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[proxmark3-svn] / common / mbedtls / rsa_internal.c
1 /*
2 * Helper functions for the RSA module
3 *
4 * Copyright (C) 2006-2017, ARM Limited, All Rights Reserved
5 * SPDX-License-Identifier: GPL-2.0
6 *
7 * This program is free software; you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation; either version 2 of the License, or
10 * (at your option) any later version.
11 *
12 * This program is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License along
18 * with this program; if not, write to the Free Software Foundation, Inc.,
19 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * This file is part of mbed TLS (https://tls.mbed.org)
22 *
23 */
24
25 #if !defined(MBEDTLS_CONFIG_FILE)
26 #include "mbedtls/config.h"
27 #else
28 #include MBEDTLS_CONFIG_FILE
29 #endif
30
31 #if defined(MBEDTLS_RSA_C)
32
33 #include "mbedtls/rsa.h"
34 #include "mbedtls/bignum.h"
35 #include "mbedtls/rsa_internal.h"
36
37 /*
38 * Compute RSA prime factors from public and private exponents
39 *
40 * Summary of algorithm:
41 * Setting F := lcm(P-1,Q-1), the idea is as follows:
42 *
43 * (a) For any 1 <= X < N with gcd(X,N)=1, we have X^F = 1 modulo N, so X^(F/2)
44 * is a square root of 1 in Z/NZ. Since Z/NZ ~= Z/PZ x Z/QZ by CRT and the
45 * square roots of 1 in Z/PZ and Z/QZ are +1 and -1, this leaves the four
46 * possibilities X^(F/2) = (+-1, +-1). If it happens that X^(F/2) = (-1,+1)
47 * or (+1,-1), then gcd(X^(F/2) + 1, N) will be equal to one of the prime
48 * factors of N.
49 *
50 * (b) If we don't know F/2 but (F/2) * K for some odd (!) K, then the same
51 * construction still applies since (-)^K is the identity on the set of
52 * roots of 1 in Z/NZ.
53 *
54 * The public and private key primitives (-)^E and (-)^D are mutually inverse
55 * bijections on Z/NZ if and only if (-)^(DE) is the identity on Z/NZ, i.e.
56 * if and only if DE - 1 is a multiple of F, say DE - 1 = F * L.
57 * Splitting L = 2^t * K with K odd, we have
58 *
59 * DE - 1 = FL = (F/2) * (2^(t+1)) * K,
60 *
61 * so (F / 2) * K is among the numbers
62 *
63 * (DE - 1) >> 1, (DE - 1) >> 2, ..., (DE - 1) >> ord
64 *
65 * where ord is the order of 2 in (DE - 1).
66 * We can therefore iterate through these numbers apply the construction
67 * of (a) and (b) above to attempt to factor N.
68 *
69 */
70 int mbedtls_rsa_deduce_primes( mbedtls_mpi const *N,
71 mbedtls_mpi const *E, mbedtls_mpi const *D,
72 mbedtls_mpi *P, mbedtls_mpi *Q )
73 {
74 int ret = 0;
75
76 uint16_t attempt; /* Number of current attempt */
77 uint16_t iter; /* Number of squares computed in the current attempt */
78
79 uint16_t order; /* Order of 2 in DE - 1 */
80
81 mbedtls_mpi T; /* Holds largest odd divisor of DE - 1 */
82 mbedtls_mpi K; /* Temporary holding the current candidate */
83
84 const unsigned char primes[] = { 2,
85 3, 5, 7, 11, 13, 17, 19, 23,
86 29, 31, 37, 41, 43, 47, 53, 59,
87 61, 67, 71, 73, 79, 83, 89, 97,
88 101, 103, 107, 109, 113, 127, 131, 137,
89 139, 149, 151, 157, 163, 167, 173, 179,
90 181, 191, 193, 197, 199, 211, 223, 227,
91 229, 233, 239, 241, 251
92 };
93
94 const size_t num_primes = sizeof( primes ) / sizeof( *primes );
95
96 if( P == NULL || Q == NULL || P->p != NULL || Q->p != NULL )
97 return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
98
99 if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 ||
100 mbedtls_mpi_cmp_int( D, 1 ) <= 0 ||
101 mbedtls_mpi_cmp_mpi( D, N ) >= 0 ||
102 mbedtls_mpi_cmp_int( E, 1 ) <= 0 ||
103 mbedtls_mpi_cmp_mpi( E, N ) >= 0 )
104 {
105 return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
106 }
107
108 /*
109 * Initializations and temporary changes
110 */
111
112 mbedtls_mpi_init( &K );
113 mbedtls_mpi_init( &T );
114
115 /* T := DE - 1 */
116 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, D, E ) );
117 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &T, &T, 1 ) );
118
119 if( ( order = (uint16_t) mbedtls_mpi_lsb( &T ) ) == 0 )
120 {
121 ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
122 goto cleanup;
123 }
124
125 /* After this operation, T holds the largest odd divisor of DE - 1. */
126 MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &T, order ) );
127
128 /*
129 * Actual work
130 */
131
132 /* Skip trying 2 if N == 1 mod 8 */
133 attempt = 0;
134 if( N->p[0] % 8 == 1 )
135 attempt = 1;
136
137 for( ; attempt < num_primes; ++attempt )
138 {
139 mbedtls_mpi_lset( &K, primes[attempt] );
140
141 /* Check if gcd(K,N) = 1 */
142 MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) );
143 if( mbedtls_mpi_cmp_int( P, 1 ) != 0 )
144 continue;
145
146 /* Go through K^T + 1, K^(2T) + 1, K^(4T) + 1, ...
147 * and check whether they have nontrivial GCD with N. */
148 MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &K, &K, &T, N,
149 Q /* temporarily use Q for storing Montgomery
150 * multiplication helper values */ ) );
151
152 for( iter = 1; iter <= order; ++iter )
153 {
154 /* If we reach 1 prematurely, there's no point
155 * in continuing to square K */
156 if( mbedtls_mpi_cmp_int( &K, 1 ) == 0 )
157 break;
158
159 MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &K, &K, 1 ) );
160 MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) );
161
162 if( mbedtls_mpi_cmp_int( P, 1 ) == 1 &&
163 mbedtls_mpi_cmp_mpi( P, N ) == -1 )
164 {
165 /*
166 * Have found a nontrivial divisor P of N.
167 * Set Q := N / P.
168 */
169
170 MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( Q, NULL, N, P ) );
171 goto cleanup;
172 }
173
174 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
175 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &K ) );
176 MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, N ) );
177 }
178
179 /*
180 * If we get here, then either we prematurely aborted the loop because
181 * we reached 1, or K holds primes[attempt]^(DE - 1) mod N, which must
182 * be 1 if D,E,N were consistent.
183 * Check if that's the case and abort if not, to avoid very long,
184 * yet eventually failing, computations if N,D,E were not sane.
185 */
186 if( mbedtls_mpi_cmp_int( &K, 1 ) != 0 )
187 {
188 break;
189 }
190 }
191
192 ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
193
194 cleanup:
195
196 mbedtls_mpi_free( &K );
197 mbedtls_mpi_free( &T );
198 return( ret );
199 }
200
201 /*
202 * Given P, Q and the public exponent E, deduce D.
203 * This is essentially a modular inversion.
204 */
205 int mbedtls_rsa_deduce_private_exponent( mbedtls_mpi const *P,
206 mbedtls_mpi const *Q,
207 mbedtls_mpi const *E,
208 mbedtls_mpi *D )
209 {
210 int ret = 0;
211 mbedtls_mpi K, L;
212
213 if( D == NULL || mbedtls_mpi_cmp_int( D, 0 ) != 0 )
214 return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
215
216 if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 ||
217 mbedtls_mpi_cmp_int( Q, 1 ) <= 0 ||
218 mbedtls_mpi_cmp_int( E, 0 ) == 0 )
219 {
220 return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
221 }
222
223 mbedtls_mpi_init( &K );
224 mbedtls_mpi_init( &L );
225
226 /* Temporarily put K := P-1 and L := Q-1 */
227 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );
228 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) );
229
230 /* Temporarily put D := gcd(P-1, Q-1) */
231 MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( D, &K, &L ) );
232
233 /* K := LCM(P-1, Q-1) */
234 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &L ) );
235 MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &K, NULL, &K, D ) );
236
237 /* Compute modular inverse of E in LCM(P-1, Q-1) */
238 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( D, E, &K ) );
239
240 cleanup:
241
242 mbedtls_mpi_free( &K );
243 mbedtls_mpi_free( &L );
244
245 return( ret );
246 }
247
248 /*
249 * Check that RSA CRT parameters are in accordance with core parameters.
250 */
251 int mbedtls_rsa_validate_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q,
252 const mbedtls_mpi *D, const mbedtls_mpi *DP,
253 const mbedtls_mpi *DQ, const mbedtls_mpi *QP )
254 {
255 int ret = 0;
256
257 mbedtls_mpi K, L;
258 mbedtls_mpi_init( &K );
259 mbedtls_mpi_init( &L );
260
261 /* Check that DP - D == 0 mod P - 1 */
262 if( DP != NULL )
263 {
264 if( P == NULL )
265 {
266 ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
267 goto cleanup;
268 }
269
270 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );
271 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DP, D ) );
272 MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) );
273
274 if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 )
275 {
276 ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
277 goto cleanup;
278 }
279 }
280
281 /* Check that DQ - D == 0 mod Q - 1 */
282 if( DQ != NULL )
283 {
284 if( Q == NULL )
285 {
286 ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
287 goto cleanup;
288 }
289
290 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) );
291 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DQ, D ) );
292 MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) );
293
294 if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 )
295 {
296 ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
297 goto cleanup;
298 }
299 }
300
301 /* Check that QP * Q - 1 == 0 mod P */
302 if( QP != NULL )
303 {
304 if( P == NULL || Q == NULL )
305 {
306 ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
307 goto cleanup;
308 }
309
310 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, QP, Q ) );
311 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
312 MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, P ) );
313 if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
314 {
315 ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
316 goto cleanup;
317 }
318 }
319
320 cleanup:
321
322 /* Wrap MPI error codes by RSA check failure error code */
323 if( ret != 0 &&
324 ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED &&
325 ret != MBEDTLS_ERR_RSA_BAD_INPUT_DATA )
326 {
327 ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
328 }
329
330 mbedtls_mpi_free( &K );
331 mbedtls_mpi_free( &L );
332
333 return( ret );
334 }
335
336 /*
337 * Check that core RSA parameters are sane.
338 */
339 int mbedtls_rsa_validate_params( const mbedtls_mpi *N, const mbedtls_mpi *P,
340 const mbedtls_mpi *Q, const mbedtls_mpi *D,
341 const mbedtls_mpi *E,
342 int (*f_rng)(void *, unsigned char *, size_t),
343 void *p_rng )
344 {
345 int ret = 0;
346 mbedtls_mpi K, L;
347
348 mbedtls_mpi_init( &K );
349 mbedtls_mpi_init( &L );
350
351 /*
352 * Step 1: If PRNG provided, check that P and Q are prime
353 */
354
355 #if defined(MBEDTLS_GENPRIME)
356 if( f_rng != NULL && P != NULL &&
357 ( ret = mbedtls_mpi_is_prime( P, f_rng, p_rng ) ) != 0 )
358 {
359 ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
360 goto cleanup;
361 }
362
363 if( f_rng != NULL && Q != NULL &&
364 ( ret = mbedtls_mpi_is_prime( Q, f_rng, p_rng ) ) != 0 )
365 {
366 ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
367 goto cleanup;
368 }
369 #else
370 ((void) f_rng);
371 ((void) p_rng);
372 #endif /* MBEDTLS_GENPRIME */
373
374 /*
375 * Step 2: Check that 1 < N = P * Q
376 */
377
378 if( P != NULL && Q != NULL && N != NULL )
379 {
380 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, P, Q ) );
381 if( mbedtls_mpi_cmp_int( N, 1 ) <= 0 ||
382 mbedtls_mpi_cmp_mpi( &K, N ) != 0 )
383 {
384 ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
385 goto cleanup;
386 }
387 }
388
389 /*
390 * Step 3: Check and 1 < D, E < N if present.
391 */
392
393 if( N != NULL && D != NULL && E != NULL )
394 {
395 if ( mbedtls_mpi_cmp_int( D, 1 ) <= 0 ||
396 mbedtls_mpi_cmp_int( E, 1 ) <= 0 ||
397 mbedtls_mpi_cmp_mpi( D, N ) >= 0 ||
398 mbedtls_mpi_cmp_mpi( E, N ) >= 0 )
399 {
400 ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
401 goto cleanup;
402 }
403 }
404
405 /*
406 * Step 4: Check that D, E are inverse modulo P-1 and Q-1
407 */
408
409 if( P != NULL && Q != NULL && D != NULL && E != NULL )
410 {
411 if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 ||
412 mbedtls_mpi_cmp_int( Q, 1 ) <= 0 )
413 {
414 ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
415 goto cleanup;
416 }
417
418 /* Compute DE-1 mod P-1 */
419 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) );
420 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
421 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, P, 1 ) );
422 MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) );
423 if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
424 {
425 ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
426 goto cleanup;
427 }
428
429 /* Compute DE-1 mod Q-1 */
430 MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) );
431 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
432 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) );
433 MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) );
434 if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
435 {
436 ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
437 goto cleanup;
438 }
439 }
440
441 cleanup:
442
443 mbedtls_mpi_free( &K );
444 mbedtls_mpi_free( &L );
445
446 /* Wrap MPI error codes by RSA check failure error code */
447 if( ret != 0 && ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED )
448 {
449 ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
450 }
451
452 return( ret );
453 }
454
455 int mbedtls_rsa_deduce_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q,
456 const mbedtls_mpi *D, mbedtls_mpi *DP,
457 mbedtls_mpi *DQ, mbedtls_mpi *QP )
458 {
459 int ret = 0;
460 mbedtls_mpi K;
461 mbedtls_mpi_init( &K );
462
463 /* DP = D mod P-1 */
464 if( DP != NULL )
465 {
466 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );
467 MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DP, D, &K ) );
468 }
469
470 /* DQ = D mod Q-1 */
471 if( DQ != NULL )
472 {
473 MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) );
474 MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DQ, D, &K ) );
475 }
476
477 /* QP = Q^{-1} mod P */
478 if( QP != NULL )
479 {
480 MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( QP, Q, P ) );
481 }
482
483 cleanup:
484 mbedtls_mpi_free( &K );
485
486 return( ret );
487 }
488
489 #endif /* MBEDTLS_RSA_C */
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