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[proxmark3-svn] / client / hardnested / hardnested_bruteforce.c
1 //-----------------------------------------------------------------------------
2 // Copyright (C) 2016, 2017 by piwi
3 //
4 // This code is licensed to you under the terms of the GNU GPL, version 2 or,
5 // at your option, any later version. See the LICENSE.txt file for the text of
6 // the license.
7 //-----------------------------------------------------------------------------
8 // Implements a card only attack based on crypto text (encrypted nonces
9 // received during a nested authentication) only. Unlike other card only
10 // attacks this doesn't rely on implementation errors but only on the
11 // inherent weaknesses of the crypto1 cypher. Described in
12 // Carlo Meijer, Roel Verdult, "Ciphertext-only Cryptanalysis on Hardened
13 // Mifare Classic Cards" in Proceedings of the 22nd ACM SIGSAC Conference on
14 // Computer and Communications Security, 2015
15 //-----------------------------------------------------------------------------
16 //
17 // brute forcing is based on @aczids bitsliced brute forcer
18 // https://github.com/aczid/crypto1_bs with some modifications. Mainly:
19 // - don't rollback. Start with 2nd byte of nonce instead
20 // - reuse results of filter subfunctions
21 // - reuse results of previous nonces if some first bits are identical
22 //
23 //-----------------------------------------------------------------------------
24 // aczid's Copyright notice:
25 //
26 // Bit-sliced Crypto-1 brute-forcing implementation
27 // Builds on the data structures returned by CraptEV1 craptev1_get_space(nonces, threshold, uid)
28 /*
29 Copyright (c) 2015-2016 Aram Verstegen
30
31 Permission is hereby granted, free of charge, to any person obtaining a copy
32 of this software and associated documentation files (the "Software"), to deal
33 in the Software without restriction, including without limitation the rights
34 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
35 copies of the Software, and to permit persons to whom the Software is
36 furnished to do so, subject to the following conditions:
37
38 The above copyright notice and this permission notice shall be included in
39 all copies or substantial portions of the Software.
40
41 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
42 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
43 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
44 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
45 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
46 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
47 THE SOFTWARE.
48 */
49
50 #include "hardnested_bruteforce.h"
51
52 #include <inttypes.h>
53 #include <stdbool.h>
54 #include <stdio.h>
55 #include <pthread.h>
56 #include <string.h>
57 #include <stdlib.h>
58 #include "proxmark3.h"
59 #include "cmdhfmfhard.h"
60 #include "hardnested_bf_core.h"
61 #include "ui.h"
62 #include "util.h"
63 #include "util_posix.h"
64 #include "crapto1/crapto1.h"
65 #include "parity.h"
66
67 #define NUM_BRUTE_FORCE_THREADS (num_CPUs())
68 #define DEFAULT_BRUTE_FORCE_RATE (120000000.0) // if benchmark doesn't succeed
69 #define TEST_BENCH_SIZE (6000) // number of odd and even states for brute force benchmark
70 #define TEST_BENCH_FILENAME "hardnested/bf_bench_data.bin"
71 //#define WRITE_BENCH_FILE
72
73 // debugging options
74 #define DEBUG_KEY_ELIMINATION
75 // #define DEBUG_BRUTE_FORCE
76
77 typedef enum {
78 EVEN_STATE = 0,
79 ODD_STATE = 1
80 } odd_even_t;
81
82 static uint32_t nonces_to_bruteforce = 0;
83 static uint32_t bf_test_nonce[256];
84 static uint8_t bf_test_nonce_2nd_byte[256];
85 static uint8_t bf_test_nonce_par[256];
86 static uint32_t bucket_count = 0;
87 static statelist_t* buckets[128];
88 static uint32_t keys_found = 0;
89 static uint64_t num_keys_tested;
90
91
92 uint8_t trailing_zeros(uint8_t byte)
93 {
94 static const uint8_t trailing_zeros_LUT[256] = {
95 8, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
96 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
97 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
98 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
99 6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
100 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
101 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
102 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
103 7, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
104 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
105 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
106 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
107 6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
108 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
109 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
110 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
111 };
112
113 return trailing_zeros_LUT[byte];
114 }
115
116
117 bool verify_key(uint32_t cuid, noncelist_t *nonces, uint8_t *best_first_bytes, uint32_t odd, uint32_t even)
118 {
119 struct Crypto1State pcs;
120 for (uint16_t test_first_byte = 1; test_first_byte < 256; test_first_byte++) {
121 noncelistentry_t *test_nonce = nonces[best_first_bytes[test_first_byte]].first;
122 while (test_nonce != NULL) {
123 pcs.odd = odd;
124 pcs.even = even;
125 lfsr_rollback_byte(&pcs, (cuid >> 24) ^ best_first_bytes[0], true);
126 for (int8_t byte_pos = 3; byte_pos >= 0; byte_pos--) {
127 uint8_t test_par_enc_bit = (test_nonce->par_enc >> byte_pos) & 0x01; // the encoded parity bit
128 uint8_t test_byte_enc = (test_nonce->nonce_enc >> (8*byte_pos)) & 0xff; // the encoded nonce byte
129 uint8_t test_byte_dec = crypto1_byte(&pcs, test_byte_enc /* ^ (cuid >> (8*byte_pos)) */, true) ^ test_byte_enc; // decode the nonce byte
130 uint8_t ks_par = filter(pcs.odd); // the keystream bit to encode/decode the parity bit
131 uint8_t test_par_enc2 = ks_par ^ evenparity8(test_byte_dec); // determine the decoded byte's parity and encode it
132 if (test_par_enc_bit != test_par_enc2) {
133 return false;
134 }
135 }
136 test_nonce = test_nonce->next;
137 }
138 }
139 return true;
140 }
141
142
143 static void* crack_states_thread(void* x){
144
145 struct arg {
146 bool silent;
147 int thread_ID;
148 uint32_t cuid;
149 uint32_t num_acquired_nonces;
150 uint64_t maximum_states;
151 noncelist_t *nonces;
152 uint8_t* best_first_bytes;
153 } *thread_arg;
154
155 thread_arg = (struct arg *)x;
156 const int thread_id = thread_arg->thread_ID;
157 uint32_t current_bucket = thread_id;
158 while(current_bucket < bucket_count){
159 statelist_t *bucket = buckets[current_bucket];
160 if(bucket){
161 #if defined (DEBUG_BRUTE_FORCE)
162 printf("Thread %u starts working on bucket %u\n", thread_id, current_bucket);
163 #endif
164 const uint64_t key = crack_states_bitsliced(thread_arg->cuid, thread_arg->best_first_bytes, bucket, &keys_found, &num_keys_tested, nonces_to_bruteforce, bf_test_nonce_2nd_byte, thread_arg->nonces);
165 if(key != -1){
166 __sync_fetch_and_add(&keys_found, 1);
167 char progress_text[80];
168 sprintf(progress_text, "Brute force phase completed. Key found: %012" PRIx64, key);
169 hardnested_print_progress(thread_arg->num_acquired_nonces, progress_text, 0.0, 0);
170 break;
171 } else if(keys_found){
172 break;
173 } else {
174 if (!thread_arg->silent) {
175 char progress_text[80];
176 sprintf(progress_text, "Brute force phase: %6.02f%%", 100.0*(float)num_keys_tested/(float)(thread_arg->maximum_states));
177 float remaining_bruteforce = thread_arg->nonces[thread_arg->best_first_bytes[0]].expected_num_brute_force - (float)num_keys_tested/2;
178 hardnested_print_progress(thread_arg->num_acquired_nonces, progress_text, remaining_bruteforce, 5000);
179 }
180 }
181 }
182 current_bucket += NUM_BRUTE_FORCE_THREADS;
183 }
184 return NULL;
185 }
186
187
188 void prepare_bf_test_nonces(noncelist_t *nonces, uint8_t best_first_byte)
189 {
190 // we do bitsliced brute forcing with best_first_bytes[0] only.
191 // Extract the corresponding 2nd bytes
192 noncelistentry_t *test_nonce = nonces[best_first_byte].first;
193 uint32_t i = 0;
194 while (test_nonce != NULL) {
195 bf_test_nonce[i] = test_nonce->nonce_enc;
196 bf_test_nonce_par[i] = test_nonce->par_enc;
197 bf_test_nonce_2nd_byte[i] = (test_nonce->nonce_enc >> 16) & 0xff;
198 test_nonce = test_nonce->next;
199 i++;
200 }
201 nonces_to_bruteforce = i;
202
203 // printf("Nonces to bruteforce: %d\n", nonces_to_bruteforce);
204 // printf("Common bits of first 4 2nd nonce bytes (before sorting): %u %u %u\n",
205 // trailing_zeros(bf_test_nonce_2nd_byte[1] ^ bf_test_nonce_2nd_byte[0]),
206 // trailing_zeros(bf_test_nonce_2nd_byte[2] ^ bf_test_nonce_2nd_byte[1]),
207 // trailing_zeros(bf_test_nonce_2nd_byte[3] ^ bf_test_nonce_2nd_byte[2]));
208
209 uint8_t best_4[4] = {0};
210 int sum_best = -1;
211 for (uint16_t n1 = 0; n1 < nonces_to_bruteforce; n1++) {
212 for (uint16_t n2 = 0; n2 < nonces_to_bruteforce; n2++) {
213 if (n2 != n1) {
214 for (uint16_t n3 = 0; n3 < nonces_to_bruteforce; n3++) {
215 if ((n3 != n2 && n3 != n1) || nonces_to_bruteforce < 3
216 // && trailing_zeros(bf_test_nonce_2nd_byte[n1] ^ bf_test_nonce_2nd_byte[n2])
217 // > trailing_zeros(bf_test_nonce_2nd_byte[n2] ^ bf_test_nonce_2nd_byte[n3])
218 ) {
219 for (uint16_t n4 = 0; n4 < nonces_to_bruteforce; n4++) {
220 if ((n4 != n3 && n4 != n2 && n4 != n1) || nonces_to_bruteforce < 4
221 // && trailing_zeros(bf_test_nonce_2nd_byte[n2] ^ bf_test_nonce_2nd_byte[n3])
222 // > trailing_zeros(bf_test_nonce_2nd_byte[n3] ^ bf_test_nonce_2nd_byte[n4])
223 ) {
224 int sum = nonces_to_bruteforce > 1 ? trailing_zeros(bf_test_nonce_2nd_byte[n1] ^ bf_test_nonce_2nd_byte[n2]) : 0.0
225 + nonces_to_bruteforce > 2 ? trailing_zeros(bf_test_nonce_2nd_byte[n2] ^ bf_test_nonce_2nd_byte[n3]) : 0.0
226 + nonces_to_bruteforce > 3 ? trailing_zeros(bf_test_nonce_2nd_byte[n3] ^ bf_test_nonce_2nd_byte[n4]) : 0.0;
227 if (sum > sum_best) {
228 sum_best = sum;
229 best_4[0] = n1;
230 best_4[1] = n2;
231 best_4[2] = n3;
232 best_4[3] = n4;
233 }
234 }
235 }
236 }
237 }
238 }
239 }
240 }
241
242 uint32_t bf_test_nonce_temp[4];
243 uint8_t bf_test_nonce_par_temp[4];
244 uint8_t bf_test_nonce_2nd_byte_temp[4];
245 for (uint8_t i = 0; i < 4 && i < nonces_to_bruteforce; i++) {
246 bf_test_nonce_temp[i] = bf_test_nonce[best_4[i]];
247
248 bf_test_nonce_par_temp[i] = bf_test_nonce_par[best_4[i]];
249 bf_test_nonce_2nd_byte_temp[i] = bf_test_nonce_2nd_byte[best_4[i]];
250 }
251 for (uint8_t i = 0; i < 4 && i < nonces_to_bruteforce; i++) {
252 bf_test_nonce[i] = bf_test_nonce_temp[i];
253 bf_test_nonce_par[i] = bf_test_nonce_par_temp[i];
254 bf_test_nonce_2nd_byte[i] = bf_test_nonce_2nd_byte_temp[i];
255 }
256 }
257
258
259 #if defined (WRITE_BENCH_FILE)
260 static void write_benchfile(statelist_t *candidates) {
261
262 printf("Writing brute force benchmark data...");
263 FILE *benchfile = fopen(TEST_BENCH_FILENAME, "wb");
264 fwrite(&nonces_to_bruteforce, 1, sizeof(nonces_to_bruteforce), benchfile);
265 for (uint32_t i = 0; i < nonces_to_bruteforce; i++) {
266 fwrite(&(bf_test_nonce[i]), 1, sizeof(bf_test_nonce[i]), benchfile);
267 fwrite(&(bf_test_nonce_par[i]), 1, sizeof(bf_test_nonce_par[i]), benchfile);
268 }
269 uint32_t num_states = MIN(candidates->len[EVEN_STATE], TEST_BENCH_SIZE);
270 fwrite(&num_states, 1, sizeof(num_states), benchfile);
271 for (uint32_t i = 0; i < num_states; i++) {
272 fwrite(&(candidates->states[EVEN_STATE][i]), 1, sizeof(uint32_t), benchfile);
273 }
274 num_states = MIN(candidates->len[ODD_STATE], TEST_BENCH_SIZE);
275 fwrite(&num_states, 1, sizeof(num_states), benchfile);
276 for (uint32_t i = 0; i < num_states; i++) {
277 fwrite(&(candidates->states[ODD_STATE][i]), 1, sizeof(uint32_t), benchfile);
278 }
279 fclose(benchfile);
280 printf("done.\n");
281 }
282 #endif
283
284
285 bool brute_force_bs(float *bf_rate, statelist_t *candidates, uint32_t cuid, uint32_t num_acquired_nonces, uint64_t maximum_states, noncelist_t *nonces, uint8_t *best_first_bytes)
286 {
287 #if defined (WRITE_BENCH_FILE)
288 write_benchfile(candidates);
289 #endif
290 bool silent = (bf_rate != NULL);
291
292 // if (!silent) {
293 // PrintAndLog("Brute force phase starting.");
294 // PrintAndLog("Using %u-bit bitslices", MAX_BITSLICES);
295 // }
296
297 keys_found = 0;
298 num_keys_tested = 0;
299
300 bitslice_test_nonces(nonces_to_bruteforce, bf_test_nonce, bf_test_nonce_par);
301
302 // count number of states to go
303 bucket_count = 0;
304 for (statelist_t *p = candidates; p != NULL; p = p->next) {
305 if (p->states[ODD_STATE] != NULL && p->states[EVEN_STATE] != NULL) {
306 buckets[bucket_count] = p;
307 bucket_count++;
308 }
309 }
310
311 uint64_t start_time = msclock();
312 // enumerate states using all hardware threads, each thread handles one bucket
313 // if (!silent) {
314 // PrintAndLog("Starting %u cracking threads to search %u buckets containing a total of %" PRIu64" states...\n", NUM_BRUTE_FORCE_THREADS, bucket_count, maximum_states);
315 // printf("Common bits of first 4 2nd nonce bytes: %u %u %u\n",
316 // trailing_zeros(bf_test_nonce_2nd_byte[1] ^ bf_test_nonce_2nd_byte[0]),
317 // trailing_zeros(bf_test_nonce_2nd_byte[2] ^ bf_test_nonce_2nd_byte[1]),
318 // trailing_zeros(bf_test_nonce_2nd_byte[3] ^ bf_test_nonce_2nd_byte[2]));
319 // }
320
321 pthread_t threads[NUM_BRUTE_FORCE_THREADS];
322 struct args {
323 bool silent;
324 int thread_ID;
325 uint32_t cuid;
326 uint32_t num_acquired_nonces;
327 uint64_t maximum_states;
328 noncelist_t *nonces;
329 uint8_t *best_first_bytes;
330 } thread_args[NUM_BRUTE_FORCE_THREADS];
331
332 for(uint32_t i = 0; i < NUM_BRUTE_FORCE_THREADS; i++){
333 thread_args[i].thread_ID = i;
334 thread_args[i].silent = silent;
335 thread_args[i].cuid = cuid;
336 thread_args[i].num_acquired_nonces = num_acquired_nonces;
337 thread_args[i].maximum_states = maximum_states;
338 thread_args[i].nonces = nonces;
339 thread_args[i].best_first_bytes = best_first_bytes;
340 pthread_create(&threads[i], NULL, crack_states_thread, (void*)&thread_args[i]);
341 }
342 for(uint32_t i = 0; i < NUM_BRUTE_FORCE_THREADS; i++){
343 pthread_join(threads[i], 0);
344 }
345
346 uint64_t elapsed_time = msclock() - start_time;
347
348 // if (!silent) {
349 // printf("Brute force completed after testing %" PRIu64" (2^%1.1f) keys in %1.1f seconds at a rate of %1.0f (2^%1.1f) keys per second.\n",
350 // num_keys_tested,
351 // log(num_keys_tested) / log(2.0),
352 // (float)elapsed_time/1000.0,
353 // (float)num_keys_tested / ((float)elapsed_time / 1000.0),
354 // log((float)num_keys_tested / ((float)elapsed_time/1000.0)) / log(2.0));
355 // }
356
357 if (bf_rate != NULL) {
358 *bf_rate = (float)num_keys_tested / ((float)elapsed_time / 1000.0);
359 }
360
361 return (keys_found != 0);
362 }
363
364
365 static bool read_bench_data(statelist_t *test_candidates) {
366
367 size_t bytes_read = 0;
368 uint32_t temp = 0;
369 uint32_t num_states = 0;
370 uint32_t states_read = 0;
371
372 char bench_file_path[strlen(get_my_executable_directory()) + strlen(TEST_BENCH_FILENAME) + 1];
373 strcpy(bench_file_path, get_my_executable_directory());
374 strcat(bench_file_path, TEST_BENCH_FILENAME);
375
376 FILE *benchfile = fopen(bench_file_path, "rb");
377 if (benchfile == NULL) {
378 return false;
379 }
380 bytes_read = fread(&nonces_to_bruteforce, 1, sizeof(nonces_to_bruteforce), benchfile);
381 if (bytes_read != sizeof(nonces_to_bruteforce)) {
382 fclose(benchfile);
383 return false;
384 }
385 for (uint16_t i = 0; i < nonces_to_bruteforce && i < 256; i++) {
386 bytes_read = fread(&bf_test_nonce[i], 1, sizeof(uint32_t), benchfile);
387 if (bytes_read != sizeof(uint32_t)) {
388 fclose(benchfile);
389 return false;
390 }
391 bf_test_nonce_2nd_byte[i] = (bf_test_nonce[i] >> 16) & 0xff;
392 bytes_read = fread(&bf_test_nonce_par[i], 1, sizeof(uint8_t), benchfile);
393 if (bytes_read != sizeof(uint8_t)) {
394 fclose(benchfile);
395 return false;
396 }
397 }
398 bytes_read = fread(&num_states, 1, sizeof(uint32_t), benchfile);
399 if (bytes_read != sizeof(uint32_t)) {
400 fclose(benchfile);
401 return false;
402 }
403 for (states_read = 0; states_read < MIN(num_states, TEST_BENCH_SIZE); states_read++) {
404 bytes_read = fread(test_candidates->states[EVEN_STATE] + states_read, 1, sizeof(uint32_t), benchfile);
405 if (bytes_read != sizeof(uint32_t)) {
406 fclose(benchfile);
407 return false;
408 }
409 }
410 for (uint32_t i = states_read; i < TEST_BENCH_SIZE; i++) {
411 test_candidates->states[EVEN_STATE][i] = test_candidates->states[EVEN_STATE][i-states_read];
412 }
413 for (uint32_t i = states_read; i < num_states; i++) {
414 bytes_read = fread(&temp, 1, sizeof(uint32_t), benchfile);
415 if (bytes_read != sizeof(uint32_t)) {
416 fclose(benchfile);
417 return false;
418 }
419 }
420 for (states_read = 0; states_read < MIN(num_states, TEST_BENCH_SIZE); states_read++) {
421 bytes_read = fread(test_candidates->states[ODD_STATE] + states_read, 1, sizeof(uint32_t), benchfile);
422 if (bytes_read != sizeof(uint32_t)) {
423 fclose(benchfile);
424 return false;
425 }
426 }
427 for (uint32_t i = states_read; i < TEST_BENCH_SIZE; i++) {
428 test_candidates->states[ODD_STATE][i] = test_candidates->states[ODD_STATE][i-states_read];
429 }
430
431 fclose(benchfile);
432 return true;
433 }
434
435
436 float brute_force_benchmark()
437 {
438 statelist_t test_candidates[NUM_BRUTE_FORCE_THREADS];
439
440 test_candidates[0].states[ODD_STATE] = malloc((TEST_BENCH_SIZE+1) * sizeof(uint32_t));
441 test_candidates[0].states[EVEN_STATE] = malloc((TEST_BENCH_SIZE+1) * sizeof(uint32_t));
442 for (uint8_t i = 0; i < NUM_BRUTE_FORCE_THREADS - 1; i++){
443 test_candidates[i].next = test_candidates + i + 1;
444 test_candidates[i+1].states[ODD_STATE] = test_candidates[0].states[ODD_STATE];
445 test_candidates[i+1].states[EVEN_STATE] = test_candidates[0].states[EVEN_STATE];
446 }
447 test_candidates[NUM_BRUTE_FORCE_THREADS-1].next = NULL;
448
449 if (!read_bench_data(test_candidates)) {
450 PrintAndLog("Couldn't read benchmark data. Assuming brute force rate of %1.0f states per second", DEFAULT_BRUTE_FORCE_RATE);
451 return DEFAULT_BRUTE_FORCE_RATE;
452 }
453
454 for (uint8_t i = 0; i < NUM_BRUTE_FORCE_THREADS; i++) {
455 test_candidates[i].len[ODD_STATE] = TEST_BENCH_SIZE;
456 test_candidates[i].len[EVEN_STATE] = TEST_BENCH_SIZE;
457 test_candidates[i].states[ODD_STATE][TEST_BENCH_SIZE] = -1;
458 test_candidates[i].states[EVEN_STATE][TEST_BENCH_SIZE] = -1;
459 }
460
461 uint64_t maximum_states = TEST_BENCH_SIZE*TEST_BENCH_SIZE*(uint64_t)NUM_BRUTE_FORCE_THREADS;
462
463 float bf_rate;
464 brute_force_bs(&bf_rate, test_candidates, 0, 0, maximum_states, NULL, 0);
465
466 free(test_candidates[0].states[ODD_STATE]);
467 free(test_candidates[0].states[EVEN_STATE]);
468
469 return bf_rate;
470 }
471
472
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