1 /*
2 * Copyright 2018-2021 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2018-2019, Oracle and/or its affiliates. All rights reserved.
4 *
5 * Licensed under the Apache License 2.0 (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
9 */
10
11 #include <openssl/err.h>
12 #include <openssl/bn.h>
13 #include "crypto/bn.h"
14 #include "rsa_local.h"
15
16 /*
17 * Part of the RSA keypair test.
18 * Check the Chinese Remainder Theorem components are valid.
19 *
20 * See SP800-5bBr1
21 * 6.4.1.2.3: rsakpv1-crt Step 7
22 * 6.4.1.3.3: rsakpv2-crt Step 7
23 */
ossl_rsa_check_crt_components(const RSA * rsa,BN_CTX * ctx)24 int ossl_rsa_check_crt_components(const RSA *rsa, BN_CTX *ctx)
25 {
26 int ret = 0;
27 BIGNUM *r = NULL, *p1 = NULL, *q1 = NULL;
28
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)
32 return 0;
33 return 1; /* return ok if all components are NULL */
34 }
35
36 BN_CTX_start(ctx);
37 r = BN_CTX_get(ctx);
38 p1 = BN_CTX_get(ctx);
39 q1 = BN_CTX_get(ctx);
40 if (q1 != NULL) {
41 BN_set_flags(r, BN_FLG_CONSTTIME);
42 BN_set_flags(p1, BN_FLG_CONSTTIME);
43 BN_set_flags(q1, BN_FLG_CONSTTIME);
44 ret = 1;
45 } else {
46 ret = 0;
47 }
48 ret = ret
49 /* p1 = p -1 */
50 && (BN_copy(p1, rsa->p) != NULL)
51 && BN_sub_word(p1, 1)
52 /* q1 = q - 1 */
53 && (BN_copy(q1, rsa->q) != NULL)
54 && BN_sub_word(q1, 1)
55 /* (a) 1 < dP < (p – 1). */
56 && (BN_cmp(rsa->dmp1, BN_value_one()) > 0)
57 && (BN_cmp(rsa->dmp1, p1) < 0)
58 /* (b) 1 < dQ < (q - 1). */
59 && (BN_cmp(rsa->dmq1, BN_value_one()) > 0)
60 && (BN_cmp(rsa->dmq1, q1) < 0)
61 /* (c) 1 < qInv < p */
62 && (BN_cmp(rsa->iqmp, BN_value_one()) > 0)
63 && (BN_cmp(rsa->iqmp, rsa->p) < 0)
64 /* (d) 1 = (dP . e) mod (p - 1)*/
65 && BN_mod_mul(r, rsa->dmp1, rsa->e, p1, ctx)
66 && BN_is_one(r)
67 /* (e) 1 = (dQ . e) mod (q - 1) */
68 && BN_mod_mul(r, rsa->dmq1, rsa->e, q1, ctx)
69 && BN_is_one(r)
70 /* (f) 1 = (qInv . q) mod p */
71 && BN_mod_mul(r, rsa->iqmp, rsa->q, rsa->p, ctx)
72 && BN_is_one(r);
73 BN_clear(r);
74 BN_clear(p1);
75 BN_clear(q1);
76 BN_CTX_end(ctx);
77 return ret;
78 }
79
80 /*
81 * Part of the RSA keypair test.
82 * Check that (√2)(2^(nbits/2 - 1) <= p <= 2^(nbits/2) - 1
83 *
84 * See SP800-5bBr1 6.4.1.2.1 Part 5 (c) & (g) - used for both p and q.
85 *
86 * (√2)(2^(nbits/2 - 1) = (√2/2)(2^(nbits/2))
87 */
ossl_rsa_check_prime_factor_range(const BIGNUM * p,int nbits,BN_CTX * ctx)88 int ossl_rsa_check_prime_factor_range(const BIGNUM *p, int nbits, BN_CTX *ctx)
89 {
90 int ret = 0;
91 BIGNUM *low;
92 int shift;
93
94 nbits >>= 1;
95 shift = nbits - BN_num_bits(&ossl_bn_inv_sqrt_2);
96
97 /* Upper bound check */
98 if (BN_num_bits(p) != nbits)
99 return 0;
100
101 BN_CTX_start(ctx);
102 low = BN_CTX_get(ctx);
103 if (low == NULL)
104 goto err;
105
106 /* set low = (√2)(2^(nbits/2 - 1) */
107 if (!BN_copy(low, &ossl_bn_inv_sqrt_2))
108 goto err;
109
110 if (shift >= 0) {
111 /*
112 * We don't have all the bits. ossl_bn_inv_sqrt_2 contains a rounded up
113 * value, so there is a very low probability that we'll reject a valid
114 * value.
115 */
116 if (!BN_lshift(low, low, shift))
117 goto err;
118 } else if (!BN_rshift(low, low, -shift)) {
119 goto err;
120 }
121 if (BN_cmp(p, low) <= 0)
122 goto err;
123 ret = 1;
124 err:
125 BN_CTX_end(ctx);
126 return ret;
127 }
128
129 /*
130 * Part of the RSA keypair test.
131 * Check the prime factor (for either p or q)
132 * i.e: p is prime AND GCD(p - 1, e) = 1
133 *
134 * See SP800-56Br1 6.4.1.2.3 Step 5 (a to d) & (e to h).
135 */
ossl_rsa_check_prime_factor(BIGNUM * p,BIGNUM * e,int nbits,BN_CTX * ctx)136 int ossl_rsa_check_prime_factor(BIGNUM *p, BIGNUM *e, int nbits, BN_CTX *ctx)
137 {
138 int ret = 0;
139 BIGNUM *p1 = NULL, *gcd = NULL;
140
141 /* (Steps 5 a-b) prime test */
142 if (BN_check_prime(p, ctx, NULL) != 1
143 /* (Step 5c) (√2)(2^(nbits/2 - 1) <= p <= 2^(nbits/2 - 1) */
144 || ossl_rsa_check_prime_factor_range(p, nbits, ctx) != 1)
145 return 0;
146
147 BN_CTX_start(ctx);
148 p1 = BN_CTX_get(ctx);
149 gcd = BN_CTX_get(ctx);
150 if (gcd != NULL) {
151 BN_set_flags(p1, BN_FLG_CONSTTIME);
152 BN_set_flags(gcd, BN_FLG_CONSTTIME);
153 ret = 1;
154 } else {
155 ret = 0;
156 }
157 ret = ret
158 /* (Step 5d) GCD(p-1, e) = 1 */
159 && (BN_copy(p1, p) != NULL)
160 && BN_sub_word(p1, 1)
161 && BN_gcd(gcd, p1, e, ctx)
162 && BN_is_one(gcd);
163
164 BN_clear(p1);
165 BN_CTX_end(ctx);
166 return ret;
167 }
168
169 /*
170 * See SP800-56Br1 6.4.1.2.3 Part 6(a-b) Check the private exponent d
171 * satisfies:
172 * (Step 6a) 2^(nBit/2) < d < LCM(p–1, q–1).
173 * (Step 6b) 1 = (d*e) mod LCM(p–1, q–1)
174 */
ossl_rsa_check_private_exponent(const RSA * rsa,int nbits,BN_CTX * ctx)175 int ossl_rsa_check_private_exponent(const RSA *rsa, int nbits, BN_CTX *ctx)
176 {
177 int ret;
178 BIGNUM *r, *p1, *q1, *lcm, *p1q1, *gcd;
179
180 /* (Step 6a) 2^(nbits/2) < d */
181 if (BN_num_bits(rsa->d) <= (nbits >> 1))
182 return 0;
183
184 BN_CTX_start(ctx);
185 r = BN_CTX_get(ctx);
186 p1 = BN_CTX_get(ctx);
187 q1 = BN_CTX_get(ctx);
188 lcm = BN_CTX_get(ctx);
189 p1q1 = BN_CTX_get(ctx);
190 gcd = BN_CTX_get(ctx);
191 if (gcd != NULL) {
192 BN_set_flags(r, BN_FLG_CONSTTIME);
193 BN_set_flags(p1, BN_FLG_CONSTTIME);
194 BN_set_flags(q1, BN_FLG_CONSTTIME);
195 BN_set_flags(lcm, BN_FLG_CONSTTIME);
196 BN_set_flags(p1q1, BN_FLG_CONSTTIME);
197 BN_set_flags(gcd, BN_FLG_CONSTTIME);
198 ret = 1;
199 } else {
200 ret = 0;
201 }
202 ret = (ret
203 /* LCM(p - 1, q - 1) */
204 && (ossl_rsa_get_lcm(ctx, rsa->p, rsa->q, lcm, gcd, p1, q1,
205 p1q1) == 1)
206 /* (Step 6a) d < LCM(p - 1, q - 1) */
207 && (BN_cmp(rsa->d, lcm) < 0)
208 /* (Step 6b) 1 = (e . d) mod LCM(p - 1, q - 1) */
209 && BN_mod_mul(r, rsa->e, rsa->d, lcm, ctx)
210 && BN_is_one(r));
211
212 BN_clear(r);
213 BN_clear(p1);
214 BN_clear(q1);
215 BN_clear(lcm);
216 BN_clear(gcd);
217 BN_CTX_end(ctx);
218 return ret;
219 }
220
221 /*
222 * Check exponent is odd.
223 * For FIPS also check the bit length is in the range [17..256]
224 */
ossl_rsa_check_public_exponent(const BIGNUM * e)225 int ossl_rsa_check_public_exponent(const BIGNUM *e)
226 {
227 #ifdef FIPS_MODULE
228 int bitlen;
229
230 bitlen = BN_num_bits(e);
231 return (BN_is_odd(e) && bitlen > 16 && bitlen < 257);
232 #else
233 /* Allow small exponents larger than 1 for legacy purposes */
234 return BN_is_odd(e) && BN_cmp(e, BN_value_one()) > 0;
235 #endif /* FIPS_MODULE */
236 }
237
238 /*
239 * SP800-56Br1 6.4.1.2.1 (Step 5i): |p - q| > 2^(nbits/2 - 100)
240 * i.e- numbits(p-q-1) > (nbits/2 -100)
241 */
ossl_rsa_check_pminusq_diff(BIGNUM * diff,const BIGNUM * p,const BIGNUM * q,int nbits)242 int ossl_rsa_check_pminusq_diff(BIGNUM *diff, const BIGNUM *p, const BIGNUM *q,
243 int nbits)
244 {
245 int bitlen = (nbits >> 1) - 100;
246
247 if (!BN_sub(diff, p, q))
248 return -1;
249 BN_set_negative(diff, 0);
250
251 if (BN_is_zero(diff))
252 return 0;
253
254 if (!BN_sub_word(diff, 1))
255 return -1;
256 return (BN_num_bits(diff) > bitlen);
257 }
258
259 /*
260 * return LCM(p-1, q-1)
261 *
262 * Caller should ensure that lcm, gcd, p1, q1, p1q1 are flagged with
263 * BN_FLG_CONSTTIME.
264 */
ossl_rsa_get_lcm(BN_CTX * ctx,const BIGNUM * p,const BIGNUM * q,BIGNUM * lcm,BIGNUM * gcd,BIGNUM * p1,BIGNUM * q1,BIGNUM * p1q1)265 int ossl_rsa_get_lcm(BN_CTX *ctx, const BIGNUM *p, const BIGNUM *q,
266 BIGNUM *lcm, BIGNUM *gcd, BIGNUM *p1, BIGNUM *q1,
267 BIGNUM *p1q1)
268 {
269 return BN_sub(p1, p, BN_value_one()) /* p-1 */
270 && BN_sub(q1, q, BN_value_one()) /* q-1 */
271 && BN_mul(p1q1, p1, q1, ctx) /* (p-1)(q-1) */
272 && BN_gcd(gcd, p1, q1, ctx)
273 && BN_div(lcm, NULL, p1q1, gcd, ctx); /* LCM((p-1, q-1)) */
274 }
275
276 /*
277 * SP800-56Br1 6.4.2.2 Partial Public Key Validation for RSA refers to
278 * SP800-89 5.3.3 (Explicit) Partial Public Key Validation for RSA
279 * caveat is that the modulus must be as specified in SP800-56Br1
280 */
ossl_rsa_sp800_56b_check_public(const RSA * rsa)281 int ossl_rsa_sp800_56b_check_public(const RSA *rsa)
282 {
283 int ret = 0, status;
284 int nbits;
285 BN_CTX *ctx = NULL;
286 BIGNUM *gcd = NULL;
287
288 if (rsa->n == NULL || rsa->e == NULL)
289 return 0;
290
291 nbits = BN_num_bits(rsa->n);
292 #ifdef FIPS_MODULE
293 /*
294 * (Step a): modulus must be 2048 or 3072 (caveat from SP800-56Br1)
295 * NOTE: changed to allow keys >= 2048
296 */
297 if (!ossl_rsa_sp800_56b_validate_strength(nbits, -1)) {
298 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_KEY_LENGTH);
299 return 0;
300 }
301 #endif
302 if (!BN_is_odd(rsa->n)) {
303 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_MODULUS);
304 return 0;
305 }
306 /* (Steps b-c): 2^16 < e < 2^256, n and e must be odd */
307 if (!ossl_rsa_check_public_exponent(rsa->e)) {
308 ERR_raise(ERR_LIB_RSA, RSA_R_PUB_EXPONENT_OUT_OF_RANGE);
309 return 0;
310 }
311
312 ctx = BN_CTX_new_ex(rsa->libctx);
313 gcd = BN_new();
314 if (ctx == NULL || gcd == NULL)
315 goto err;
316
317 /* (Steps d-f):
318 * The modulus is composite, but not a power of a prime.
319 * The modulus has no factors smaller than 752.
320 */
321 if (!BN_gcd(gcd, rsa->n, ossl_bn_get0_small_factors(), ctx)
322 || !BN_is_one(gcd)) {
323 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_MODULUS);
324 goto err;
325 }
326
327 ret = ossl_bn_miller_rabin_is_prime(rsa->n, 0, ctx, NULL, 1, &status);
328 #ifdef FIPS_MODULE
329 if (ret != 1 || status != BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME) {
330 #else
331 if (ret != 1 || (status != BN_PRIMETEST_COMPOSITE_NOT_POWER_OF_PRIME
332 && (nbits >= RSA_MIN_MODULUS_BITS
333 || status != BN_PRIMETEST_COMPOSITE_WITH_FACTOR))) {
334 #endif
335 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_MODULUS);
336 ret = 0;
337 goto err;
338 }
339
340 ret = 1;
341 err:
342 BN_free(gcd);
343 BN_CTX_free(ctx);
344 return ret;
345 }
346
347 /*
348 * Perform validation of the RSA private key to check that 0 < D < N.
349 */
350 int ossl_rsa_sp800_56b_check_private(const RSA *rsa)
351 {
352 if (rsa->d == NULL || rsa->n == NULL)
353 return 0;
354 return BN_cmp(rsa->d, BN_value_one()) >= 0 && BN_cmp(rsa->d, rsa->n) < 0;
355 }
356
357 /*
358 * RSA key pair validation.
359 *
360 * SP800-56Br1.
361 * 6.4.1.2 "RSAKPV1 Family: RSA Key - Pair Validation with a Fixed Exponent"
362 * 6.4.1.3 "RSAKPV2 Family: RSA Key - Pair Validation with a Random Exponent"
363 *
364 * It uses:
365 * 6.4.1.2.3 "rsakpv1 - crt"
366 * 6.4.1.3.3 "rsakpv2 - crt"
367 */
368 int ossl_rsa_sp800_56b_check_keypair(const RSA *rsa, const BIGNUM *efixed,
369 int strength, int nbits)
370 {
371 int ret = 0;
372 BN_CTX *ctx = NULL;
373 BIGNUM *r = NULL;
374
375 if (rsa->p == NULL
376 || rsa->q == NULL
377 || rsa->e == NULL
378 || rsa->d == NULL
379 || rsa->n == NULL) {
380 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_REQUEST);
381 return 0;
382 }
383 /* (Step 1): Check Ranges */
384 if (!ossl_rsa_sp800_56b_validate_strength(nbits, strength))
385 return 0;
386
387 /* If the exponent is known */
388 if (efixed != NULL) {
389 /* (2): Check fixed exponent matches public exponent. */
390 if (BN_cmp(efixed, rsa->e) != 0) {
391 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_REQUEST);
392 return 0;
393 }
394 }
395 /* (Step 1.c): e is odd integer 65537 <= e < 2^256 */
396 if (!ossl_rsa_check_public_exponent(rsa->e)) {
397 /* exponent out of range */
398 ERR_raise(ERR_LIB_RSA, RSA_R_PUB_EXPONENT_OUT_OF_RANGE);
399 return 0;
400 }
401 /* (Step 3.b): check the modulus */
402 if (nbits != BN_num_bits(rsa->n)) {
403 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_KEYPAIR);
404 return 0;
405 }
406
407 ctx = BN_CTX_new_ex(rsa->libctx);
408 if (ctx == NULL)
409 return 0;
410
411 BN_CTX_start(ctx);
412 r = BN_CTX_get(ctx);
413 if (r == NULL || !BN_mul(r, rsa->p, rsa->q, ctx))
414 goto err;
415 /* (Step 4.c): Check n = pq */
416 if (BN_cmp(rsa->n, r) != 0) {
417 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_REQUEST);
418 goto err;
419 }
420
421 /* (Step 5): check prime factors p & q */
422 ret = ossl_rsa_check_prime_factor(rsa->p, rsa->e, nbits, ctx)
423 && ossl_rsa_check_prime_factor(rsa->q, rsa->e, nbits, ctx)
424 && (ossl_rsa_check_pminusq_diff(r, rsa->p, rsa->q, nbits) > 0)
425 /* (Step 6): Check the private exponent d */
426 && ossl_rsa_check_private_exponent(rsa, nbits, ctx)
427 /* 6.4.1.2.3 (Step 7): Check the CRT components */
428 && ossl_rsa_check_crt_components(rsa, ctx);
429 if (ret != 1)
430 ERR_raise(ERR_LIB_RSA, RSA_R_INVALID_KEYPAIR);
431
432 err:
433 BN_clear(r);
434 BN_CTX_end(ctx);
435 BN_CTX_free(ctx);
436 return ret;
437 }
438