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))
78 * √2/2 = 0.707106781186547524400 = 0.B504F333F9DE6484597D8
79 * 0.B504F334 gives an approximation to 11 decimal places.
80 * The range is then from
81 * 0xB504F334_0000.......................000 to
82 * 0xFFFFFFFF_FFFF.......................FFF
84 int rsa_check_prime_factor_range(const BIGNUM
*p
, int nbits
, BN_CTX
*ctx
)
91 /* Upper bound check */
92 if (BN_num_bits(p
) != nbits
)
96 tmp
= BN_CTX_get(ctx
);
97 low
= BN_CTX_get(ctx
);
99 /* set low = (√2)(2^(nbits/2 - 1) */
100 if (low
== NULL
|| !BN_set_word(tmp
, 0xB504F334))
104 if (!BN_lshift(low
, tmp
, nbits
- 32))
106 } else if (!BN_rshift(low
, tmp
, 32 - nbits
)) {
109 if (BN_cmp(p
, low
) < 0)
118 * Part of the RSA keypair test.
119 * Check the prime factor (for either p or q)
120 * i.e: p is prime AND GCD(p - 1, e) = 1
122 * See SP800-56Br1 6.4.1.2.3 Step 5 (a to d) & (e to h).
124 int rsa_check_prime_factor(BIGNUM
*p
, BIGNUM
*e
, int nbits
, BN_CTX
*ctx
)
127 BIGNUM
*p1
= NULL
, *gcd
= NULL
;
129 /* (Steps 5 a-b) prime test */
130 if (BN_check_prime(p
, ctx
, NULL
) != 1
131 /* (Step 5c) (√2)(2^(nbits/2 - 1) <= p <= 2^(nbits/2 - 1) */
132 || rsa_check_prime_factor_range(p
, nbits
, ctx
) != 1)
136 p1
= BN_CTX_get(ctx
);
137 gcd
= BN_CTX_get(ctx
);
139 /* (Step 5d) GCD(p-1, e) = 1 */
140 && (BN_copy(p1
, p
) != NULL
)
141 && BN_sub_word(p1
, 1)
142 && BN_gcd(gcd
, p1
, e
, ctx
)
151 * See SP800-56Br1 6.4.1.2.3 Part 6(a-b) Check the private exponent d
153 * (Step 6a) 2^(nBit/2) < d < LCM(p–1, q–1).
154 * (Step 6b) 1 = (d*e) mod LCM(p–1, q–1)
156 int rsa_check_private_exponent(const RSA
*rsa
, int nbits
, BN_CTX
*ctx
)
159 BIGNUM
*r
, *p1
, *q1
, *lcm
, *p1q1
, *gcd
;
161 /* (Step 6a) 2^(nbits/2) < d */
162 if (BN_num_bits(rsa
->d
) <= (nbits
>> 1))
167 p1
= BN_CTX_get(ctx
);
168 q1
= BN_CTX_get(ctx
);
169 lcm
= BN_CTX_get(ctx
);
170 p1q1
= BN_CTX_get(ctx
);
171 gcd
= BN_CTX_get(ctx
);
173 /* LCM(p - 1, q - 1) */
174 && (rsa_get_lcm(ctx
, rsa
->p
, rsa
->q
, lcm
, gcd
, p1
, q1
, p1q1
) == 1)
175 /* (Step 6a) d < LCM(p - 1, q - 1) */
176 && (BN_cmp(rsa
->d
, lcm
) < 0)
177 /* (Step 6b) 1 = (e . d) mod LCM(p - 1, q - 1) */
178 && BN_mod_mul(r
, rsa
->e
, rsa
->d
, lcm
, ctx
)
189 /* Check exponent is odd, and has a bitlen ranging from [17..256] */
190 int rsa_check_public_exponent(const BIGNUM
*e
)
192 int bitlen
= BN_num_bits(e
);
194 return (BN_is_odd(e
) && bitlen
> 16 && bitlen
< 257);
198 * SP800-56Br1 6.4.1.2.1 (Step 5i): |p - q| > 2^(nbits/2 - 100)
199 * i.e- numbits(p-q-1) > (nbits/2 -100)
201 int rsa_check_pminusq_diff(BIGNUM
*diff
, const BIGNUM
*p
, const BIGNUM
*q
,
204 int bitlen
= (nbits
>> 1) - 100;
206 if (!BN_sub(diff
, p
, q
))
208 BN_set_negative(diff
, 0);
210 if (BN_is_zero(diff
))
213 if (!BN_sub_word(diff
, 1))
215 return (BN_num_bits(diff
) > bitlen
);
218 /* return LCM(p-1, q-1) */
219 int rsa_get_lcm(BN_CTX
*ctx
, const BIGNUM
*p
, const BIGNUM
*q
,
220 BIGNUM
*lcm
, BIGNUM
*gcd
, BIGNUM
*p1
, BIGNUM
*q1
,
223 return BN_sub(p1
, p
, BN_value_one()) /* p-1 */
224 && BN_sub(q1
, q
, BN_value_one()) /* q-1 */
225 && BN_mul(p1q1
, p1
, q1
, ctx
) /* (p-1)(q-1) */
226 && BN_gcd(gcd
, p1
, q1
, ctx
)
227 && BN_div(lcm
, NULL
, p1q1
, gcd
, ctx
); /* LCM((p-1, q-1)) */
231 * SP800-56Br1 6.4.2.2 Partial Public Key Validation for RSA refers to
232 * SP800-89 5.3.3 (Explicit) Partial Public Key Validation for RSA
233 * caveat is that the modulus must be as specified in SP800-56Br1
235 int rsa_sp800_56b_check_public(const RSA
*rsa
)
237 int ret
= 0, nbits
, status
;
241 if (rsa
->n
== NULL
|| rsa
->e
== NULL
)
245 * (Step a): modulus must be 2048 or 3072 (caveat from SP800-56Br1)
246 * NOTE: changed to allow keys >= 2048
248 nbits
= BN_num_bits(rsa
->n
);
249 if (!rsa_sp800_56b_validate_strength(nbits
, -1)) {
250 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC
, RSA_R_INVALID_KEY_LENGTH
);
253 if (!BN_is_odd(rsa
->n
)) {
254 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC
, RSA_R_INVALID_MODULUS
);
258 /* (Steps b-c): 2^16 < e < 2^256, n and e must be odd */
259 if (!rsa_check_public_exponent(rsa
->e
)) {
260 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC
,
261 RSA_R_PUB_EXPONENT_OUT_OF_RANGE
);
267 if (ctx
== NULL
|| gcd
== NULL
)
271 * The modulus is composite, but not a power of a prime.
272 * The modulus has no factors smaller than 752.
274 if (!BN_gcd(gcd
, rsa
->n
, bn_get0_small_factors(), ctx
) || !BN_is_one(gcd
)) {
275 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC
, RSA_R_INVALID_MODULUS
);
279 ret
= bn_miller_rabin_is_prime(rsa
->n
, 0, ctx
, NULL
, 1, &status
);
280 if (ret
!= 1 || status
!= BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME
) {
281 RSAerr(RSA_F_RSA_SP800_56B_CHECK_PUBLIC
, RSA_R_INVALID_MODULUS
);
294 * Perform validation of the RSA private key to check that 0 < D < N.
296 int rsa_sp800_56b_check_private(const RSA
*rsa
)
298 if (rsa
->d
== NULL
|| rsa
->n
== NULL
)
300 return BN_cmp(rsa
->d
, BN_value_one()) >= 0 && BN_cmp(rsa
->d
, rsa
->n
) < 0;
304 * RSA key pair validation.
307 * 6.4.1.2 "RSAKPV1 Family: RSA Key - Pair Validation with a Fixed Exponent"
308 * 6.4.1.3 "RSAKPV2 Family: RSA Key - Pair Validation with a Random Exponent"
311 * 6.4.1.2.3 "rsakpv1 - crt"
312 * 6.4.1.3.3 "rsakpv2 - crt"
314 int rsa_sp800_56b_check_keypair(const RSA
*rsa
, const BIGNUM
*efixed
,
315 int strength
, int nbits
)
326 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR
, RSA_R_INVALID_REQUEST
);
329 /* (Step 1): Check Ranges */
330 if (!rsa_sp800_56b_validate_strength(nbits
, strength
))
333 /* If the exponent is known */
334 if (efixed
!= NULL
) {
335 /* (2): Check fixed exponent matches public exponent. */
336 if (BN_cmp(efixed
, rsa
->e
) != 0) {
337 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR
, RSA_R_INVALID_REQUEST
);
341 /* (Step 1.c): e is odd integer 65537 <= e < 2^256 */
342 if (!rsa_check_public_exponent(rsa
->e
)) {
343 /* exponent out of range */
344 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR
,
345 RSA_R_PUB_EXPONENT_OUT_OF_RANGE
);
348 /* (Step 3.b): check the modulus */
349 if (nbits
!= BN_num_bits(rsa
->n
)) {
350 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR
, RSA_R_INVALID_KEYPAIR
);
360 if (r
== NULL
|| !BN_mul(r
, rsa
->p
, rsa
->q
, ctx
))
362 /* (Step 4.c): Check n = pq */
363 if (BN_cmp(rsa
->n
, r
) != 0) {
364 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR
, RSA_R_INVALID_REQUEST
);
368 /* (Step 5): check prime factors p & q */
369 ret
= rsa_check_prime_factor(rsa
->p
, rsa
->e
, nbits
, ctx
)
370 && rsa_check_prime_factor(rsa
->q
, rsa
->e
, nbits
, ctx
)
371 && (rsa_check_pminusq_diff(r
, rsa
->p
, rsa
->q
, nbits
) > 0)
372 /* (Step 6): Check the private exponent d */
373 && rsa_check_private_exponent(rsa
, nbits
, ctx
)
374 /* 6.4.1.2.3 (Step 7): Check the CRT components */
375 && rsa_check_crt_components(rsa
, ctx
);
377 RSAerr(RSA_F_RSA_SP800_56B_CHECK_KEYPAIR
, RSA_R_INVALID_KEYPAIR
);