4 Table B.1. "Min length of auxiliary primes p1, p2, q1, q2".
39 * nbits The key size in bits.
41 * The minimum size of the auxiliary primes or 0 if nbits is invalid.
43 static int bn_rsa_fips186_4_aux_prime_min_size(int nbits)
53 * FIPS 186-4 Table B.1 "Maximum length of len(p1) + len(p2) and
54 * len(q1) + len(q2) for p,q Probable Primes".
57 * nbits The key size in bits.
59 * The maximum length or 0 if nbits is invalid.
61 static int bn_rsa_fips186_4_aux_prime_max_sum_size_for_prob_primes(int nbits)
71 * FIPS 186-4 Table C.3 for error probability of 2^-100
72 * Minimum number of Miller Rabin Rounds for p1, p2, q1 & q2.
75 * aux_prime_bits The auxiliary prime size in bits.
77 * The minimum number of Miller Rabin Rounds for an auxiliary prime, or
78 * 0 if aux_prime_bits is invalid.
80 static int bn_rsa_fips186_4_aux_prime_MR_min_checks(int aux_prime_bits)
82 if (aux_prime_bits > 170)
84 if (aux_prime_bits > 140)
86 return 0; /* Error case */
90 * FIPS 186-4 Table C.3 for error probability of 2^-100
91 * Minimum number of Miller Rabin Rounds for p, q.
94 * nbits The key size in bits.
96 * The minimum number of Miller Rabin Rounds required,
97 * or 0 if nbits is invalid.
99 int bn_rsa_fips186_4_prime_MR_min_checks(int nbits)
101 if (nbits >= 3072) /* > 170 */
103 if (nbits == 2048) /* > 140 */
105 return 0; /* Error case */
109 * Find the first odd integer that is a probable prime.
111 * See section FIPS 186-4 B.3.6 (Steps 4.2/5.2).
114 * Xp1 The passed in starting point to find a probably prime.
115 * p1 The returned probable prime (first odd integer >= Xp1)
116 * ctx A BN_CTX object.
117 * cb An optional BIGNUM callback.
118 * Returns: 1 on success otherwise it returns 0.
120 static int bn_rsa_fips186_4_find_aux_prob_prime(const BIGNUM *Xp1,
121 BIGNUM *p1, BN_CTX *ctx,
126 int checks = bn_rsa_fips186_4_aux_prime_MR_min_checks(BN_num_bits(Xp1));
128 if (checks == 0 || BN_copy(p1, Xp1) == NULL)
131 /* Find the first odd number >= Xp1 that is probably prime */
134 BN_GENCB_call(cb, 0, i);
135 /* MR test with trial division */
136 if (BN_is_prime_fasttest_ex(p1, checks, ctx, 1, cb))
138 /* Get next odd number */
139 if (!BN_add_word(p1, 2))
142 BN_GENCB_call(cb, 2, i);
149 * Generate a probable prime (p or q).
151 * See FIPS 186-4 B.3.6 (Steps 4 & 5)
154 * p The returned probable prime.
155 * Xpout An optionally returned random number used during generation of p.
156 * p1, p2 The returned auxiliary primes. If NULL they are not returned.
157 * Xp An optional passed in value (that is random number used during
159 * Xp1, Xp2 Optional passed in values that are normally generated
160 * internally. Used to find p1, p2.
161 * nlen The bit length of the modulus (the key size).
162 * e The public exponent.
163 * ctx A BN_CTX object.
164 * cb An optional BIGNUM callback.
165 * Returns: 1 on success otherwise it returns 0.
167 int bn_rsa_fips186_4_gen_prob_primes(BIGNUM *p, BIGNUM *Xpout,
168 BIGNUM *p1, BIGNUM *p2,
169 const BIGNUM *Xp, const BIGNUM *Xp1,
170 const BIGNUM *Xp2, int nlen,
171 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
174 BIGNUM *p1i = NULL, *p2i = NULL, *Xp1i = NULL, *Xp2i = NULL;
177 if (p == NULL || Xpout == NULL)
182 p1i = (p1 != NULL) ? p1 : BN_CTX_get(ctx);
183 p2i = (p2 != NULL) ? p2 : BN_CTX_get(ctx);
184 Xp1i = (Xp1 != NULL) ? (BIGNUM *)Xp1 : BN_CTX_get(ctx);
185 Xp2i = (Xp2 != NULL) ? (BIGNUM *)Xp2 : BN_CTX_get(ctx);
186 if (p1i == NULL || p2i == NULL || Xp1i == NULL || Xp2i == NULL)
189 bitlen = bn_rsa_fips186_4_aux_prime_min_size(nlen);
193 /* (Steps 4.1/5.1): Randomly generate Xp1 if it is not passed in */
195 /* Set the top and bottom bits to make it odd and the correct size */
196 if (!BN_priv_rand_ex(Xp1i, bitlen, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD,
200 /* (Steps 4.1/5.1): Randomly generate Xp2 if it is not passed in */
202 /* Set the top and bottom bits to make it odd and the correct size */
203 if (!BN_priv_rand_ex(Xp2i, bitlen, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD,
208 /* (Steps 4.2/5.2) - find first auxiliary probable primes */
209 if (!bn_rsa_fips186_4_find_aux_prob_prime(Xp1i, p1i, ctx, cb)
210 || !bn_rsa_fips186_4_find_aux_prob_prime(Xp2i, p2i, ctx, cb))
212 /* (Table B.1) auxiliary prime Max length check */
213 if ((BN_num_bits(p1i) + BN_num_bits(p2i)) >=
214 bn_rsa_fips186_4_aux_prime_max_sum_size_for_prob_primes(nlen))
216 /* (Steps 4.3/5.3) - generate prime */
217 if (!bn_rsa_fips186_4_derive_prime(p, Xpout, Xp, p1i, p2i, nlen, e, ctx, cb))
221 /* Zeroize any internally generated values that are not returned */
235 * Constructs a probable prime (a candidate for p or q) using 2 auxiliary
236 * prime numbers and the Chinese Remainder Theorem.
238 * See FIPS 186-4 C.9 "Compute a Probable Prime Factor Based on Auxiliary
239 * Primes". Used by FIPS 186-4 B.3.6 Section (4.3) for p and Section (5.3) for q.
242 * Y The returned prime factor (private_prime_factor) of the modulus n.
243 * X The returned random number used during generation of the prime factor.
244 * Xin An optional passed in value for X used for testing purposes.
245 * r1 An auxiliary prime.
246 * r2 An auxiliary prime.
247 * nlen The desired length of n (the RSA modulus).
248 * e The public exponent.
249 * ctx A BN_CTX object.
250 * cb An optional BIGNUM callback object.
251 * Returns: 1 on success otherwise it returns 0.
253 * Y, X, r1, r2, e are not NULL.
255 int bn_rsa_fips186_4_derive_prime(BIGNUM *Y, BIGNUM *X, const BIGNUM *Xin,
256 const BIGNUM *r1, const BIGNUM *r2, int nlen,
257 const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
261 int bits = nlen >> 1;
262 int checks = bn_rsa_fips186_4_prime_MR_min_checks(nlen);
263 BIGNUM *tmp, *R, *r1r2x2, *y1, *r1x2;
270 tmp = BN_CTX_get(ctx);
271 r1r2x2 = BN_CTX_get(ctx);
272 y1 = BN_CTX_get(ctx);
273 r1x2 = BN_CTX_get(ctx);
277 if (Xin != NULL && BN_copy(X, Xin) == NULL)
280 if (!(BN_lshift1(r1x2, r1)
281 /* (Step 1) GCD(2r1, r2) = 1 */
282 && BN_gcd(tmp, r1x2, r2, ctx)
284 /* (Step 2) R = ((r2^-1 mod 2r1) * r2) - ((2r1^-1 mod r2)*2r1) */
285 && BN_mod_inverse(R, r2, r1x2, ctx)
286 && BN_mul(R, R, r2, ctx) /* R = (r2^-1 mod 2r1) * r2 */
287 && BN_mod_inverse(tmp, r1x2, r2, ctx)
288 && BN_mul(tmp, tmp, r1x2, ctx) /* tmp = (2r1^-1 mod r2)*2r1 */
290 /* Calculate 2r1r2 */
291 && BN_mul(r1r2x2, r1x2, r2, ctx)))
293 /* Make positive by adding the modulus */
294 if (BN_is_negative(R) && !BN_add(R, R, r1r2x2))
297 imax = 5 * bits; /* max = 5/2 * nbits */
301 * (Step 3) Choose Random X such that
302 * sqrt(2) * 2^(nlen/2-1) < Random X < (2^(nlen/2)) - 1.
304 * For the lower bound:
305 * sqrt(2) * 2^(nlen/2 - 1) == sqrt(2)/2 * 2^(nlen/2)
306 * where sqrt(2)/2 = 0.70710678.. = 0.B504FC33F9DE...
307 * so largest number will have B5... as the top byte
308 * Setting the top 2 bits gives 0xC0.
310 if (!BN_priv_rand_ex(X, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY,
314 /* (Step 4) Y = X + ((R - X) mod 2r1r2) */
315 if (!BN_mod_sub(Y, R, X, r1r2x2, ctx) || !BN_add(Y, Y, X))
321 if (BN_num_bits(Y) > bits) {
323 break; /* Randomly Generated X so Go back to Step 3 */
325 goto err; /* X is not random so it will always fail */
327 BN_GENCB_call(cb, 0, 2);
329 /* (Step 7) If GCD(Y-1) == 1 & Y is probably prime then return Y */
330 if (BN_copy(y1, Y) == NULL
331 || !BN_sub_word(y1, 1)
332 || !BN_gcd(tmp, y1, e, ctx))
335 && BN_is_prime_fasttest_ex(Y, checks, ctx, 1, cb))
338 if (++i >= imax || !BN_add(Y, Y, r1r2x2))
344 BN_GENCB_call(cb, 3, 0);