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
11 #include <openssl/err.h>
12 #include <openssl/bn.h>
13 #include "crypto/bn.h"
14 #include "rsa_local.h"
17 * Part of the RSA keypair test.
18 * Check the Chinese Remainder Theorem components are valid.
21 * 6.4.1.2.3: rsakpv1-crt Step 7
22 * 6.4.1.3.3: rsakpv2-crt Step 7
24 int rsa_check_crt_components(const RSA
*rsa
, BN_CTX
*ctx
)
27 BIGNUM
*r
= NULL
, *p1
= NULL
, *q1
= NULL
;
29 /* check if only some of the crt components are set */
30 if (rsa
->dmp1
== NULL
|| rsa
->dmq1
== NULL
|| rsa
->iqmp
== NULL
) {
31 if (rsa
->dmp1
!= NULL
|| rsa
->dmq1
!= NULL
|| rsa
->iqmp
!= NULL
)
33 return 1; /* return ok if all components are NULL */
42 && (BN_copy(p1
, rsa
->p
) != NULL
)
45 && (BN_copy(q1
, rsa
->q
) != NULL
)
47 /* (a) 1 < dP < (p – 1). */
48 && (BN_cmp(rsa
->dmp1
, BN_value_one()) > 0)
49 && (BN_cmp(rsa
->dmp1
, p1
) < 0)
50 /* (b) 1 < dQ < (q - 1). */
51 && (BN_cmp(rsa
->dmq1
, BN_value_one()) > 0)
52 && (BN_cmp(rsa
->dmq1
, q1
) < 0)
53 /* (c) 1 < qInv < p */
54 && (BN_cmp(rsa
->iqmp
, BN_value_one()) > 0)
55 && (BN_cmp(rsa
->iqmp
, rsa
->p
) < 0)
56 /* (d) 1 = (dP . e) mod (p - 1)*/
57 && BN_mod_mul(r
, rsa
->dmp1
, rsa
->e
, p1
, ctx
)
59 /* (e) 1 = (dQ . e) mod (q - 1) */
60 && BN_mod_mul(r
, rsa
->dmq1
, rsa
->e
, q1
, ctx
)
62 /* (f) 1 = (qInv . q) mod p */
63 && BN_mod_mul(r
, rsa
->iqmp
, rsa
->q
, rsa
->p
, ctx
)
72 * Part of the RSA keypair test.
73 * Check that (√2)(2^(nbits/2 - 1) <= p <= 2^(nbits/2) - 1
75 * See SP800-5bBr1 6.4.1.2.1 Part 5 (c) & (g) - used for both p and q.
77 * (√2)(2^(nbits/2 - 1) = (√2/2)(2^(nbits/2))
79 int rsa_check_prime_factor_range(const BIGNUM
*p
, int nbits
, BN_CTX
*ctx
)
86 shift
= nbits
- BN_num_bits(&bn_inv_sqrt_2
);
88 /* Upper bound check */
89 if (BN_num_bits(p
) != nbits
)
93 low
= BN_CTX_get(ctx
);
97 /* set low = (√2)(2^(nbits/2 - 1) */
98 if (!BN_copy(low
, &bn_inv_sqrt_2
))
103 * We don't have all the bits. bn_inv_sqrt_2 contains a rounded up
104 * value, so there is a very low probability that we'll reject a valid
107 if (!BN_lshift(low
, low
, shift
))
109 } else if (!BN_rshift(low
, low
, -shift
)) {
112 if (BN_cmp(p
, low
) <= 0)
121 * Part of the RSA keypair test.
122 * Check the prime factor (for either p or q)
123 * i.e: p is prime AND GCD(p - 1, e) = 1
125 * See SP800-56Br1 6.4.1.2.3 Step 5 (a to d) & (e to h).
127 int rsa_check_prime_factor(BIGNUM
*p
, BIGNUM
*e
, int nbits
, BN_CTX
*ctx
)
130 BIGNUM
*p1
= NULL
, *gcd
= NULL
;
132 /* (Steps 5 a-b) prime test */
133 if (BN_check_prime(p
, ctx
, NULL
) != 1
134 /* (Step 5c) (√2)(2^(nbits/2 - 1) <= p <= 2^(nbits/2 - 1) */
135 || rsa_check_prime_factor_range(p
, nbits
, ctx
) != 1)
139 p1
= BN_CTX_get(ctx
);
140 gcd
= BN_CTX_get(ctx
);
142 /* (Step 5d) GCD(p-1, e) = 1 */
143 && (BN_copy(p1
, p
) != NULL
)
144 && BN_sub_word(p1
, 1)
145 && BN_gcd(gcd
, p1
, e
, ctx
)
154 * See SP800-56Br1 6.4.1.2.3 Part 6(a-b) Check the private exponent d
156 * (Step 6a) 2^(nBit/2) < d < LCM(p–1, q–1).
157 * (Step 6b) 1 = (d*e) mod LCM(p–1, q–1)
159 int rsa_check_private_exponent(const RSA
*rsa
, int nbits
, BN_CTX
*ctx
)
162 BIGNUM
*r
, *p1
, *q1
, *lcm
, *p1q1
, *gcd
;
164 /* (Step 6a) 2^(nbits/2) < d */
165 if (BN_num_bits(rsa
->d
) <= (nbits
>> 1))
170 p1
= BN_CTX_get(ctx
);
171 q1
= BN_CTX_get(ctx
);
172 lcm
= BN_CTX_get(ctx
);
173 p1q1
= BN_CTX_get(ctx
);
174 gcd
= BN_CTX_get(ctx
);
176 /* LCM(p - 1, q - 1) */
177 && (rsa_get_lcm(ctx
, rsa
->p
, rsa
->q
, lcm
, gcd
, p1
, q1
, p1q1
) == 1)
178 /* (Step 6a) d < LCM(p - 1, q - 1) */
179 && (BN_cmp(rsa
->d
, lcm
) < 0)
180 /* (Step 6b) 1 = (e . d) mod LCM(p - 1, q - 1) */
181 && BN_mod_mul(r
, rsa
->e
, rsa
->d
, lcm
, ctx
)
192 /* Check exponent is odd, and has a bitlen ranging from [17..256] */
193 int rsa_check_public_exponent(const BIGNUM
*e
)
195 int bitlen
= BN_num_bits(e
);
197 return (BN_is_odd(e
) && bitlen
> 16 && bitlen
< 257);
201 * SP800-56Br1 6.4.1.2.1 (Step 5i): |p - q| > 2^(nbits/2 - 100)
202 * i.e- numbits(p-q-1) > (nbits/2 -100)
204 int rsa_check_pminusq_diff(BIGNUM
*diff
, const BIGNUM
*p
, const BIGNUM
*q
,
207 int bitlen
= (nbits
>> 1) - 100;
209 if (!BN_sub(diff
, p
, q
))
211 BN_set_negative(diff
, 0);
213 if (BN_is_zero(diff
))
216 if (!BN_sub_word(diff
, 1))
218 return (BN_num_bits(diff
) > bitlen
);
221 /* return LCM(p-1, q-1) */
222 int rsa_get_lcm(BN_CTX
*ctx
, const BIGNUM
*p
, const BIGNUM
*q
,
223 BIGNUM
*lcm
, BIGNUM
*gcd
, BIGNUM
*p1
, BIGNUM
*q1
,
226 return BN_sub(p1
, p
, BN_value_one()) /* p-1 */
227 && BN_sub(q1
, q
, BN_value_one()) /* q-1 */
228 && BN_mul(p1q1
, p1
, q1
, ctx
) /* (p-1)(q-1) */
229 && BN_gcd(gcd
, p1
, q1
, ctx
)
230 && BN_div(lcm
, NULL
, p1q1
, gcd
, ctx
); /* LCM((p-1, q-1)) */
234 * SP800-56Br1 6.4.2.2 Partial Public Key Validation for RSA refers to
235 * SP800-89 5.3.3 (Explicit) Partial Public Key Validation for RSA
236 * caveat is that the modulus must be as specified in SP800-56Br1
238 int rsa_sp800_56b_check_public(const RSA
*rsa
)
247 if (rsa
->n
== NULL
|| rsa
->e
== NULL
)
252 * (Step a): modulus must be 2048 or 3072 (caveat from SP800-56Br1)
253 * NOTE: changed to allow keys >= 2048
255 nbits
= BN_num_bits(rsa
->n
);
256 if (!rsa_sp800_56b_validate_strength(nbits
, -1)) {
257 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC
, RSA_R_INVALID_KEY_LENGTH
);
261 if (!BN_is_odd(rsa
->n
)) {
262 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC
, RSA_R_INVALID_MODULUS
);
265 /* (Steps b-c): 2^16 < e < 2^256, n and e must be odd */
266 if (!rsa_check_public_exponent(rsa
->e
)) {
267 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC
,
268 RSA_R_PUB_EXPONENT_OUT_OF_RANGE
);
274 if (ctx
== NULL
|| gcd
== NULL
)
278 * The modulus is composite, but not a power of a prime.
279 * The modulus has no factors smaller than 752.
281 if (!BN_gcd(gcd
, rsa
->n
, bn_get0_small_factors(), ctx
) || !BN_is_one(gcd
)) {
282 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC
, RSA_R_INVALID_MODULUS
);
286 ret
= bn_miller_rabin_is_prime(rsa
->n
, 0, ctx
, NULL
, 1, &status
);
287 if (ret
!= 1 || status
!= BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME
) {
288 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC
, RSA_R_INVALID_MODULUS
);
301 * Perform validation of the RSA private key to check that 0 < D < N.
303 int rsa_sp800_56b_check_private(const RSA
*rsa
)
305 if (rsa
->d
== NULL
|| rsa
->n
== NULL
)
307 return BN_cmp(rsa
->d
, BN_value_one()) >= 0 && BN_cmp(rsa
->d
, rsa
->n
) < 0;
311 * RSA key pair validation.
314 * 6.4.1.2 "RSAKPV1 Family: RSA Key - Pair Validation with a Fixed Exponent"
315 * 6.4.1.3 "RSAKPV2 Family: RSA Key - Pair Validation with a Random Exponent"
318 * 6.4.1.2.3 "rsakpv1 - crt"
319 * 6.4.1.3.3 "rsakpv2 - crt"
321 int rsa_sp800_56b_check_keypair(const RSA
*rsa
, const BIGNUM
*efixed
,
322 int strength
, int nbits
)
333 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR
, RSA_R_INVALID_REQUEST
);
336 /* (Step 1): Check Ranges */
337 if (!rsa_sp800_56b_validate_strength(nbits
, strength
))
340 /* If the exponent is known */
341 if (efixed
!= NULL
) {
342 /* (2): Check fixed exponent matches public exponent. */
343 if (BN_cmp(efixed
, rsa
->e
) != 0) {
344 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR
, RSA_R_INVALID_REQUEST
);
348 /* (Step 1.c): e is odd integer 65537 <= e < 2^256 */
349 if (!rsa_check_public_exponent(rsa
->e
)) {
350 /* exponent out of range */
351 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR
,
352 RSA_R_PUB_EXPONENT_OUT_OF_RANGE
);
355 /* (Step 3.b): check the modulus */
356 if (nbits
!= BN_num_bits(rsa
->n
)) {
357 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR
, RSA_R_INVALID_KEYPAIR
);
367 if (r
== NULL
|| !BN_mul(r
, rsa
->p
, rsa
->q
, ctx
))
369 /* (Step 4.c): Check n = pq */
370 if (BN_cmp(rsa
->n
, r
) != 0) {
371 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR
, RSA_R_INVALID_REQUEST
);
375 /* (Step 5): check prime factors p & q */
376 ret
= rsa_check_prime_factor(rsa
->p
, rsa
->e
, nbits
, ctx
)
377 && rsa_check_prime_factor(rsa
->q
, rsa
->e
, nbits
, ctx
)
378 && (rsa_check_pminusq_diff(r
, rsa
->p
, rsa
->q
, nbits
) > 0)
379 /* (Step 6): Check the private exponent d */
380 && rsa_check_private_exponent(rsa
, nbits
, ctx
)
381 /* 6.4.1.2.3 (Step 7): Check the CRT components */
382 && rsa_check_crt_components(rsa
, ctx
);
384 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR
, RSA_R_INVALID_KEYPAIR
);