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[proxmark3-svn] / client / cmdhfmfhard.c
1 //-----------------------------------------------------------------------------
2 // Copyright (C) 2015 piwi
3 // fiddled with 2016 Azcid (hardnested bitsliced Bruteforce imp)
4 // fiddled with 2016 Matrix ( sub testing of nonces while collecting )
5 // This code is licensed to you under the terms of the GNU GPL, version 2 or,
6 // at your option, any later version. See the LICENSE.txt file for the text of
7 // the license.
8 //-----------------------------------------------------------------------------
9 // Implements a card only attack based on crypto text (encrypted nonces
10 // received during a nested authentication) only. Unlike other card only
11 // attacks this doesn't rely on implementation errors but only on the
12 // inherent weaknesses of the crypto1 cypher. Described in
13 // Carlo Meijer, Roel Verdult, "Ciphertext-only Cryptanalysis on Hardened
14 // Mifare Classic Cards" in Proceedings of the 22nd ACM SIGSAC Conference on
15 // Computer and Communications Security, 2015
16 //-----------------------------------------------------------------------------
17 #include "cmdhfmfhard.h"
18 #include "cmdhw.h"
19
20 #define CONFIDENCE_THRESHOLD 0.95 // Collect nonces until we are certain enough that the following brute force is successfull
21 #define GOOD_BYTES_REQUIRED 13 // default 28, could be smaller == faster
22 #define NONCES_THRESHOLD 5000 // every N nonces check if we can crack the key
23 #define CRACKING_THRESHOLD 36.0f //38.50f // as 2^38.5
24 #define MAX_BUCKETS 128
25
26 #define END_OF_LIST_MARKER 0xFFFFFFFF
27
28 static const float p_K[257] = { // the probability that a random nonce has a Sum Property == K
29 0.0290, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
30 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
31 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
32 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
33 0.0083, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
34 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
35 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
36 0.0006, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
37 0.0339, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
38 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
39 0.0048, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
40 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
41 0.0934, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
42 0.0119, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
43 0.0489, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
44 0.0602, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
45 0.4180, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
46 0.0602, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
47 0.0489, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
48 0.0119, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
49 0.0934, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
50 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
51 0.0048, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
52 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
53 0.0339, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
54 0.0006, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
55 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
56 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
57 0.0083, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
58 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
59 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
60 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
61 0.0290 };
62
63 typedef struct noncelistentry {
64 uint32_t nonce_enc;
65 uint8_t par_enc;
66 void *next;
67 } noncelistentry_t;
68
69 typedef struct noncelist {
70 uint16_t num;
71 uint16_t Sum;
72 uint16_t Sum8_guess;
73 uint8_t BitFlip[2];
74 float Sum8_prob;
75 bool updated;
76 noncelistentry_t *first;
77 float score1;
78 uint_fast8_t score2;
79 } noncelist_t;
80
81 static size_t nonces_to_bruteforce = 0;
82 static noncelistentry_t *brute_force_nonces[256];
83 static uint32_t cuid = 0;
84 static noncelist_t nonces[256];
85 static uint8_t best_first_bytes[256];
86 static uint16_t first_byte_Sum = 0;
87 static uint16_t first_byte_num = 0;
88 static uint16_t num_good_first_bytes = 0;
89 static uint64_t maximum_states = 0;
90 static uint64_t known_target_key;
91 static bool write_stats = false;
92 static FILE *fstats = NULL;
93
94
95 typedef enum {
96 EVEN_STATE = 0,
97 ODD_STATE = 1
98 } odd_even_t;
99
100 #define STATELIST_INDEX_WIDTH 16
101 #define STATELIST_INDEX_SIZE (1<<STATELIST_INDEX_WIDTH)
102
103 typedef struct {
104 uint32_t *states[2];
105 uint32_t len[2];
106 uint32_t *index[2][STATELIST_INDEX_SIZE];
107 } partial_indexed_statelist_t;
108
109 typedef struct {
110 uint32_t *states[2];
111 uint32_t len[2];
112 void* next;
113 } statelist_t;
114
115
116 static partial_indexed_statelist_t partial_statelist[17];
117 static partial_indexed_statelist_t statelist_bitflip;
118 static statelist_t *candidates = NULL;
119
120 bool field_off = false;
121
122 uint64_t foundkey = 0;
123 size_t keys_found = 0;
124 size_t bucket_count = 0;
125 statelist_t* buckets[MAX_BUCKETS];
126 static uint64_t total_states_tested = 0;
127 size_t thread_count = 4;
128
129 // these bitsliced states will hold identical states in all slices
130 bitslice_t bitsliced_rollback_byte[ROLLBACK_SIZE];
131
132 // arrays of bitsliced states with identical values in all slices
133 bitslice_t bitsliced_encrypted_nonces[NONCE_TESTS][STATE_SIZE];
134 bitslice_t bitsliced_encrypted_parity_bits[NONCE_TESTS][ROLLBACK_SIZE];
135
136 #define EXACT_COUNT
137
138 static bool generate_candidates(uint16_t, uint16_t);
139 static bool brute_force(void);
140
141 static int add_nonce(uint32_t nonce_enc, uint8_t par_enc)
142 {
143 uint8_t first_byte = nonce_enc >> 24;
144 noncelistentry_t *p1 = nonces[first_byte].first;
145 noncelistentry_t *p2 = NULL;
146
147 if (p1 == NULL) { // first nonce with this 1st byte
148 first_byte_num++;
149 first_byte_Sum += evenparity32((nonce_enc & 0xff000000) | (par_enc & 0x08));
150 // printf("Adding nonce 0x%08x, par_enc 0x%02x, parity(0x%08x) = %d\n",
151 // nonce_enc,
152 // par_enc,
153 // (nonce_enc & 0xff000000) | (par_enc & 0x08) |0x01,
154 // parity((nonce_enc & 0xff000000) | (par_enc & 0x08));
155 }
156
157 while (p1 != NULL && (p1->nonce_enc & 0x00ff0000) < (nonce_enc & 0x00ff0000)) {
158 p2 = p1;
159 p1 = p1->next;
160 }
161
162 if (p1 == NULL) { // need to add at the end of the list
163 if (p2 == NULL) { // list is empty yet. Add first entry.
164 p2 = nonces[first_byte].first = malloc(sizeof(noncelistentry_t));
165 } else { // add new entry at end of existing list.
166 p2 = p2->next = malloc(sizeof(noncelistentry_t));
167 }
168 if (p2 == NULL) return 0; // memory allocation failed
169 }
170 else if ((p1->nonce_enc & 0x00ff0000) != (nonce_enc & 0x00ff0000)) { // found distinct 2nd byte. Need to insert.
171 if (p2 == NULL) { // need to insert at start of list
172 p2 = nonces[first_byte].first = malloc(sizeof(noncelistentry_t));
173 } else {
174 p2 = p2->next = malloc(sizeof(noncelistentry_t));
175 }
176 if (p2 == NULL) return 0; // memory allocation failed
177 } else {
178 return 0; // we have seen this 2nd byte before. Nothing to add or insert.
179 }
180
181 // add or insert new data
182 p2->next = p1;
183 p2->nonce_enc = nonce_enc;
184 p2->par_enc = par_enc;
185
186 if(nonces_to_bruteforce < 256){
187 brute_force_nonces[nonces_to_bruteforce] = p2;
188 nonces_to_bruteforce++;
189 }
190
191 nonces[first_byte].num++;
192 nonces[first_byte].Sum += evenparity32((nonce_enc & 0x00ff0000) | (par_enc & 0x04));
193 nonces[first_byte].updated = true; // indicates that we need to recalculate the Sum(a8) probability for this first byte
194
195 return 1; // new nonce added
196 }
197
198 static void init_nonce_memory(void)
199 {
200 for (uint16_t i = 0; i < 256; i++) {
201 nonces[i].num = 0;
202 nonces[i].Sum = 0;
203 nonces[i].Sum8_guess = 0;
204 nonces[i].Sum8_prob = 0.0;
205 nonces[i].updated = true;
206 nonces[i].first = NULL;
207 }
208 first_byte_num = 0;
209 first_byte_Sum = 0;
210 num_good_first_bytes = 0;
211 }
212
213 static void free_nonce_list(noncelistentry_t *p)
214 {
215 if (p == NULL) {
216 return;
217 } else {
218 free_nonce_list(p->next);
219 free(p);
220 }
221 }
222
223 static void free_nonces_memory(void)
224 {
225 for (uint16_t i = 0; i < 256; i++) {
226 free_nonce_list(nonces[i].first);
227 }
228 }
229
230 static uint16_t PartialSumProperty(uint32_t state, odd_even_t odd_even)
231 {
232 uint16_t sum = 0;
233 for (uint16_t j = 0; j < 16; j++) {
234 uint32_t st = state;
235 uint16_t part_sum = 0;
236 if (odd_even == ODD_STATE) {
237 for (uint16_t i = 0; i < 5; i++) {
238 part_sum ^= filter(st);
239 st = (st << 1) | ((j >> (3-i)) & 0x01) ;
240 }
241 part_sum ^= 1; // XOR 1 cancelled out for the other 8 bits
242 } else {
243 for (uint16_t i = 0; i < 4; i++) {
244 st = (st << 1) | ((j >> (3-i)) & 0x01) ;
245 part_sum ^= filter(st);
246 }
247 }
248 sum += part_sum;
249 }
250 return sum;
251 }
252
253 // static uint16_t SumProperty(struct Crypto1State *s)
254 // {
255 // uint16_t sum_odd = PartialSumProperty(s->odd, ODD_STATE);
256 // uint16_t sum_even = PartialSumProperty(s->even, EVEN_STATE);
257 // return (sum_odd*(16-sum_even) + (16-sum_odd)*sum_even);
258 // }
259
260 static double p_hypergeometric(uint16_t N, uint16_t K, uint16_t n, uint16_t k)
261 {
262 // for efficient computation we are using the recursive definition
263 // (K-k+1) * (n-k+1)
264 // P(X=k) = P(X=k-1) * --------------------
265 // k * (N-K-n+k)
266 // and
267 // (N-K)*(N-K-1)*...*(N-K-n+1)
268 // P(X=0) = -----------------------------
269 // N*(N-1)*...*(N-n+1)
270
271 if (n-k > N-K || k > K) return 0.0; // avoids log(x<=0) in calculation below
272 if (k == 0) {
273 // use logarithms to avoid overflow with huge factorials (double type can only hold 170!)
274 double log_result = 0.0;
275 for (int16_t i = N-K; i >= N-K-n+1; i--) {
276 log_result += log(i);
277 }
278 for (int16_t i = N; i >= N-n+1; i--) {
279 log_result -= log(i);
280 }
281 return exp(log_result);
282 } else {
283 if (n-k == N-K) { // special case. The published recursion below would fail with a divide by zero exception
284 double log_result = 0.0;
285 for (int16_t i = k+1; i <= n; i++) {
286 log_result += log(i);
287 }
288 for (int16_t i = K+1; i <= N; i++) {
289 log_result -= log(i);
290 }
291 return exp(log_result);
292 } else { // recursion
293 return (p_hypergeometric(N, K, n, k-1) * (K-k+1) * (n-k+1) / (k * (N-K-n+k)));
294 }
295 }
296 }
297
298 static float sum_probability(uint16_t K, uint16_t n, uint16_t k)
299 {
300 const uint16_t N = 256;
301
302 if (k > K || p_K[K] == 0.0) return 0.0;
303
304 double p_T_is_k_when_S_is_K = p_hypergeometric(N, K, n, k);
305 if (p_T_is_k_when_S_is_K == 0.0) return 0.0;
306
307 double p_S_is_K = p_K[K];
308 double p_T_is_k = 0.0;
309 for (uint16_t i = 0; i <= 256; i++) {
310 if (p_K[i] != 0.0) {
311 p_T_is_k += p_K[i] * p_hypergeometric(N, i, n, k);
312 }
313 }
314 if (p_T_is_k == 0.0) return 0.0;
315 return(p_T_is_k_when_S_is_K * p_S_is_K / p_T_is_k);
316 }
317
318 static inline uint_fast8_t common_bits(uint_fast8_t bytes_diff)
319 {
320 static const uint_fast8_t common_bits_LUT[256] = {
321 8, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
322 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
323 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
324 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
325 6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
326 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
327 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
328 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
329 7, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
330 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
331 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
332 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
333 6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
334 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
335 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
336 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
337 };
338
339 return common_bits_LUT[bytes_diff];
340 }
341
342 static void Tests()
343 {
344 // printf("Tests: Partial Statelist sizes\n");
345 // for (uint16_t i = 0; i <= 16; i+=2) {
346 // printf("Partial State List Odd [%2d] has %8d entries\n", i, partial_statelist[i].len[ODD_STATE]);
347 // }
348 // for (uint16_t i = 0; i <= 16; i+=2) {
349 // printf("Partial State List Even [%2d] has %8d entries\n", i, partial_statelist[i].len[EVEN_STATE]);
350 // }
351
352 // #define NUM_STATISTICS 100000
353 // uint32_t statistics_odd[17];
354 // uint64_t statistics[257];
355 // uint32_t statistics_even[17];
356 // struct Crypto1State cs;
357 // time_t time1 = clock();
358
359 // for (uint16_t i = 0; i < 257; i++) {
360 // statistics[i] = 0;
361 // }
362 // for (uint16_t i = 0; i < 17; i++) {
363 // statistics_odd[i] = 0;
364 // statistics_even[i] = 0;
365 // }
366
367 // for (uint64_t i = 0; i < NUM_STATISTICS; i++) {
368 // cs.odd = (rand() & 0xfff) << 12 | (rand() & 0xfff);
369 // cs.even = (rand() & 0xfff) << 12 | (rand() & 0xfff);
370 // uint16_t sum_property = SumProperty(&cs);
371 // statistics[sum_property] += 1;
372 // sum_property = PartialSumProperty(cs.even, EVEN_STATE);
373 // statistics_even[sum_property]++;
374 // sum_property = PartialSumProperty(cs.odd, ODD_STATE);
375 // statistics_odd[sum_property]++;
376 // if (i%(NUM_STATISTICS/100) == 0) printf(".");
377 // }
378
379 // printf("\nTests: Calculated %d Sum properties in %0.3f seconds (%0.0f calcs/second)\n", NUM_STATISTICS, ((float)clock() - time1)/CLOCKS_PER_SEC, NUM_STATISTICS/((float)clock() - time1)*CLOCKS_PER_SEC);
380 // for (uint16_t i = 0; i < 257; i++) {
381 // if (statistics[i] != 0) {
382 // printf("probability[%3d] = %0.5f\n", i, (float)statistics[i]/NUM_STATISTICS);
383 // }
384 // }
385 // for (uint16_t i = 0; i <= 16; i++) {
386 // if (statistics_odd[i] != 0) {
387 // printf("probability odd [%2d] = %0.5f\n", i, (float)statistics_odd[i]/NUM_STATISTICS);
388 // }
389 // }
390 // for (uint16_t i = 0; i <= 16; i++) {
391 // if (statistics_odd[i] != 0) {
392 // printf("probability even [%2d] = %0.5f\n", i, (float)statistics_even[i]/NUM_STATISTICS);
393 // }
394 // }
395
396 // printf("Tests: Sum Probabilities based on Partial Sums\n");
397 // for (uint16_t i = 0; i < 257; i++) {
398 // statistics[i] = 0;
399 // }
400 // uint64_t num_states = 0;
401 // for (uint16_t oddsum = 0; oddsum <= 16; oddsum += 2) {
402 // for (uint16_t evensum = 0; evensum <= 16; evensum += 2) {
403 // uint16_t sum = oddsum*(16-evensum) + (16-oddsum)*evensum;
404 // statistics[sum] += (uint64_t)partial_statelist[oddsum].len[ODD_STATE] * partial_statelist[evensum].len[EVEN_STATE] * (1<<8);
405 // num_states += (uint64_t)partial_statelist[oddsum].len[ODD_STATE] * partial_statelist[evensum].len[EVEN_STATE] * (1<<8);
406 // }
407 // }
408 // printf("num_states = %lld, expected %lld\n", num_states, (1LL<<48));
409 // for (uint16_t i = 0; i < 257; i++) {
410 // if (statistics[i] != 0) {
411 // printf("probability[%3d] = %0.5f\n", i, (float)statistics[i]/num_states);
412 // }
413 // }
414
415 // printf("\nTests: Hypergeometric Probability for selected parameters\n");
416 // printf("p_hypergeometric(256, 206, 255, 206) = %0.8f\n", p_hypergeometric(256, 206, 255, 206));
417 // printf("p_hypergeometric(256, 206, 255, 205) = %0.8f\n", p_hypergeometric(256, 206, 255, 205));
418 // printf("p_hypergeometric(256, 156, 1, 1) = %0.8f\n", p_hypergeometric(256, 156, 1, 1));
419 // printf("p_hypergeometric(256, 156, 1, 0) = %0.8f\n", p_hypergeometric(256, 156, 1, 0));
420 // printf("p_hypergeometric(256, 1, 1, 1) = %0.8f\n", p_hypergeometric(256, 1, 1, 1));
421 // printf("p_hypergeometric(256, 1, 1, 0) = %0.8f\n", p_hypergeometric(256, 1, 1, 0));
422
423 // struct Crypto1State *pcs;
424 // pcs = crypto1_create(0xffffffffffff);
425 // printf("\nTests: for key = 0xffffffffffff:\nSum(a0) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
426 // SumProperty(pcs), pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
427 // crypto1_byte(pcs, (cuid >> 24) ^ best_first_bytes[0], true);
428 // printf("After adding best first byte 0x%02x:\nSum(a8) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
429 // best_first_bytes[0],
430 // SumProperty(pcs),
431 // pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
432 // //test_state_odd = pcs->odd & 0x00ffffff;
433 // //test_state_even = pcs->even & 0x00ffffff;
434 // crypto1_destroy(pcs);
435 // pcs = crypto1_create(0xa0a1a2a3a4a5);
436 // printf("Tests: for key = 0xa0a1a2a3a4a5:\nSum(a0) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
437 // SumProperty(pcs), pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
438 // crypto1_byte(pcs, (cuid >> 24) ^ best_first_bytes[0], true);
439 // printf("After adding best first byte 0x%02x:\nSum(a8) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
440 // best_first_bytes[0],
441 // SumProperty(pcs),
442 // pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
443 // //test_state_odd = pcs->odd & 0x00ffffff;
444 // //test_state_even = pcs->even & 0x00ffffff;
445 // crypto1_destroy(pcs);
446 // pcs = crypto1_create(0xa6b9aa97b955);
447 // printf("Tests: for key = 0xa6b9aa97b955:\nSum(a0) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
448 // SumProperty(pcs), pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
449 // crypto1_byte(pcs, (cuid >> 24) ^ best_first_bytes[0], true);
450 // printf("After adding best first byte 0x%02x:\nSum(a8) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
451 // best_first_bytes[0],
452 // SumProperty(pcs),
453 // pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
454 //test_state_odd = pcs->odd & 0x00ffffff;
455 //test_state_even = pcs->even & 0x00ffffff;
456 // crypto1_destroy(pcs);
457
458
459 // printf("\nTests: number of states with BitFlipProperty: %d, (= %1.3f%% of total states)\n", statelist_bitflip.len[0], 100.0 * statelist_bitflip.len[0] / (1<<20));
460
461 // printf("\nTests: Actual BitFlipProperties odd/even:\n");
462 // for (uint16_t i = 0; i < 256; i++) {
463 // printf("[%02x]:%c ", i, nonces[i].BitFlip[ODD_STATE]?'o':nonces[i].BitFlip[EVEN_STATE]?'e':' ');
464 // if (i % 8 == 7) {
465 // printf("\n");
466 // }
467 // }
468
469 // printf("\nTests: Sorted First Bytes:\n");
470 // for (uint16_t i = 0; i < 256; i++) {
471 // uint8_t best_byte = best_first_bytes[i];
472 // printf("#%03d Byte: %02x, n = %3d, k = %3d, Sum(a8): %3d, Confidence: %5.1f%%, Bitflip: %c\n",
473 // //printf("#%03d Byte: %02x, n = %3d, k = %3d, Sum(a8): %3d, Confidence: %5.1f%%, Bitflip: %c, score1: %1.5f, score2: %1.0f\n",
474 // i, best_byte,
475 // nonces[best_byte].num,
476 // nonces[best_byte].Sum,
477 // nonces[best_byte].Sum8_guess,
478 // nonces[best_byte].Sum8_prob * 100,
479 // nonces[best_byte].BitFlip[ODD_STATE]?'o':nonces[best_byte].BitFlip[EVEN_STATE]?'e':' '
480 // //nonces[best_byte].score1,
481 // //nonces[best_byte].score2
482 // );
483 // }
484
485 // printf("\nTests: parity performance\n");
486 // time_t time1p = clock();
487 // uint32_t par_sum = 0;
488 // for (uint32_t i = 0; i < 100000000; i++) {
489 // par_sum += parity(i);
490 // }
491 // printf("parsum oldparity = %d, time = %1.5fsec\n", par_sum, (float)(clock() - time1p)/CLOCKS_PER_SEC);
492
493 // time1p = clock();
494 // par_sum = 0;
495 // for (uint32_t i = 0; i < 100000000; i++) {
496 // par_sum += evenparity32(i);
497 // }
498 // printf("parsum newparity = %d, time = %1.5fsec\n", par_sum, (float)(clock() - time1p)/CLOCKS_PER_SEC);
499
500
501 }
502
503 static uint16_t sort_best_first_bytes(void)
504 {
505 // sort based on probability for correct guess
506 for (uint16_t i = 0; i < 256; i++ ) {
507 uint16_t j = 0;
508 float prob1 = nonces[i].Sum8_prob;
509 float prob2 = nonces[best_first_bytes[0]].Sum8_prob;
510 while (prob1 < prob2 && j < i) {
511 prob2 = nonces[best_first_bytes[++j]].Sum8_prob;
512 }
513 if (j < i) {
514 for (uint16_t k = i; k > j; k--) {
515 best_first_bytes[k] = best_first_bytes[k-1];
516 }
517 }
518 best_first_bytes[j] = i;
519 }
520
521 // determine how many are above the CONFIDENCE_THRESHOLD
522 uint16_t num_good_nonces = 0;
523 for (uint16_t i = 0; i < 256; i++) {
524 if (nonces[best_first_bytes[i]].Sum8_prob >= CONFIDENCE_THRESHOLD) {
525 ++num_good_nonces;
526 }
527 }
528
529 if (num_good_nonces == 0) return 0;
530
531 uint16_t best_first_byte = 0;
532
533 // select the best possible first byte based on number of common bits with all {b'}
534 // uint16_t max_common_bits = 0;
535 // for (uint16_t i = 0; i < num_good_nonces; i++) {
536 // uint16_t sum_common_bits = 0;
537 // for (uint16_t j = 0; j < num_good_nonces; j++) {
538 // if (i != j) {
539 // sum_common_bits += common_bits(best_first_bytes[i],best_first_bytes[j]);
540 // }
541 // }
542 // if (sum_common_bits > max_common_bits) {
543 // max_common_bits = sum_common_bits;
544 // best_first_byte = i;
545 // }
546 // }
547
548 // select best possible first byte {b} based on least likely sum/bitflip property
549 float min_p_K = 1.0;
550 for (uint16_t i = 0; i < num_good_nonces; i++ ) {
551 uint16_t sum8 = nonces[best_first_bytes[i]].Sum8_guess;
552 float bitflip_prob = 1.0;
553
554 if (nonces[best_first_bytes[i]].BitFlip[ODD_STATE] || nonces[best_first_bytes[i]].BitFlip[EVEN_STATE])
555 bitflip_prob = 0.09375;
556
557 nonces[best_first_bytes[i]].score1 = p_K[sum8] * bitflip_prob;
558
559 if (p_K[sum8] * bitflip_prob <= min_p_K)
560 min_p_K = p_K[sum8] * bitflip_prob;
561
562 }
563
564
565 // use number of commmon bits as a tie breaker
566 uint_fast8_t max_common_bits = 0;
567 for (uint16_t i = 0; i < num_good_nonces; i++) {
568
569 float bitflip_prob = 1.0;
570 if (nonces[best_first_bytes[i]].BitFlip[ODD_STATE] || nonces[best_first_bytes[i]].BitFlip[EVEN_STATE])
571 bitflip_prob = 0.09375;
572
573 if (p_K[nonces[best_first_bytes[i]].Sum8_guess] * bitflip_prob == min_p_K) {
574 uint_fast8_t sum_common_bits = 0;
575 for (uint16_t j = 0; j < num_good_nonces; j++) {
576 sum_common_bits += common_bits(best_first_bytes[i] ^ best_first_bytes[j]);
577 }
578 nonces[best_first_bytes[i]].score2 = sum_common_bits;
579 if (sum_common_bits > max_common_bits) {
580 max_common_bits = sum_common_bits;
581 best_first_byte = i;
582 }
583 }
584 }
585
586 // swap best possible first byte to the pole position
587 if (best_first_byte != 0) {
588 uint16_t temp = best_first_bytes[0];
589 best_first_bytes[0] = best_first_bytes[best_first_byte];
590 best_first_bytes[best_first_byte] = temp;
591 }
592
593 return num_good_nonces;
594 }
595
596 static uint16_t estimate_second_byte_sum(void)
597 {
598 for (uint16_t first_byte = 0; first_byte < 256; first_byte++) {
599 float Sum8_prob = 0.0;
600 uint16_t Sum8 = 0;
601 if (nonces[first_byte].updated) {
602 for (uint16_t sum = 0; sum <= 256; sum++) {
603 float prob = sum_probability(sum, nonces[first_byte].num, nonces[first_byte].Sum);
604 if (prob > Sum8_prob) {
605 Sum8_prob = prob;
606 Sum8 = sum;
607 }
608 }
609 nonces[first_byte].Sum8_guess = Sum8;
610 nonces[first_byte].Sum8_prob = Sum8_prob;
611 nonces[first_byte].updated = false;
612 }
613 }
614 return sort_best_first_bytes();
615 }
616
617 static int read_nonce_file(void)
618 {
619 FILE *fnonces = NULL;
620 uint8_t trgBlockNo = 0;
621 uint8_t trgKeyType = 0;
622 uint8_t read_buf[9];
623 uint32_t nt_enc1 = 0, nt_enc2 = 0;
624 uint8_t par_enc = 0;
625 int total_num_nonces = 0;
626
627 if ((fnonces = fopen("nonces.bin","rb")) == NULL) {
628 PrintAndLog("Could not open file nonces.bin");
629 return 1;
630 }
631
632 PrintAndLog("Reading nonces from file nonces.bin...");
633 memset (read_buf, 0, sizeof (read_buf));
634 size_t bytes_read = fread(read_buf, 1, 6, fnonces);
635 if ( bytes_read == 0) {
636 PrintAndLog("File reading error.");
637 fclose(fnonces);
638 return 1;
639 }
640 cuid = bytes_to_num(read_buf, 4);
641 trgBlockNo = bytes_to_num(read_buf+4, 1);
642 trgKeyType = bytes_to_num(read_buf+5, 1);
643 size_t ret = 0;
644 do {
645 memset (read_buf, 0, sizeof (read_buf));
646 if ((ret = fread(read_buf, 1, 9, fnonces)) == 9) {
647 nt_enc1 = bytes_to_num(read_buf, 4);
648 nt_enc2 = bytes_to_num(read_buf+4, 4);
649 par_enc = bytes_to_num(read_buf+8, 1);
650 //printf("Encrypted nonce: %08x, encrypted_parity: %02x\n", nt_enc1, par_enc >> 4);
651 //printf("Encrypted nonce: %08x, encrypted_parity: %02x\n", nt_enc2, par_enc & 0x0f);
652 add_nonce(nt_enc1, par_enc >> 4);
653 add_nonce(nt_enc2, par_enc & 0x0f);
654 total_num_nonces += 2;
655 }
656 } while (ret == 9);
657
658 fclose(fnonces);
659 PrintAndLog("Read %d nonces from file. cuid=%08x, Block=%d, Keytype=%c", total_num_nonces, cuid, trgBlockNo, trgKeyType==0?'A':'B');
660 return 0;
661 }
662
663 static void Check_for_FilterFlipProperties(void)
664 {
665 printf("Checking for Filter Flip Properties...\n");
666 uint16_t num_bitflips = 0;
667
668 for (uint16_t i = 0; i < 256; i++) {
669 nonces[i].BitFlip[ODD_STATE] = false;
670 nonces[i].BitFlip[EVEN_STATE] = false;
671 }
672
673 for (uint16_t i = 0; i < 256; i++) {
674 if (!nonces[i].first || !nonces[i^0x80].first || !nonces[i^0x40].first) continue;
675
676 uint8_t parity1 = (nonces[i].first->par_enc) >> 3; // parity of first byte
677 uint8_t parity2_odd = (nonces[i^0x80].first->par_enc) >> 3; // XOR 0x80 = last bit flipped
678 uint8_t parity2_even = (nonces[i^0x40].first->par_enc) >> 3; // XOR 0x40 = second last bit flipped
679
680 if (parity1 == parity2_odd) { // has Bit Flip Property for odd bits
681 nonces[i].BitFlip[ODD_STATE] = true;
682 num_bitflips++;
683 } else if (parity1 == parity2_even) { // has Bit Flip Property for even bits
684 nonces[i].BitFlip[EVEN_STATE] = true;
685 num_bitflips++;
686 }
687 }
688
689 if (write_stats)
690 fprintf(fstats, "%d;", num_bitflips);
691 }
692
693 static void simulate_MFplus_RNG(uint32_t test_cuid, uint64_t test_key, uint32_t *nt_enc, uint8_t *par_enc)
694 {
695 struct Crypto1State sim_cs = {0, 0};
696 // init cryptostate with key:
697 for(int8_t i = 47; i > 0; i -= 2) {
698 sim_cs.odd = sim_cs.odd << 1 | BIT(test_key, (i - 1) ^ 7);
699 sim_cs.even = sim_cs.even << 1 | BIT(test_key, i ^ 7);
700 }
701
702 *par_enc = 0;
703 uint32_t nt = (rand() & 0xff) << 24 | (rand() & 0xff) << 16 | (rand() & 0xff) << 8 | (rand() & 0xff);
704 for (int8_t byte_pos = 3; byte_pos >= 0; byte_pos--) {
705 uint8_t nt_byte_dec = (nt >> (8*byte_pos)) & 0xff;
706 uint8_t nt_byte_enc = crypto1_byte(&sim_cs, nt_byte_dec ^ (test_cuid >> (8*byte_pos)), false) ^ nt_byte_dec; // encode the nonce byte
707 *nt_enc = (*nt_enc << 8) | nt_byte_enc;
708 uint8_t ks_par = filter(sim_cs.odd); // the keystream bit to encode/decode the parity bit
709 uint8_t nt_byte_par_enc = ks_par ^ oddparity8(nt_byte_dec); // determine the nt byte's parity and encode it
710 *par_enc = (*par_enc << 1) | nt_byte_par_enc;
711 }
712
713 }
714
715 static void simulate_acquire_nonces()
716 {
717 clock_t time1 = clock();
718 bool filter_flip_checked = false;
719 uint32_t total_num_nonces = 0;
720 uint32_t next_fivehundred = 500;
721 uint32_t total_added_nonces = 0;
722
723 cuid = (rand() & 0xff) << 24 | (rand() & 0xff) << 16 | (rand() & 0xff) << 8 | (rand() & 0xff);
724 known_target_key = ((uint64_t)rand() & 0xfff) << 36 | ((uint64_t)rand() & 0xfff) << 24 | ((uint64_t)rand() & 0xfff) << 12 | ((uint64_t)rand() & 0xfff);
725
726 printf("Simulating nonce acquisition for target key %012"llx", cuid %08x ...\n", known_target_key, cuid);
727 fprintf(fstats, "%012"llx";%08x;", known_target_key, cuid);
728
729 do {
730 uint32_t nt_enc = 0;
731 uint8_t par_enc = 0;
732
733 simulate_MFplus_RNG(cuid, known_target_key, &nt_enc, &par_enc);
734 //printf("Simulated RNG: nt_enc1: %08x, nt_enc2: %08x, par_enc: %02x\n", nt_enc1, nt_enc2, par_enc);
735 total_added_nonces += add_nonce(nt_enc, par_enc);
736 total_num_nonces++;
737
738 if (first_byte_num == 256 ) {
739 // printf("first_byte_num = %d, first_byte_Sum = %d\n", first_byte_num, first_byte_Sum);
740 if (!filter_flip_checked) {
741 Check_for_FilterFlipProperties();
742 filter_flip_checked = true;
743 }
744 num_good_first_bytes = estimate_second_byte_sum();
745 if (total_num_nonces > next_fivehundred) {
746 next_fivehundred = (total_num_nonces/500+1) * 500;
747 printf("Acquired %5d nonces (%5d with distinct bytes 0,1). Bytes with probability for correctly guessed Sum(a8) > %1.1f%%: %d\n",
748 total_num_nonces,
749 total_added_nonces,
750 CONFIDENCE_THRESHOLD * 100.0,
751 num_good_first_bytes);
752 }
753 }
754
755 } while (num_good_first_bytes < GOOD_BYTES_REQUIRED);
756
757 time1 = clock() - time1;
758 if ( time1 > 0 ) {
759 PrintAndLog("Acquired a total of %d nonces in %1.1f seconds (%0.0f nonces/minute)",
760 total_num_nonces,
761 ((float)time1)/CLOCKS_PER_SEC,
762 total_num_nonces * 60.0 * CLOCKS_PER_SEC/(float)time1);
763 }
764 fprintf(fstats, "%d;%d;%d;%1.2f;", total_num_nonces, total_added_nonces, num_good_first_bytes, CONFIDENCE_THRESHOLD);
765
766 }
767
768 static int acquire_nonces(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_t trgBlockNo, uint8_t trgKeyType, bool nonce_file_write, bool slow)
769 {
770 clock_t time1 = clock();
771 bool initialize = true;
772 bool finished = false;
773 bool filter_flip_checked = false;
774 uint32_t flags = 0;
775 uint8_t write_buf[9];
776 uint32_t total_num_nonces = 0;
777 uint32_t next_fivehundred = 500;
778 uint32_t total_added_nonces = 0;
779 uint32_t idx = 1;
780 uint32_t timeout = 0;
781 FILE *fnonces = NULL;
782 field_off = false;
783 UsbCommand resp;
784 UsbCommand c = {CMD_MIFARE_ACQUIRE_ENCRYPTED_NONCES, {0,0,0} };
785 memcpy(c.d.asBytes, key, 6);
786 c.arg[0] = blockNo + (keyType * 0x100);
787 c.arg[1] = trgBlockNo + (trgKeyType * 0x100);
788
789 printf("Acquiring nonces...\n");
790 do {
791
792 flags = 0;
793 flags |= initialize ? 0x0001 : 0;
794 flags |= slow ? 0x0002 : 0;
795 flags |= field_off ? 0x0004 : 0;
796 c.arg[2] = flags;
797
798 clearCommandBuffer();
799 SendCommand(&c);
800
801 if (field_off) break;
802
803 while(!WaitForResponseTimeout(CMD_ACK, &resp, 2000)) {
804 timeout++;
805 printf(".");
806 if (timeout > 3) {
807 PrintAndLog("\nNo response from Proxmark. Aborting...");
808 if (fnonces) fclose(fnonces);
809 return 1;
810 }
811 }
812
813 if (resp.arg[0]) {
814 if (fnonces) fclose(fnonces);
815 return resp.arg[0]; // error during nested_hard
816 }
817
818 if (initialize) {
819 // global var CUID
820 cuid = resp.arg[1];
821 if (nonce_file_write && fnonces == NULL) {
822 if ((fnonces = fopen("nonces.bin","wb")) == NULL) {
823 PrintAndLog("Could not create file nonces.bin");
824 return 3;
825 }
826 PrintAndLog("Writing acquired nonces to binary file nonces.bin");
827 memset (write_buf, 0, sizeof (write_buf));
828 num_to_bytes(cuid, 4, write_buf);
829 fwrite(write_buf, 1, 4, fnonces);
830 fwrite(&trgBlockNo, 1, 1, fnonces);
831 fwrite(&trgKeyType, 1, 1, fnonces);
832 fflush(fnonces);
833 }
834 initialize = false;
835 }
836
837 uint32_t nt_enc1, nt_enc2;
838 uint8_t par_enc;
839 uint16_t num_acquired_nonces = resp.arg[2];
840 uint8_t *bufp = resp.d.asBytes;
841 for (uint16_t i = 0; i < num_acquired_nonces; i += 2) {
842 nt_enc1 = bytes_to_num(bufp, 4);
843 nt_enc2 = bytes_to_num(bufp+4, 4);
844 par_enc = bytes_to_num(bufp+8, 1);
845
846 total_added_nonces += add_nonce(nt_enc1, par_enc >> 4);
847 total_added_nonces += add_nonce(nt_enc2, par_enc & 0x0f);
848
849 if (nonce_file_write && fnonces) {
850 fwrite(bufp, 1, 9, fnonces);
851 fflush(fnonces);
852 }
853 bufp += 9;
854 }
855 total_num_nonces += num_acquired_nonces;
856
857 if (first_byte_num == 256) {
858
859 if (!filter_flip_checked) {
860 Check_for_FilterFlipProperties();
861 filter_flip_checked = true;
862 }
863
864 num_good_first_bytes = estimate_second_byte_sum();
865
866 if (total_num_nonces > next_fivehundred) {
867 next_fivehundred = (total_num_nonces/500+1) * 500;
868 printf("Acquired %5d nonces (%5d/%5d with distinct bytes 0,1). Bytes with probability for correctly guessed Sum(a8) > %1.1f%%: %d\n",
869 total_num_nonces,
870 total_added_nonces,
871 NONCES_THRESHOLD * idx,
872 CONFIDENCE_THRESHOLD * 100.0,
873 num_good_first_bytes
874 );
875 }
876
877 if (total_added_nonces >= (NONCES_THRESHOLD * idx)) {
878 if (num_good_first_bytes > 0) {
879 if (generate_candidates(first_byte_Sum, nonces[best_first_bytes[0]].Sum8_guess) || known_target_key != -1) {
880 field_off = brute_force(); // switch off field with next SendCommand and then finish
881 }
882 }
883 idx++;
884 }
885 }
886 } while (!finished);
887
888 if (nonce_file_write && fnonces)
889 fclose(fnonces);
890
891 time1 = clock() - time1;
892 if ( time1 > 0 ) {
893 PrintAndLog("Acquired a total of %d nonces in %1.1f seconds (%0.0f nonces/minute)",
894 total_num_nonces,
895 ((float)time1)/CLOCKS_PER_SEC,
896 total_num_nonces * 60.0 * CLOCKS_PER_SEC/(float)time1
897 );
898 }
899 return 0;
900 }
901
902 static int init_partial_statelists(void)
903 {
904 const uint32_t sizes_odd[17] = { 126757, 0, 18387, 0, 74241, 0, 181737, 0, 248801, 0, 182033, 0, 73421, 0, 17607, 0, 125601 };
905 // const uint32_t sizes_even[17] = { 125723, 0, 17867, 0, 74305, 0, 178707, 0, 248801, 0, 185063, 0, 73356, 0, 18127, 0, 126634 };
906 const uint32_t sizes_even[17] = { 125723, 0, 17867, 0, 74305, 0, 178707, 0, 248801, 0, 185063, 0, 73357, 0, 18127, 0, 126635 };
907
908 printf("Allocating memory for partial statelists...\n");
909 for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
910 for (uint16_t i = 0; i <= 16; i+=2) {
911 partial_statelist[i].len[odd_even] = 0;
912 uint32_t num_of_states = odd_even == ODD_STATE ? sizes_odd[i] : sizes_even[i];
913 partial_statelist[i].states[odd_even] = malloc(sizeof(uint32_t) * num_of_states);
914 if (partial_statelist[i].states[odd_even] == NULL) {
915 PrintAndLog("Cannot allocate enough memory. Aborting");
916 return 4;
917 }
918 for (uint32_t j = 0; j < STATELIST_INDEX_SIZE; j++) {
919 partial_statelist[i].index[odd_even][j] = NULL;
920 }
921 }
922 }
923
924 printf("Generating partial statelists...\n");
925 for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
926 uint32_t index = -1;
927 uint32_t num_of_states = 1<<20;
928 for (uint32_t state = 0; state < num_of_states; state++) {
929 uint16_t sum_property = PartialSumProperty(state, odd_even);
930 uint32_t *p = partial_statelist[sum_property].states[odd_even];
931 p += partial_statelist[sum_property].len[odd_even];
932 *p = state;
933 partial_statelist[sum_property].len[odd_even]++;
934 uint32_t index_mask = (STATELIST_INDEX_SIZE-1) << (20-STATELIST_INDEX_WIDTH);
935 if ((state & index_mask) != index) {
936 index = state & index_mask;
937 }
938 if (partial_statelist[sum_property].index[odd_even][index >> (20-STATELIST_INDEX_WIDTH)] == NULL) {
939 partial_statelist[sum_property].index[odd_even][index >> (20-STATELIST_INDEX_WIDTH)] = p;
940 }
941 }
942 // add End Of List markers
943 for (uint16_t i = 0; i <= 16; i += 2) {
944 uint32_t *p = partial_statelist[i].states[odd_even];
945 p += partial_statelist[i].len[odd_even];
946 *p = END_OF_LIST_MARKER;
947 }
948 }
949
950 return 0;
951 }
952
953 static void init_BitFlip_statelist(void)
954 {
955 printf("Generating bitflip statelist...\n");
956 uint32_t *p = statelist_bitflip.states[0] = malloc(sizeof(uint32_t) * 1<<20);
957 uint32_t index = -1;
958 uint32_t index_mask = (STATELIST_INDEX_SIZE-1) << (20-STATELIST_INDEX_WIDTH);
959 for (uint32_t state = 0; state < (1 << 20); state++) {
960 if (filter(state) != filter(state^1)) {
961 if ((state & index_mask) != index) {
962 index = state & index_mask;
963 }
964 if (statelist_bitflip.index[0][index >> (20-STATELIST_INDEX_WIDTH)] == NULL) {
965 statelist_bitflip.index[0][index >> (20-STATELIST_INDEX_WIDTH)] = p;
966 }
967 *p++ = state;
968 }
969 }
970 // set len and add End Of List marker
971 statelist_bitflip.len[0] = p - statelist_bitflip.states[0];
972 *p = END_OF_LIST_MARKER;
973 //statelist_bitflip.states[0] = realloc(statelist_bitflip.states[0], sizeof(uint32_t) * (statelist_bitflip.len[0] + 1));
974 }
975
976 static inline uint32_t *find_first_state(uint32_t state, uint32_t mask, partial_indexed_statelist_t *sl, odd_even_t odd_even)
977 {
978 uint32_t *p = sl->index[odd_even][(state & mask) >> (20-STATELIST_INDEX_WIDTH)]; // first Bits as index
979
980 if (p == NULL) return NULL;
981 while (*p < (state & mask)) p++;
982 if (*p == END_OF_LIST_MARKER) return NULL; // reached end of list, no match
983 if ((*p & mask) == (state & mask)) return p; // found a match.
984 return NULL; // no match
985 }
986
987 static inline bool /*__attribute__((always_inline))*/ invariant_holds(uint_fast8_t byte_diff, uint_fast32_t state1, uint_fast32_t state2, uint_fast8_t bit, uint_fast8_t state_bit)
988 {
989 uint_fast8_t j_1_bit_mask = 0x01 << (bit-1);
990 uint_fast8_t bit_diff = byte_diff & j_1_bit_mask; // difference of (j-1)th bit
991 uint_fast8_t filter_diff = filter(state1 >> (4-state_bit)) ^ filter(state2 >> (4-state_bit)); // difference in filter function
992 uint_fast8_t mask_y12_y13 = 0xc0 >> state_bit;
993 uint_fast8_t state_bits_diff = (state1 ^ state2) & mask_y12_y13; // difference in state bits 12 and 13
994 uint_fast8_t all_diff = evenparity8(bit_diff ^ state_bits_diff ^ filter_diff); // use parity function to XOR all bits
995 return !all_diff;
996 }
997
998 static inline bool /*__attribute__((always_inline))*/ invalid_state(uint_fast8_t byte_diff, uint_fast32_t state1, uint_fast32_t state2, uint_fast8_t bit, uint_fast8_t state_bit)
999 {
1000 uint_fast8_t j_bit_mask = 0x01 << bit;
1001 uint_fast8_t bit_diff = byte_diff & j_bit_mask; // difference of jth bit
1002 uint_fast8_t mask_y13_y16 = 0x48 >> state_bit;
1003 uint_fast8_t state_bits_diff = (state1 ^ state2) & mask_y13_y16; // difference in state bits 13 and 16
1004 uint_fast8_t all_diff = evenparity8(bit_diff ^ state_bits_diff); // use parity function to XOR all bits
1005 return all_diff;
1006 }
1007
1008 static inline bool remaining_bits_match(uint_fast8_t num_common_bits, uint_fast8_t byte_diff, uint_fast32_t state1, uint_fast32_t state2, odd_even_t odd_even)
1009 {
1010 if (odd_even) {
1011 // odd bits
1012 switch (num_common_bits) {
1013 case 0: if (!invariant_holds(byte_diff, state1, state2, 1, 0)) return true;
1014 case 1: if (invalid_state(byte_diff, state1, state2, 1, 0)) return false;
1015 case 2: if (!invariant_holds(byte_diff, state1, state2, 3, 1)) return true;
1016 case 3: if (invalid_state(byte_diff, state1, state2, 3, 1)) return false;
1017 case 4: if (!invariant_holds(byte_diff, state1, state2, 5, 2)) return true;
1018 case 5: if (invalid_state(byte_diff, state1, state2, 5, 2)) return false;
1019 case 6: if (!invariant_holds(byte_diff, state1, state2, 7, 3)) return true;
1020 case 7: if (invalid_state(byte_diff, state1, state2, 7, 3)) return false;
1021 }
1022 } else {
1023 // even bits
1024 switch (num_common_bits) {
1025 case 0: if (invalid_state(byte_diff, state1, state2, 0, 0)) return false;
1026 case 1: if (!invariant_holds(byte_diff, state1, state2, 2, 1)) return true;
1027 case 2: if (invalid_state(byte_diff, state1, state2, 2, 1)) return false;
1028 case 3: if (!invariant_holds(byte_diff, state1, state2, 4, 2)) return true;
1029 case 4: if (invalid_state(byte_diff, state1, state2, 4, 2)) return false;
1030 case 5: if (!invariant_holds(byte_diff, state1, state2, 6, 3)) return true;
1031 case 6: if (invalid_state(byte_diff, state1, state2, 6, 3)) return false;
1032 }
1033 }
1034
1035 return true; // valid state
1036 }
1037
1038 static bool all_other_first_bytes_match(uint32_t state, odd_even_t odd_even)
1039 {
1040 for (uint16_t i = 1; i < num_good_first_bytes; i++) {
1041 uint16_t sum_a8 = nonces[best_first_bytes[i]].Sum8_guess;
1042 uint_fast8_t bytes_diff = best_first_bytes[0] ^ best_first_bytes[i];
1043 uint_fast8_t j = common_bits(bytes_diff);
1044 uint32_t mask = 0xfffffff0;
1045 if (odd_even == ODD_STATE) {
1046 mask >>= j/2;
1047 } else {
1048 mask >>= (j+1)/2;
1049 }
1050 mask &= 0x000fffff;
1051 //printf("bytes 0x%02x and 0x%02x: %d common bits, mask = 0x%08x, state = 0x%08x, sum_a8 = %d", best_first_bytes[0], best_first_bytes[i], j, mask, state, sum_a8);
1052 bool found_match = false;
1053 for (uint16_t r = 0; r <= 16 && !found_match; r += 2) {
1054 for (uint16_t s = 0; s <= 16 && !found_match; s += 2) {
1055 if (r*(16-s) + (16-r)*s == sum_a8) {
1056 //printf("Checking byte 0x%02x for partial sum (%s) %d\n", best_first_bytes[i], odd_even==ODD_STATE?"odd":"even", odd_even==ODD_STATE?r:s);
1057 uint16_t part_sum_a8 = (odd_even == ODD_STATE) ? r : s;
1058 uint32_t *p = find_first_state(state, mask, &partial_statelist[part_sum_a8], odd_even);
1059 if (p != NULL) {
1060 while ((state & mask) == (*p & mask) && (*p != END_OF_LIST_MARKER)) {
1061 if (remaining_bits_match(j, bytes_diff, state, (state&0x00fffff0) | *p, odd_even)) {
1062 found_match = true;
1063 // if ((odd_even == ODD_STATE && state == test_state_odd)
1064 // || (odd_even == EVEN_STATE && state == test_state_even)) {
1065 // printf("all_other_first_bytes_match(): %s test state: remaining bits matched. Bytes = %02x, %02x, Common Bits=%d, mask=0x%08x, PartSum(a8)=%d\n",
1066 // odd_even==ODD_STATE?"odd":"even", best_first_bytes[0], best_first_bytes[i], j, mask, part_sum_a8);
1067 // }
1068 break;
1069 } else {
1070 // if ((odd_even == ODD_STATE && state == test_state_odd)
1071 // || (odd_even == EVEN_STATE && state == test_state_even)) {
1072 // printf("all_other_first_bytes_match(): %s test state: remaining bits didn't match. Bytes = %02x, %02x, Common Bits=%d, mask=0x%08x, PartSum(a8)=%d\n",
1073 // odd_even==ODD_STATE?"odd":"even", best_first_bytes[0], best_first_bytes[i], j, mask, part_sum_a8);
1074 // }
1075 }
1076 p++;
1077 }
1078 } else {
1079 // if ((odd_even == ODD_STATE && state == test_state_odd)
1080 // || (odd_even == EVEN_STATE && state == test_state_even)) {
1081 // printf("all_other_first_bytes_match(): %s test state: couldn't find a matching state. Bytes = %02x, %02x, Common Bits=%d, mask=0x%08x, PartSum(a8)=%d\n",
1082 // odd_even==ODD_STATE?"odd":"even", best_first_bytes[0], best_first_bytes[i], j, mask, part_sum_a8);
1083 // }
1084 }
1085 }
1086 }
1087 }
1088
1089 if (!found_match) {
1090 // if ((odd_even == ODD_STATE && state == test_state_odd)
1091 // || (odd_even == EVEN_STATE && state == test_state_even)) {
1092 // printf("all_other_first_bytes_match(): %s test state: Eliminated. Bytes = %02x, %02x, Common Bits = %d\n", odd_even==ODD_STATE?"odd":"even", best_first_bytes[0], best_first_bytes[i], j);
1093 // }
1094 return false;
1095 }
1096 }
1097
1098 return true;
1099 }
1100
1101 static bool all_bit_flips_match(uint32_t state, odd_even_t odd_even)
1102 {
1103 for (uint16_t i = 0; i < 256; i++) {
1104 if (nonces[i].BitFlip[odd_even] && i != best_first_bytes[0]) {
1105 uint_fast8_t bytes_diff = best_first_bytes[0] ^ i;
1106 uint_fast8_t j = common_bits(bytes_diff);
1107 uint32_t mask = 0xfffffff0;
1108 if (odd_even == ODD_STATE) {
1109 mask >>= j/2;
1110 } else {
1111 mask >>= (j+1)/2;
1112 }
1113 mask &= 0x000fffff;
1114 //printf("bytes 0x%02x and 0x%02x: %d common bits, mask = 0x%08x, state = 0x%08x, sum_a8 = %d", best_first_bytes[0], best_first_bytes[i], j, mask, state, sum_a8);
1115 bool found_match = false;
1116 uint32_t *p = find_first_state(state, mask, &statelist_bitflip, 0);
1117 if (p != NULL) {
1118 while ((state & mask) == (*p & mask) && (*p != END_OF_LIST_MARKER)) {
1119 if (remaining_bits_match(j, bytes_diff, state, (state&0x00fffff0) | *p, odd_even)) {
1120 found_match = true;
1121 // if ((odd_even == ODD_STATE && state == test_state_odd)
1122 // || (odd_even == EVEN_STATE && state == test_state_even)) {
1123 // printf("all_other_first_bytes_match(): %s test state: remaining bits matched. Bytes = %02x, %02x, Common Bits=%d, mask=0x%08x, PartSum(a8)=%d\n",
1124 // odd_even==ODD_STATE?"odd":"even", best_first_bytes[0], best_first_bytes[i], j, mask, part_sum_a8);
1125 // }
1126 break;
1127 } else {
1128 // if ((odd_even == ODD_STATE && state == test_state_odd)
1129 // || (odd_even == EVEN_STATE && state == test_state_even)) {
1130 // printf("all_other_first_bytes_match(): %s test state: remaining bits didn't match. Bytes = %02x, %02x, Common Bits=%d, mask=0x%08x, PartSum(a8)=%d\n",
1131 // odd_even==ODD_STATE?"odd":"even", best_first_bytes[0], best_first_bytes[i], j, mask, part_sum_a8);
1132 // }
1133 }
1134 p++;
1135 }
1136 } else {
1137 // if ((odd_even == ODD_STATE && state == test_state_odd)
1138 // || (odd_even == EVEN_STATE && state == test_state_even)) {
1139 // printf("all_other_first_bytes_match(): %s test state: couldn't find a matching state. Bytes = %02x, %02x, Common Bits=%d, mask=0x%08x, PartSum(a8)=%d\n",
1140 // odd_even==ODD_STATE?"odd":"even", best_first_bytes[0], best_first_bytes[i], j, mask, part_sum_a8);
1141 // }
1142 }
1143 if (!found_match) {
1144 // if ((odd_even == ODD_STATE && state == test_state_odd)
1145 // || (odd_even == EVEN_STATE && state == test_state_even)) {
1146 // printf("all_other_first_bytes_match(): %s test state: Eliminated. Bytes = %02x, %02x, Common Bits = %d\n", odd_even==ODD_STATE?"odd":"even", best_first_bytes[0], best_first_bytes[i], j);
1147 // }
1148 return false;
1149 }
1150 }
1151
1152 }
1153
1154 return true;
1155 }
1156
1157 static struct sl_cache_entry {
1158 uint32_t *sl;
1159 uint32_t len;
1160 } sl_cache[17][17][2];
1161
1162 static void init_statelist_cache(void)
1163 {
1164 for (uint16_t i = 0; i < 17; i+=2) {
1165 for (uint16_t j = 0; j < 17; j+=2) {
1166 for (uint16_t k = 0; k < 2; k++) {
1167 sl_cache[i][j][k].sl = NULL;
1168 sl_cache[i][j][k].len = 0;
1169 }
1170 }
1171 }
1172 }
1173
1174 static int add_matching_states(statelist_t *candidates, uint16_t part_sum_a0, uint16_t part_sum_a8, odd_even_t odd_even)
1175 {
1176 uint32_t worstcase_size = 1<<20;
1177
1178 // check cache for existing results
1179 if (sl_cache[part_sum_a0][part_sum_a8][odd_even].sl != NULL) {
1180 candidates->states[odd_even] = sl_cache[part_sum_a0][part_sum_a8][odd_even].sl;
1181 candidates->len[odd_even] = sl_cache[part_sum_a0][part_sum_a8][odd_even].len;
1182 return 0;
1183 }
1184
1185 candidates->states[odd_even] = (uint32_t *)malloc(sizeof(uint32_t) * worstcase_size);
1186 if (candidates->states[odd_even] == NULL) {
1187 PrintAndLog("Out of memory error.\n");
1188 return 4;
1189 }
1190 uint32_t *add_p = candidates->states[odd_even];
1191 for (uint32_t *p1 = partial_statelist[part_sum_a0].states[odd_even]; *p1 != END_OF_LIST_MARKER; p1++) {
1192 uint32_t search_mask = 0x000ffff0;
1193 uint32_t *p2 = find_first_state((*p1 << 4), search_mask, &partial_statelist[part_sum_a8], odd_even);
1194 if (p1 != NULL && p2 != NULL) {
1195 while (((*p1 << 4) & search_mask) == (*p2 & search_mask) && *p2 != END_OF_LIST_MARKER) {
1196 if ((nonces[best_first_bytes[0]].BitFlip[odd_even] && find_first_state((*p1 << 4) | *p2, 0x000fffff, &statelist_bitflip, 0))
1197 || !nonces[best_first_bytes[0]].BitFlip[odd_even]) {
1198 if (all_other_first_bytes_match((*p1 << 4) | *p2, odd_even)) {
1199 if (all_bit_flips_match((*p1 << 4) | *p2, odd_even)) {
1200 *add_p++ = (*p1 << 4) | *p2;
1201 }
1202 }
1203 }
1204 p2++;
1205 }
1206 }
1207 }
1208
1209 // set end of list marker and len
1210 *add_p = END_OF_LIST_MARKER;
1211 candidates->len[odd_even] = add_p - candidates->states[odd_even];
1212
1213 candidates->states[odd_even] = realloc(candidates->states[odd_even], sizeof(uint32_t) * (candidates->len[odd_even] + 1));
1214
1215 sl_cache[part_sum_a0][part_sum_a8][odd_even].sl = candidates->states[odd_even];
1216 sl_cache[part_sum_a0][part_sum_a8][odd_even].len = candidates->len[odd_even];
1217
1218 return 0;
1219 }
1220
1221 static statelist_t *add_more_candidates(statelist_t *current_candidates)
1222 {
1223 statelist_t *new_candidates = NULL;
1224 if (current_candidates == NULL) {
1225 if (candidates == NULL) {
1226 candidates = (statelist_t *)malloc(sizeof(statelist_t));
1227 }
1228 new_candidates = candidates;
1229 } else {
1230 new_candidates = current_candidates->next = (statelist_t *)malloc(sizeof(statelist_t));
1231 }
1232 if (!new_candidates) return NULL;
1233
1234 new_candidates->next = NULL;
1235 new_candidates->len[ODD_STATE] = 0;
1236 new_candidates->len[EVEN_STATE] = 0;
1237 new_candidates->states[ODD_STATE] = NULL;
1238 new_candidates->states[EVEN_STATE] = NULL;
1239 return new_candidates;
1240 }
1241
1242 static bool TestIfKeyExists(uint64_t key)
1243 {
1244 struct Crypto1State *pcs;
1245 pcs = crypto1_create(key);
1246 crypto1_byte(pcs, (cuid >> 24) ^ best_first_bytes[0], true);
1247
1248 uint32_t state_odd = pcs->odd & 0x00ffffff;
1249 uint32_t state_even = pcs->even & 0x00ffffff;
1250 //printf("Tests: searching for key %llx after first byte 0x%02x (state_odd = 0x%06x, state_even = 0x%06x) ...\n", key, best_first_bytes[0], state_odd, state_even);
1251 printf("Validating key search space\n");
1252 uint64_t count = 0;
1253 for (statelist_t *p = candidates; p != NULL; p = p->next) {
1254 bool found_odd = false;
1255 bool found_even = false;
1256 uint32_t *p_odd = p->states[ODD_STATE];
1257 uint32_t *p_even = p->states[EVEN_STATE];
1258 while (*p_odd != END_OF_LIST_MARKER) {
1259 if ((*p_odd & 0x00ffffff) == state_odd) {
1260 found_odd = true;
1261 break;
1262 }
1263 p_odd++;
1264 }
1265 while (*p_even != END_OF_LIST_MARKER) {
1266 if ((*p_even & 0x00ffffff) == state_even)
1267 found_even = true;
1268
1269 p_even++;
1270 }
1271 count += (p_odd - p->states[ODD_STATE]) * (p_even - p->states[EVEN_STATE]);
1272 if (found_odd && found_even) {
1273 if (known_target_key != -1) {
1274 PrintAndLog("Key Found after testing %llu (2^%1.1f) out of %lld (2^%1.1f) keys.",
1275 count,
1276 log(count)/log(2),
1277 maximum_states,
1278 log(maximum_states)/log(2)
1279 );
1280 if (write_stats)
1281 fprintf(fstats, "1\n");
1282 }
1283 crypto1_destroy(pcs);
1284 return true;
1285 }
1286 }
1287
1288 if (known_target_key != -1) {
1289 printf("Key NOT found!\n");
1290 if (write_stats)
1291 fprintf(fstats, "0\n");
1292 }
1293 crypto1_destroy(pcs);
1294 return false;
1295 }
1296
1297 static bool generate_candidates(uint16_t sum_a0, uint16_t sum_a8)
1298 {
1299 printf("Generating crypto1 state candidates... \n");
1300
1301 statelist_t *current_candidates = NULL;
1302 // estimate maximum candidate states
1303 maximum_states = 0;
1304 for (uint16_t sum_odd = 0; sum_odd <= 16; sum_odd += 2) {
1305 for (uint16_t sum_even = 0; sum_even <= 16; sum_even += 2) {
1306 if (sum_odd*(16-sum_even) + (16-sum_odd)*sum_even == sum_a0) {
1307 maximum_states += (uint64_t)partial_statelist[sum_odd].len[ODD_STATE] * partial_statelist[sum_even].len[EVEN_STATE] * (1<<8);
1308 }
1309 }
1310 }
1311
1312 if (maximum_states == 0) return false; // prevent keyspace reduction error (2^-inf)
1313
1314 printf("Number of possible keys with Sum(a0) = %d: %"PRIu64" (2^%1.1f)\n", sum_a0, maximum_states, log(maximum_states)/log(2));
1315
1316 init_statelist_cache();
1317
1318 for (uint16_t p = 0; p <= 16; p += 2) {
1319 for (uint16_t q = 0; q <= 16; q += 2) {
1320 if (p*(16-q) + (16-p)*q == sum_a0) {
1321 // printf("Reducing Partial Statelists (p,q) = (%d,%d) with lengths %d, %d\n",
1322 // p, q, partial_statelist[p].len[ODD_STATE], partial_statelist[q].len[EVEN_STATE]);
1323 for (uint16_t r = 0; r <= 16; r += 2) {
1324 for (uint16_t s = 0; s <= 16; s += 2) {
1325 if (r*(16-s) + (16-r)*s == sum_a8) {
1326 current_candidates = add_more_candidates(current_candidates);
1327 if (current_candidates != NULL) {
1328 // check for the smallest partial statelist. Try this first - it might give 0 candidates
1329 // and eliminate the need to calculate the other part
1330 if (MIN(partial_statelist[p].len[ODD_STATE], partial_statelist[r].len[ODD_STATE])
1331 < MIN(partial_statelist[q].len[EVEN_STATE], partial_statelist[s].len[EVEN_STATE])) {
1332 add_matching_states(current_candidates, p, r, ODD_STATE);
1333 if(current_candidates->len[ODD_STATE]) {
1334 add_matching_states(current_candidates, q, s, EVEN_STATE);
1335 } else {
1336 current_candidates->len[EVEN_STATE] = 0;
1337 uint32_t *p = current_candidates->states[EVEN_STATE] = malloc(sizeof(uint32_t));
1338 *p = END_OF_LIST_MARKER;
1339 }
1340 } else {
1341 add_matching_states(current_candidates, q, s, EVEN_STATE);
1342 if(current_candidates->len[EVEN_STATE]) {
1343 add_matching_states(current_candidates, p, r, ODD_STATE);
1344 } else {
1345 current_candidates->len[ODD_STATE] = 0;
1346 uint32_t *p = current_candidates->states[ODD_STATE] = malloc(sizeof(uint32_t));
1347 *p = END_OF_LIST_MARKER;
1348 }
1349 }
1350 //printf("Odd state candidates: %6d (2^%0.1f)\n", current_candidates->len[ODD_STATE], log(current_candidates->len[ODD_STATE])/log(2));
1351 //printf("Even state candidates: %6d (2^%0.1f)\n", current_candidates->len[EVEN_STATE], log(current_candidates->len[EVEN_STATE])/log(2));
1352 }
1353 }
1354 }
1355 }
1356 }
1357 }
1358 }
1359
1360 maximum_states = 0;
1361 unsigned int n = 0;
1362 for (statelist_t *sl = candidates; sl != NULL && n < MAX_BUCKETS; sl = sl->next, n++) {
1363 maximum_states += (uint64_t)sl->len[ODD_STATE] * sl->len[EVEN_STATE];
1364 }
1365
1366 if (maximum_states == 0) return false; // prevent keyspace reduction error (2^-inf)
1367
1368 float kcalc = log(maximum_states)/log(2);
1369 printf("Number of remaining possible keys: %"PRIu64" (2^%1.1f)\n", maximum_states, kcalc);
1370 if (write_stats) {
1371 fprintf(fstats, "%1.1f;", (kcalc != 0) ? kcalc : 0.0);
1372 }
1373 if (kcalc < CRACKING_THRESHOLD) return true;
1374
1375 return false;
1376 }
1377
1378 static void free_candidates_memory(statelist_t *sl)
1379 {
1380 if (sl == NULL) {
1381 return;
1382 } else {
1383 free_candidates_memory(sl->next);
1384 free(sl);
1385 }
1386 }
1387
1388 static void free_statelist_cache(void)
1389 {
1390 for (uint16_t i = 0; i < 17; i+=2) {
1391 for (uint16_t j = 0; j < 17; j+=2) {
1392 for (uint16_t k = 0; k < 2; k++) {
1393 free(sl_cache[i][j][k].sl);
1394 }
1395 }
1396 }
1397 }
1398
1399 static const uint64_t crack_states_bitsliced(statelist_t *p){
1400 // the idea to roll back the half-states before combining them was suggested/explained to me by bla
1401 // first we pre-bitslice all the even state bits and roll them back, then bitslice the odd bits and combine the two in the inner loop
1402 uint64_t key = -1;
1403 uint8_t bSize = sizeof(bitslice_t);
1404
1405 #ifdef EXACT_COUNT
1406 size_t bucket_states_tested = 0;
1407 size_t bucket_size[p->len[EVEN_STATE]/MAX_BITSLICES];
1408 #else
1409 const size_t bucket_states_tested = (p->len[EVEN_STATE])*(p->len[ODD_STATE]);
1410 #endif
1411
1412 bitslice_t *bitsliced_even_states[p->len[EVEN_STATE]/MAX_BITSLICES];
1413 size_t bitsliced_blocks = 0;
1414 uint32_t const * restrict even_end = p->states[EVEN_STATE]+p->len[EVEN_STATE];
1415
1416 // bitslice all the even states
1417 for(uint32_t * restrict p_even = p->states[EVEN_STATE]; p_even < even_end; p_even += MAX_BITSLICES){
1418
1419 #ifdef __WIN32
1420 #ifdef __MINGW32__
1421 bitslice_t * restrict lstate_p = __mingw_aligned_malloc((STATE_SIZE+ROLLBACK_SIZE) * bSize, bSize);
1422 #else
1423 bitslice_t * restrict lstate_p = _aligned_malloc((STATE_SIZE+ROLLBACK_SIZE) * bSize, bSize);
1424 #endif
1425 #else
1426 #ifdef __APPLE__
1427 bitslice_t * restrict lstate_p = malloc((STATE_SIZE+ROLLBACK_SIZE) * bSize);
1428 #else
1429 bitslice_t * restrict lstate_p = memalign(bSize, (STATE_SIZE+ROLLBACK_SIZE) * bSize);
1430 #endif
1431 #endif
1432
1433 if ( !lstate_p ) {
1434 __sync_fetch_and_add(&total_states_tested, bucket_states_tested);
1435 return key;
1436 }
1437
1438 memset(lstate_p+1, 0x0, (STATE_SIZE-1)*sizeof(bitslice_t)); // zero even bits
1439
1440 // bitslice even half-states
1441 const size_t max_slices = (even_end-p_even) < MAX_BITSLICES ? even_end-p_even : MAX_BITSLICES;
1442 #ifdef EXACT_COUNT
1443 bucket_size[bitsliced_blocks] = max_slices;
1444 #endif
1445 for(size_t slice_idx = 0; slice_idx < max_slices; ++slice_idx){
1446 uint32_t e = *(p_even+slice_idx);
1447 for(size_t bit_idx = 1; bit_idx < STATE_SIZE; bit_idx+=2, e >>= 1){
1448 // set even bits
1449 if(e&1){
1450 lstate_p[bit_idx].bytes64[slice_idx>>6] |= 1ull << (slice_idx&63);
1451 }
1452 }
1453 }
1454 // compute the rollback bits
1455 for(size_t rollback = 0; rollback < ROLLBACK_SIZE; ++rollback){
1456 // inlined crypto1_bs_lfsr_rollback
1457 const bitslice_value_t feedout = lstate_p[0].value;
1458 ++lstate_p;
1459 const bitslice_value_t ks_bits = crypto1_bs_f20(lstate_p);
1460 const bitslice_value_t feedback = (feedout ^ ks_bits ^ lstate_p[47- 5].value ^ lstate_p[47- 9].value ^
1461 lstate_p[47-10].value ^ lstate_p[47-12].value ^ lstate_p[47-14].value ^
1462 lstate_p[47-15].value ^ lstate_p[47-17].value ^ lstate_p[47-19].value ^
1463 lstate_p[47-24].value ^ lstate_p[47-25].value ^ lstate_p[47-27].value ^
1464 lstate_p[47-29].value ^ lstate_p[47-35].value ^ lstate_p[47-39].value ^
1465 lstate_p[47-41].value ^ lstate_p[47-42].value ^ lstate_p[47-43].value);
1466 lstate_p[47].value = feedback ^ bitsliced_rollback_byte[rollback].value;
1467 }
1468 bitsliced_even_states[bitsliced_blocks++] = lstate_p;
1469 }
1470
1471 // bitslice every odd state to every block of even half-states with half-finished rollback
1472 for(uint32_t const * restrict p_odd = p->states[ODD_STATE]; p_odd < p->states[ODD_STATE]+p->len[ODD_STATE]; ++p_odd){
1473 // early abort
1474 if(keys_found){
1475 goto out;
1476 }
1477
1478 // set the odd bits and compute rollback
1479 uint64_t o = (uint64_t) *p_odd;
1480 lfsr_rollback_byte((struct Crypto1State*) &o, 0, 1);
1481 // pre-compute part of the odd feedback bits (minus rollback)
1482 bool odd_feedback_bit = parity(o&0x9ce5c);
1483
1484 crypto1_bs_rewind_a0();
1485 // set odd bits
1486 for(size_t state_idx = 0; state_idx < STATE_SIZE-ROLLBACK_SIZE; o >>= 1, state_idx+=2){
1487 state_p[state_idx] = (o & 1) ? bs_ones : bs_zeroes;
1488 }
1489 const bitslice_value_t odd_feedback = odd_feedback_bit ? bs_ones.value : bs_zeroes.value;
1490
1491 for(size_t block_idx = 0; block_idx < bitsliced_blocks; ++block_idx){
1492 const bitslice_t * const restrict bitsliced_even_state = bitsliced_even_states[block_idx];
1493 size_t state_idx;
1494 // set even bits
1495 for(state_idx = 0; state_idx < STATE_SIZE-ROLLBACK_SIZE; state_idx+=2){
1496 state_p[1+state_idx] = bitsliced_even_state[1+state_idx];
1497 }
1498 // set rollback bits
1499 uint64_t lo = o;
1500 for(; state_idx < STATE_SIZE; lo >>= 1, state_idx+=2){
1501 // set the odd bits and take in the odd rollback bits from the even states
1502 if(lo & 1){
1503 state_p[state_idx].value = ~bitsliced_even_state[state_idx].value;
1504 } else {
1505 state_p[state_idx] = bitsliced_even_state[state_idx];
1506 }
1507
1508 // set the even bits and take in the even rollback bits from the odd states
1509 if((lo >> 32) & 1){
1510 state_p[1+state_idx].value = ~bitsliced_even_state[1+state_idx].value;
1511 } else {
1512 state_p[1+state_idx] = bitsliced_even_state[1+state_idx];
1513 }
1514 }
1515
1516 #ifdef EXACT_COUNT
1517 bucket_states_tested += (bucket_size[block_idx] > MAX_BITSLICES) ? MAX_BITSLICES : bucket_size[block_idx];
1518 #endif
1519 // pre-compute first keystream and feedback bit vectors
1520 const bitslice_value_t ksb = crypto1_bs_f20(state_p);
1521 const bitslice_value_t fbb = (odd_feedback ^ state_p[47- 0].value ^ state_p[47- 5].value ^ // take in the even and rollback bits
1522 state_p[47-10].value ^ state_p[47-12].value ^ state_p[47-14].value ^
1523 state_p[47-24].value ^ state_p[47-42].value);
1524
1525 // vector to contain test results (1 = passed, 0 = failed)
1526 bitslice_t results = bs_ones;
1527
1528 for(size_t tests = 0; tests < NONCE_TESTS; ++tests){
1529 size_t parity_bit_idx = 0;
1530 bitslice_value_t fb_bits = fbb;
1531 bitslice_value_t ks_bits = ksb;
1532 state_p = &states[KEYSTREAM_SIZE-1];
1533 bitslice_value_t parity_bit_vector = bs_zeroes.value;
1534
1535 // highest bit is transmitted/received first
1536 for(int32_t ks_idx = KEYSTREAM_SIZE-1; ks_idx >= 0; --ks_idx, --state_p){
1537 // decrypt nonce bits
1538 const bitslice_value_t encrypted_nonce_bit_vector = bitsliced_encrypted_nonces[tests][ks_idx].value;
1539 const bitslice_value_t decrypted_nonce_bit_vector = (encrypted_nonce_bit_vector ^ ks_bits);
1540
1541 // compute real parity bits on the fly
1542 parity_bit_vector ^= decrypted_nonce_bit_vector;
1543
1544 // update state
1545 state_p[0].value = (fb_bits ^ decrypted_nonce_bit_vector);
1546
1547 // compute next keystream bit
1548 ks_bits = crypto1_bs_f20(state_p);
1549
1550 // for each byte:
1551 if((ks_idx&7) == 0){
1552 // get encrypted parity bits
1553 const bitslice_value_t encrypted_parity_bit_vector = bitsliced_encrypted_parity_bits[tests][parity_bit_idx++].value;
1554
1555 // decrypt parity bits
1556 const bitslice_value_t decrypted_parity_bit_vector = (encrypted_parity_bit_vector ^ ks_bits);
1557
1558 // compare actual parity bits with decrypted parity bits and take count in results vector
1559 results.value &= (parity_bit_vector ^ decrypted_parity_bit_vector);
1560
1561 // make sure we still have a match in our set
1562 // if(memcmp(&results, &bs_zeroes, sizeof(bitslice_t)) == 0){
1563
1564 // this is much faster on my gcc, because somehow a memcmp needlessly spills/fills all the xmm registers to/from the stack - ???
1565 // the short-circuiting also helps
1566 if(results.bytes64[0] == 0
1567 #if MAX_BITSLICES > 64
1568 && results.bytes64[1] == 0
1569 #endif
1570 #if MAX_BITSLICES > 128
1571 && results.bytes64[2] == 0
1572 && results.bytes64[3] == 0
1573 #endif
1574 ){
1575 goto stop_tests;
1576 }
1577 // this is about as fast but less portable (requires -std=gnu99)
1578 // asm goto ("ptest %1, %0\n\t"
1579 // "jz %l2" :: "xm" (results.value), "xm" (bs_ones.value) : "cc" : stop_tests);
1580 parity_bit_vector = bs_zeroes.value;
1581 }
1582 // compute next feedback bit vector
1583 fb_bits = (state_p[47- 0].value ^ state_p[47- 5].value ^ state_p[47- 9].value ^
1584 state_p[47-10].value ^ state_p[47-12].value ^ state_p[47-14].value ^
1585 state_p[47-15].value ^ state_p[47-17].value ^ state_p[47-19].value ^
1586 state_p[47-24].value ^ state_p[47-25].value ^ state_p[47-27].value ^
1587 state_p[47-29].value ^ state_p[47-35].value ^ state_p[47-39].value ^
1588 state_p[47-41].value ^ state_p[47-42].value ^ state_p[47-43].value);
1589 }
1590 }
1591 // all nonce tests were successful: we've found the key in this block!
1592 state_t keys[MAX_BITSLICES];
1593 crypto1_bs_convert_states(&states[KEYSTREAM_SIZE], keys);
1594 for(size_t results_idx = 0; results_idx < MAX_BITSLICES; ++results_idx){
1595 if(get_vector_bit(results_idx, results)){
1596 key = keys[results_idx].value;
1597 goto out;
1598 }
1599 }
1600 stop_tests:
1601 // prepare to set new states
1602 crypto1_bs_rewind_a0();
1603 continue;
1604 }
1605 }
1606
1607 out:
1608 for(size_t block_idx = 0; block_idx < bitsliced_blocks; ++block_idx){
1609
1610 #ifdef __WIN32
1611 #ifdef __MINGW32__
1612 __mingw_aligned_free(bitsliced_even_states[block_idx]-ROLLBACK_SIZE);
1613 #else
1614 _aligned_free(bitsliced_even_states[block_idx]-ROLLBACK_SIZE);
1615 #endif
1616 #else
1617 free(bitsliced_even_states[block_idx]-ROLLBACK_SIZE);
1618 #endif
1619
1620 }
1621 __sync_fetch_and_add(&total_states_tested, bucket_states_tested);
1622 return key;
1623 }
1624
1625 static void* crack_states_thread(void* x){
1626 const size_t thread_id = (size_t)x;
1627 size_t current_bucket = thread_id;
1628 statelist_t *bucket = NULL;
1629
1630 while(current_bucket < bucket_count){
1631 if (keys_found) break;
1632
1633 if ((bucket = buckets[current_bucket])) {
1634 const uint64_t key = crack_states_bitsliced(bucket);
1635
1636 if (keys_found) break;
1637 else if(key != -1) {
1638 if (TestIfKeyExists(key)) {
1639 __sync_fetch_and_add(&keys_found, 1);
1640 __sync_fetch_and_add(&foundkey, key);
1641 printf("*");
1642 fflush(stdout);
1643 break;
1644 }
1645 printf("!");
1646 fflush(stdout);
1647 } else {
1648 printf(".");
1649 fflush(stdout);
1650 }
1651 }
1652 current_bucket += thread_count;
1653 }
1654 return NULL;
1655 }
1656
1657 static bool brute_force(void) {
1658 bool ret = false;
1659 if (known_target_key != -1) {
1660 PrintAndLog("Looking for known target key in remaining key space...");
1661 ret = TestIfKeyExists(known_target_key);
1662 } else {
1663 if (maximum_states == 0) return false; // prevent keyspace reduction error (2^-inf)
1664
1665 PrintAndLog("Brute force phase starting.");
1666
1667 clock_t time1 = clock();
1668 keys_found = 0;
1669 foundkey = 0;
1670
1671 crypto1_bs_init();
1672 memset (bitsliced_rollback_byte, 0, sizeof (bitsliced_rollback_byte));
1673 memset (bitsliced_encrypted_nonces, 0, sizeof (bitsliced_encrypted_nonces));
1674 memset (bitsliced_encrypted_parity_bits, 0, sizeof (bitsliced_encrypted_parity_bits));
1675
1676 PrintAndLog("Using %u-bit bitslices", MAX_BITSLICES);
1677 PrintAndLog("Bitslicing best_first_byte^uid[3] (rollback byte): %02X ...", best_first_bytes[0]^(cuid>>24));
1678 // convert to 32 bit little-endian
1679 crypto1_bs_bitslice_value32((best_first_bytes[0]<<24)^cuid, bitsliced_rollback_byte, 8);
1680
1681 PrintAndLog("Bitslicing nonces...");
1682 for(size_t tests = 0; tests < NONCE_TESTS; tests++){
1683 uint32_t test_nonce = brute_force_nonces[tests]->nonce_enc;
1684 uint8_t test_parity = brute_force_nonces[tests]->par_enc;
1685 // pre-xor the uid into the decrypted nonces, and also pre-xor the cuid parity into the encrypted parity bits - otherwise an exta xor is required in the decryption routine
1686 crypto1_bs_bitslice_value32(cuid^test_nonce, bitsliced_encrypted_nonces[tests], 32);
1687 // convert to 32 bit little-endian
1688 crypto1_bs_bitslice_value32(rev32( ~(test_parity ^ ~(parity(cuid>>24 & 0xff)<<3 | parity(cuid>>16 & 0xff)<<2 | parity(cuid>>8 & 0xff)<<1 | parity(cuid&0xff)))), bitsliced_encrypted_parity_bits[tests], 4);
1689 }
1690 total_states_tested = 0;
1691
1692 // count number of states to go
1693 bucket_count = 0;
1694 buckets[MAX_BUCKETS-1] = NULL;
1695 for (statelist_t *p = candidates; p != NULL && bucket_count < MAX_BUCKETS; p = p->next) {
1696 buckets[bucket_count] = p;
1697 bucket_count++;
1698 }
1699 if (bucket_count < MAX_BUCKETS) buckets[bucket_count] = NULL;
1700
1701 #ifndef __WIN32
1702 thread_count = sysconf(_SC_NPROCESSORS_CONF);
1703 if ( thread_count < 1)
1704 thread_count = 1;
1705 #endif /* _WIN32 */
1706
1707 pthread_t threads[thread_count];
1708
1709 // enumerate states using all hardware threads, each thread handles one bucket
1710 PrintAndLog("Starting %u cracking threads to search %u buckets containing a total of %"PRIu64" states...", thread_count, bucket_count, maximum_states);
1711
1712 for(size_t i = 0; i < thread_count; i++){
1713 pthread_create(&threads[i], NULL, crack_states_thread, (void*) i);
1714 }
1715 for(size_t i = 0; i < thread_count; i++){
1716 pthread_join(threads[i], 0);
1717 }
1718
1719 time1 = clock() - time1;
1720 PrintAndLog("\nTime for bruteforce %0.1f seconds.",((float)time1)/CLOCKS_PER_SEC);
1721
1722 if (keys_found) {
1723 PrintAndLog("\nFound key: %012"PRIx64"\n", foundkey);
1724 ret = true;
1725 }
1726 // reset this counter for the next call
1727 nonces_to_bruteforce = 0;
1728 }
1729 return ret;
1730 }
1731
1732 int mfnestedhard(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_t trgBlockNo, uint8_t trgKeyType, uint8_t *trgkey, bool nonce_file_read, bool nonce_file_write, bool slow, int tests, uint64_t *found_key)
1733 {
1734 // initialize Random number generator
1735 time_t t;
1736 srand((unsigned) time(&t));
1737
1738 *found_key = 0;
1739
1740 if (trgkey != NULL) {
1741 known_target_key = bytes_to_num(trgkey, 6);
1742 } else {
1743 known_target_key = -1;
1744 }
1745
1746 init_partial_statelists();
1747 init_BitFlip_statelist();
1748 write_stats = false;
1749
1750 if (tests) {
1751 // set the correct locale for the stats printing
1752 setlocale(LC_ALL, "");
1753 write_stats = true;
1754 if ((fstats = fopen("hardnested_stats.txt","a")) == NULL) {
1755 PrintAndLog("Could not create/open file hardnested_stats.txt");
1756 return 3;
1757 }
1758 for (uint32_t i = 0; i < tests; i++) {
1759 init_nonce_memory();
1760 simulate_acquire_nonces();
1761 Tests();
1762 printf("Sum(a0) = %d\n", first_byte_Sum);
1763 fprintf(fstats, "%d;", first_byte_Sum);
1764 generate_candidates(first_byte_Sum, nonces[best_first_bytes[0]].Sum8_guess);
1765 brute_force();
1766 free_nonces_memory();
1767 free_statelist_cache();
1768 free_candidates_memory(candidates);
1769 candidates = NULL;
1770 }
1771 fclose(fstats);
1772 fstats = NULL;
1773 } else {
1774 init_nonce_memory();
1775 if (nonce_file_read) { // use pre-acquired data from file nonces.bin
1776 if (read_nonce_file() != 0) {
1777 return 3;
1778 }
1779 Check_for_FilterFlipProperties();
1780 num_good_first_bytes = MIN(estimate_second_byte_sum(), GOOD_BYTES_REQUIRED);
1781 PrintAndLog("Number of first bytes with confidence > %2.1f%%: %d", CONFIDENCE_THRESHOLD*100.0, num_good_first_bytes);
1782
1783 bool cracking = generate_candidates(first_byte_Sum, nonces[best_first_bytes[0]].Sum8_guess);
1784 if (cracking || known_target_key != -1) {
1785 brute_force();
1786 }
1787
1788 } else { // acquire nonces.
1789 uint16_t is_OK = acquire_nonces(blockNo, keyType, key, trgBlockNo, trgKeyType, nonce_file_write, slow);
1790 if (is_OK != 0) {
1791 free_nonces_memory();
1792 //free_statelist_cache();
1793 free_candidates_memory(candidates);
1794 candidates = NULL;
1795 return is_OK;
1796 }
1797 }
1798
1799 //Tests();
1800 free_nonces_memory();
1801 free_statelist_cache();
1802 free_candidates_memory(candidates);
1803 candidates = NULL;
1804 }
1805 *found_key = foundkey;
1806 return 0;
1807 }
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