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