aboutsummaryrefslogtreecommitdiff
path: root/rsa.c
blob: 6c1e12e6837300e9ac72482ae392d2c1e6449537 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
/*
 * rsa.c
 * -----
 * Basic RSA functions based on Cryptech ModExp core.
 *
 * The mix of what we're doing in software vs what we're doing on the
 * FPGA is a moving target.  Goal for now is to have the bits we need
 * to do in C be straightforward to review and as simple as possible
 * (but no simpler).
 *
 * Much of the code in this module is based, at least loosely, on Tom
 * St Denis's libtomcrypt code.  
 *
 * Authors: Rob Austein
 * Copyright (c) 2015, SUNET
 *
 * Redistribution and use in source and binary forms, with or
 * without modification, are permitted provided that the following
 * conditions are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in
 *    the documentation and/or other materials provided with the
 *    distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
 * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>

#include "cryptech.h"

/*
 * Use "Tom's Fast Math" library for our bignum implementation.  This
 * particular implementation has a couple of nice features:
 *
 * - The code is relatively readable, thus reviewable.
 *
 * - The bignum representation doesn't use dynamic memory, which
 *   simplifies things for us.
 *
 * The price tag for not using dynamic memory is that libtfm has to be
 * configured to know about the largest bignum one wants it to be able
 * to support at compile time.  This should not be a serious problem.
 */

#include "tfm.h"

/*
 * Whether we want debug output.
 */

static int debug = 0;

void hal_rsa_set_debug(const int onoff)
{
  debug = onoff;
}

/*
 * Check a result, report on failure if debugging, pass failures up
 * the chain.
 */

#define check(_expr_)                                                   \
  do {                                                                  \
    hal_error_t _err = (_expr_);                                        \
    if (_err != HAL_OK && debug)                                        \
      printf("%s failed: %s\n", #_expr_, hal_error_string(_err));       \
    if (_err != HAL_OK)                                                 \
      return _err;                                                      \
  } while (0)

/*
 * RSA key implementation.  This structure type is private to this
 * module, anything else that needs to touch one of these just gets a
 * typed opaque pointer.  We do, however, export the size, so that we
 * can make memory allocation the caller's problem (well, maybe).
 */

struct rsa_key {
  hal_rsa_key_type_t type;      /* What kind of key this is */
  fp_int n;                     /* The modulus */
  fp_int e;                     /* Public exponent */
  fp_int d;                     /* Private exponent */
  fp_int p;                     /* 1st prime factor */
  fp_int q;                     /* 2nd prime factor */
  fp_int u;                     /* 1/q mod p */
  fp_int dP;                    /* d mod (p - 1) */
  fp_int dQ;                    /* d mod (q - 1) */
};

const size_t hal_rsa_key_t_size = sizeof(struct rsa_key);

/*
 * In the long run we want a full RSA implementation, or enough of one
 * to cover what we need in PKCS #11.  For the moment, though, the
 * most urgent thing is to see whether this approach to performing the
 * CRT calculation works (and is any faster), followed by whether we
 * can use this approach for key generation.
 *
 * So don't worry about whether the following functions are what we
 * want in the long run, they'll probably evolve as we go.
 */

#warning Should do RSA blinding, skipping for now

#define lose(_code_)                                    \
  do { err = _code_; goto fail; } while (0)

#define FP_CHECK(_expr_)                                \
  do {                                                  \
    switch (_expr_) {                                   \
    case FP_OKAY: break;                                \
    case FP_VAL:  lose(HAL_ERROR_BAD_ARGUMENTS);        \
    case FP_MEM:  lose(HAL_ERROR_ALLOCATION_FAILURE);   \
    default:      lose(HAL_ERROR_IMPOSSIBLE);  		\
    }                                                   \
  } while (0)


/*
 * Unpack a bignum into a byte array, with length check.
 */

static hal_error_t unpack_fp(fp_int *bn, uint8_t *buffer, const size_t length)
{
  hal_error_t err = HAL_OK;

  assert(bn != NULL && buffer != NULL);

  const size_t bytes = fp_unsigned_bin_size(bn);

  if (bytes > length)
    lose(HAL_ERROR_RESULT_TOO_LONG);

  memset(buffer, 0, length);
  fp_to_unsigned_bin(bn, buffer + length - bytes);

 fail:
  return err;
}

/*
 * Unwrap bignums into byte arrays, feeds them into hal_modexp(), and
 * wrap result back up as a bignum.
 */

static hal_error_t modexp_fp(fp_int *msg, fp_int *exp, fp_int *mod, fp_int *res)
{
  hal_error_t err = HAL_OK;

  assert(msg != NULL && exp != NULL && mod != NULL && res != NULL);

  const size_t msg_len = fp_unsigned_bin_size(msg);
  const size_t exp_len = fp_unsigned_bin_size(exp);
  const size_t mod_len = fp_unsigned_bin_size(mod);

  const size_t len = (MAX(MAX(msg_len, exp_len), mod_len) + 3) & ~3;

  uint8_t msgbuf[len], expbuf[len], modbuf[len], resbuf[len];

  if ((err = unpack_fp(msg, msgbuf, sizeof(msgbuf))) != HAL_OK ||
      (err = unpack_fp(exp, expbuf, sizeof(expbuf))) != HAL_OK ||
      (err = unpack_fp(mod, modbuf, sizeof(modbuf))) != HAL_OK ||
      (err = hal_modexp(msgbuf, sizeof(msgbuf),
                        expbuf, sizeof(expbuf),
                        modbuf, sizeof(modbuf),
                        resbuf, sizeof(resbuf))) != HAL_OK)
    goto fail;

  fp_read_unsigned_bin(res, resbuf, sizeof(resbuf));

 fail:
  memset(msgbuf, 0, sizeof(msgbuf));
  memset(expbuf, 0, sizeof(expbuf));
  memset(modbuf, 0, sizeof(modbuf));
  return err;
}


/*
 * Clear a key.  We might want to do something a bit more energetic
 * than plain old memset() eventually.
 */

void hal_rsa_key_clear(hal_rsa_key_t key)
{
  if (key.key != NULL)
    memset(key.key, 0, sizeof(struct rsa_key));
}

/*
 * Load a key from raw components.  This is a simplistic version: we
 * don't attempt to generate missing private key components, we just
 * reject the key if it doesn't have everything we expect.
 *
 * In theory, the only things we'd really need for the private key if
 * we were being nicer about this would be e, p, and q, as we could
 * calculate everything else from them.
 */

hal_error_t hal_rsa_key_load(const hal_rsa_key_type_t type,
                             hal_rsa_key_t *key_,
                             void *keybuf, const size_t keybuf_len,
                             const uint8_t * const n,  const size_t n_len,
                             const uint8_t * const e,  const size_t e_len,
                             const uint8_t * const d,  const size_t d_len,
                             const uint8_t * const p,  const size_t p_len,
                             const uint8_t * const q,  const size_t q_len,
                             const uint8_t * const u,  const size_t u_len,
                             const uint8_t * const dP, const size_t dP_len,
                             const uint8_t * const dQ, const size_t dQ_len)
{
  if (key_ == NULL || keybuf == NULL || keybuf_len < sizeof(struct rsa_key))
    return HAL_ERROR_BAD_ARGUMENTS;

  memset(keybuf, 0, keybuf_len);

  struct rsa_key *key = keybuf;

  key->type = type;

#define _(x) do { fp_init(&key->x); if (x == NULL) goto fail; fp_read_unsigned_bin(&key->x, (uint8_t *) x, x##_len); } while (0)
  switch (type) {
  case HAL_RSA_PRIVATE:
    _(d); _(p); _(q); _(u); _(dP); _(dQ);
  case HAL_RSA_PUBLIC:
    _(n); _(e);
    key_->key = key;
    return HAL_OK;
  }
#undef _

 fail:
  memset(key, 0, sizeof(*key));
  return HAL_ERROR_BAD_ARGUMENTS;
}

/*
 * RSA decyrption/signature using the Chinese Remainder Theorem
 * (Garner's formula).
 */

hal_error_t hal_rsa_crt(hal_rsa_key_t key_,
                        const uint8_t * const m,  const size_t m_len,
                        uint8_t * result, const size_t result_len)
{
  hal_error_t err = HAL_OK;
  struct rsa_key *key = key_.key;
  struct { fp_int t, msg, m1, m2; } tmp;

  fp_init(&tmp.t);
  fp_init(&tmp.msg);
  fp_init(&tmp.m1);
  fp_init(&tmp.m2);

  fp_read_unsigned_bin(&tmp.msg, (uint8_t *) m, m_len);

  /*
   * m1 = msg ** dP mod p
   * m2 = msg ** dQ mod q
   */
  if ((err = modexp_fp(&tmp.msg, &key->dP, &key->p, &tmp.m1)) != HAL_OK ||
      (err = modexp_fp(&tmp.msg, &key->dQ, &key->q, &tmp.m2)) != HAL_OK)
    goto fail;

  /*
   * t = m1 - m2.
   * Add zero (mod p) once or twice if necessary to get positive result.
   */
  fp_sub(&tmp.m1, &tmp.m2, &tmp.t);
  if (fp_cmp_d(&tmp.t, 0) == FP_LT)
    fp_add(&tmp.t, &key->p, &tmp.t);
  if (fp_cmp_d(&tmp.t, 0) == FP_LT)
    fp_add(&tmp.t, &key->p, &tmp.t);
  if (fp_cmp_d(&tmp.t, 0) == FP_LT)
    lose(HAL_ERROR_IMPOSSIBLE);

  /*
   * t = (t * u mod p) * q + m2
   */
  FP_CHECK(fp_mulmod(&tmp.t, &key->u, &key->p, &tmp.t));
  fp_mul(&tmp.t, &key->q, &tmp.t);
  fp_add(&tmp.t, &tmp.m2, &tmp.t);

  /*
   * t now holds result, write it back to caller
   */
  if ((err = unpack_fp(&tmp.t, result, result_len)) != HAL_OK)
    goto fail;

  /*
   * Done, fall through into cleanup.
   */

 fail:
  memset(&tmp, 0, sizeof(tmp));
  return err;
}

static hal_error_t find_prime(unsigned prime_length, fp_int *e, fp_int *result)
{
  uint8_t buffer[prime_length];
  hal_error_t err;
  fp_int t;

  /*
   * Get random bytes, munge a few bits, and stuff into a bignum.
   * Keep doing this until we find a result that's (probably) prime
   * and for which result - 1 is relatively prime with respect to e.
   */

  do {
    if ((err = hal_get_random(buffer, sizeof(buffer))) != HAL_OK)
      return err;
    buffer[0                 ] |= 0xc0;
    buffer[sizeof(buffer) - 1] |= 0x01;
    fp_read_unsigned_bin(result, buffer, sizeof(buffer));

  } while (!fp_isprime(result) ||
           (fp_sub_d(result, 1, &t), fp_gcd(&t, e, &t), fp_cmp_d(&t, 1) != FP_EQ));

  fp_zero(&t);
  return HAL_OK;
}

hal_error_t hal_rsa_gen(hal_rsa_key_t *key_,
                        void *keybuf, const size_t keybuf_len,
                        const unsigned key_length,
                        const unsigned long public_exponent)
{
  struct rsa_key *key = keybuf;
  hal_error_t err = HAL_OK;
  fp_int p_1, q_1;

  if (key_ == NULL || keybuf == NULL || keybuf_len < sizeof(struct rsa_key))
    return HAL_ERROR_BAD_ARGUMENTS;

  switch (key_length) {
  case bitsToBytes(1024):
  case bitsToBytes(2048):
  case bitsToBytes(4096):
  case bitsToBytes(8192):
    break;
  default:
    return HAL_ERROR_UNSUPPORTED_KEY;
  }

  switch (public_exponent) {
  case 0x010001:
    break;
  default:
    return HAL_ERROR_UNSUPPORTED_KEY;
  }

  /*
   * Initialize key
   */

  memset(keybuf, 0, keybuf_len);
  key->type = HAL_RSA_PRIVATE;
  fp_set(&key->e, public_exponent);

  /*
   * Find a good pair of prime numbers.
   */

  if ((err = find_prime(key_length / 2, &key->e, &key->p)) != HAL_OK ||
      (err = find_prime(key_length / 2, &key->e, &key->q)) != HAL_OK)
    return err;

  /*
   * Calculate remaining key components.
   */

  fp_sub_d(&key->p, 1, &p_1);
  fp_sub_d(&key->q, 1, &q_1);
  fp_mul(&key->p, &key->q, &key->n);                    /* n = p * q */
  fp_lcm(&p_1, &q_1, &key->d);
  FP_CHECK(fp_invmod(&key->e, &key->d, &key->d));       /* d = (1/e) % lcm(p-1, q-1) */
  FP_CHECK(fp_mod(&key->d, &p_1, &key->dP));            /* dP = d % (p-1) */
  FP_CHECK(fp_mod(&key->d, &q_1, &key->dQ));            /* dQ = d % (q-1) */
  FP_CHECK(fp_invmod(&key->q, &key->p, &key->u));       /* u = (1/q) % p */

  /* Fall through to cleanup */

 fail:
  fp_zero(&p_1);
  fp_zero(&q_1);
  return err;
}

/*
 * Local variables:
 * indent-tabs-mode: nil
 * End:
 */