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1 /* crapto1.c
2
3 This program is free software; you can redistribute it and/or
4 modify it under the terms of the GNU General Public License
5 as published by the Free Software Foundation; either version 2
6 of the License, or (at your option) any later version.
7
8 This program is distributed in the hope that it will be useful,
9 but WITHOUT ANY WARRANTY; without even the implied warranty of
10 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
11 GNU General Public License for more details.
12
13 You should have received a copy of the GNU General Public License
14 along with this program; if not, write to the Free Software
15 Foundation, Inc., 51 Franklin Street, Fifth Floor,
16 Boston, MA 02110-1301, US$
17
18 Copyright (C) 2008-2014 bla <blapost@gmail.com>
19 */
20 #include "crapto1.h"
21 #include <stdlib.h>
22
23 #if !defined LOWMEM && defined __GNUC__
24 static uint8_t filterlut[1 << 20];
25 static void __attribute__((constructor)) fill_lut()
26 {
27 uint32_t i;
28 for(i = 0; i < 1 << 20; ++i)
29 filterlut[i] = filter(i);
30 }
31 #define filter(x) (filterlut[(x) & 0xfffff])
32 #endif
33
34 static void quicksort(uint32_t* const start, uint32_t* const stop)
35 {
36 uint32_t *it = start + 1, *rit = stop, t;
37
38 if(it > rit)
39 return;
40
41 while(it < rit)
42 if(*it <= *start)
43 ++it;
44 else if(*rit > *start)
45 --rit;
46 else
47 t = *it, *it = *rit, *rit = t;
48
49 if(*rit >= *start)
50 --rit;
51 if(rit != start)
52 t = *rit, *rit = *start, *start = t;
53
54 quicksort(start, rit - 1);
55 quicksort(rit + 1, stop);
56 }
57 /** binsearch
58 * Binary search for the first occurence of *stop's MSB in sorted [start,stop]
59 */
60 static inline uint32_t* binsearch(uint32_t *start, uint32_t *stop)
61 {
62 uint32_t mid, val = *stop & 0xff000000;
63 while(start != stop)
64 if(start[mid = (stop - start) >> 1] > val)
65 stop = &start[mid];
66 else
67 start += mid + 1;
68
69 return start;
70 }
71
72 /** update_contribution
73 * helper, calculates the partial linear feedback contributions and puts in MSB
74 */
75 static inline void
76 update_contribution(uint32_t *item, const uint32_t mask1, const uint32_t mask2)
77 {
78 uint32_t p = *item >> 25;
79
80 p = p << 1 | parity(*item & mask1);
81 p = p << 1 | parity(*item & mask2);
82 *item = p << 24 | (*item & 0xffffff);
83 }
84
85 /** extend_table
86 * using a bit of the keystream extend the table of possible lfsr states
87 */
88 static inline void
89 extend_table(uint32_t *tbl, uint32_t **end, int bit, int m1, int m2, uint32_t in)
90 {
91 in <<= 24;
92 for(*tbl <<= 1; tbl <= *end; *++tbl <<= 1)
93 if(filter(*tbl) ^ filter(*tbl | 1)) {
94 *tbl |= filter(*tbl) ^ bit;
95 update_contribution(tbl, m1, m2);
96 *tbl ^= in;
97 } else if(filter(*tbl) == bit) {
98 *++*end = tbl[1];
99 tbl[1] = tbl[0] | 1;
100 update_contribution(tbl, m1, m2);
101 *tbl++ ^= in;
102 update_contribution(tbl, m1, m2);
103 *tbl ^= in;
104 } else
105 *tbl-- = *(*end)--;
106 }
107 /** extend_table_simple
108 * using a bit of the keystream extend the table of possible lfsr states
109 */
110 static inline void extend_table_simple(uint32_t *tbl, uint32_t **end, int bit)
111 {
112 for(*tbl <<= 1; tbl <= *end; *++tbl <<= 1)
113 if(filter(*tbl) ^ filter(*tbl | 1))
114 *tbl |= filter(*tbl) ^ bit;
115 else if(filter(*tbl) == bit) {
116 *++*end = *++tbl;
117 *tbl = tbl[-1] | 1;
118 } else
119 *tbl-- = *(*end)--;
120 }
121 /** recover
122 * recursively narrow down the search space, 4 bits of keystream at a time
123 */
124 static struct Crypto1State*
125 recover(uint32_t *o_head, uint32_t *o_tail, uint32_t oks,
126 uint32_t *e_head, uint32_t *e_tail, uint32_t eks, int rem,
127 struct Crypto1State *sl, uint32_t in)
128 {
129 uint32_t *o, *e, i;
130
131 if(rem == -1) {
132 for(e = e_head; e <= e_tail; ++e) {
133 *e = *e << 1 ^ parity(*e & LF_POLY_EVEN) ^ !!(in & 4);
134 for(o = o_head; o <= o_tail; ++o, ++sl) {
135 sl->even = *o;
136 sl->odd = *e ^ parity(*o & LF_POLY_ODD);
137 sl[1].odd = sl[1].even = 0;
138 }
139 }
140 return sl;
141 }
142
143 for(i = 0; i < 4 && rem--; i++) {
144 oks >>= 1;
145 eks >>= 1;
146 in >>= 2;
147 extend_table(o_head, &o_tail, oks & 1, LF_POLY_EVEN << 1 | 1,
148 LF_POLY_ODD << 1, 0);
149 if(o_head > o_tail)
150 return sl;
151
152 extend_table(e_head, &e_tail, eks & 1, LF_POLY_ODD,
153 LF_POLY_EVEN << 1 | 1, in & 3);
154 if(e_head > e_tail)
155 return sl;
156 }
157
158 quicksort(o_head, o_tail);
159 quicksort(e_head, e_tail);
160
161 while(o_tail >= o_head && e_tail >= e_head)
162 if(((*o_tail ^ *e_tail) >> 24) == 0) {
163 o_tail = binsearch(o_head, o = o_tail);
164 e_tail = binsearch(e_head, e = e_tail);
165 sl = recover(o_tail--, o, oks,
166 e_tail--, e, eks, rem, sl, in);
167 }
168 else if(*o_tail > *e_tail)
169 o_tail = binsearch(o_head, o_tail) - 1;
170 else
171 e_tail = binsearch(e_head, e_tail) - 1;
172
173 return sl;
174 }
175 /** lfsr_recovery
176 * recover the state of the lfsr given 32 bits of the keystream
177 * additionally you can use the in parameter to specify the value
178 * that was fed into the lfsr at the time the keystream was generated
179 */
180 struct Crypto1State* lfsr_recovery32(uint32_t ks2, uint32_t in)
181 {
182 struct Crypto1State *statelist;
183 uint32_t *odd_head = 0, *odd_tail = 0, oks = 0;
184 uint32_t *even_head = 0, *even_tail = 0, eks = 0;
185 int i;
186
187 // split the keystream into an odd and even part
188 for(i = 31; i >= 0; i -= 2)
189 oks = oks << 1 | BEBIT(ks2, i);
190 for(i = 30; i >= 0; i -= 2)
191 eks = eks << 1 | BEBIT(ks2, i);
192
193 odd_head = odd_tail = malloc(sizeof(uint32_t) << 21);
194 even_head = even_tail = malloc(sizeof(uint32_t) << 21);
195 statelist = malloc(sizeof(struct Crypto1State) << 18);
196 if(!odd_tail-- || !even_tail-- || !statelist) {
197 free(statelist);
198 statelist = 0;
199 goto out;
200 }
201
202 statelist->odd = statelist->even = 0;
203
204 // initialize statelists: add all possible states which would result into the rightmost 2 bits of the keystream
205 for(i = 1 << 20; i >= 0; --i) {
206 if(filter(i) == (oks & 1))
207 *++odd_tail = i;
208 if(filter(i) == (eks & 1))
209 *++even_tail = i;
210 }
211
212 // extend the statelists. Look at the next 8 Bits of the keystream (4 Bit each odd and even):
213 for(i = 0; i < 4; i++) {
214 extend_table_simple(odd_head, &odd_tail, (oks >>= 1) & 1);
215 extend_table_simple(even_head, &even_tail, (eks >>= 1) & 1);
216 }
217
218 // the statelists now contain all states which could have generated the last 10 Bits of the keystream.
219 // 22 bits to go to recover 32 bits in total. From now on, we need to take the "in"
220 // parameter into account.
221 in = (in >> 16 & 0xff) | (in << 16) | (in & 0xff00);
222 recover(odd_head, odd_tail, oks,
223 even_head, even_tail, eks, 11, statelist, in << 1);
224
225 out:
226 free(odd_head);
227 free(even_head);
228 return statelist;
229 }
230
231 static const uint32_t S1[] = { 0x62141, 0x310A0, 0x18850, 0x0C428, 0x06214,
232 0x0310A, 0x85E30, 0xC69AD, 0x634D6, 0xB5CDE, 0xDE8DA, 0x6F46D, 0xB3C83,
233 0x59E41, 0xA8995, 0xD027F, 0x6813F, 0x3409F, 0x9E6FA};
234 static const uint32_t S2[] = { 0x3A557B00, 0x5D2ABD80, 0x2E955EC0, 0x174AAF60,
235 0x0BA557B0, 0x05D2ABD8, 0x0449DE68, 0x048464B0, 0x42423258, 0x278192A8,
236 0x156042D0, 0x0AB02168, 0x43F89B30, 0x61FC4D98, 0x765EAD48, 0x7D8FDD20,
237 0x7EC7EE90, 0x7F63F748, 0x79117020};
238 static const uint32_t T1[] = {
239 0x4F37D, 0x279BE, 0x97A6A, 0x4BD35, 0x25E9A, 0x12F4D, 0x097A6, 0x80D66,
240 0xC4006, 0x62003, 0xB56B4, 0x5AB5A, 0xA9318, 0xD0F39, 0x6879C, 0xB057B,
241 0x582BD, 0x2C15E, 0x160AF, 0x8F6E2, 0xC3DC4, 0xE5857, 0x72C2B, 0x39615,
242 0x98DBF, 0xC806A, 0xE0680, 0x70340, 0x381A0, 0x98665, 0x4C332, 0xA272C};
243 static const uint32_t T2[] = { 0x3C88B810, 0x5E445C08, 0x2982A580, 0x14C152C0,
244 0x4A60A960, 0x253054B0, 0x52982A58, 0x2FEC9EA8, 0x1156C4D0, 0x08AB6268,
245 0x42F53AB0, 0x217A9D58, 0x161DC528, 0x0DAE6910, 0x46D73488, 0x25CB11C0,
246 0x52E588E0, 0x6972C470, 0x34B96238, 0x5CFC3A98, 0x28DE96C8, 0x12CFC0E0,
247 0x4967E070, 0x64B3F038, 0x74F97398, 0x7CDC3248, 0x38CE92A0, 0x1C674950,
248 0x0E33A4A8, 0x01B959D0, 0x40DCACE8, 0x26CEDDF0};
249 static const uint32_t C1[] = { 0x846B5, 0x4235A, 0x211AD};
250 static const uint32_t C2[] = { 0x1A822E0, 0x21A822E0, 0x21A822E0};
251 /** Reverse 64 bits of keystream into possible cipher states
252 * Variation mentioned in the paper. Somewhat optimized version
253 */
254 struct Crypto1State* lfsr_recovery64(uint32_t ks2, uint32_t ks3)
255 {
256 struct Crypto1State *statelist, *sl;
257 uint8_t oks[32], eks[32], hi[32];
258 uint32_t low = 0, win = 0;
259 uint32_t *tail, table[1 << 16];
260 int i, j;
261
262 sl = statelist = malloc(sizeof(struct Crypto1State) << 4);
263 if(!sl)
264 return 0;
265 sl->odd = sl->even = 0;
266
267 for(i = 30; i >= 0; i -= 2) {
268 oks[i >> 1] = BEBIT(ks2, i);
269 oks[16 + (i >> 1)] = BEBIT(ks3, i);
270 }
271 for(i = 31; i >= 0; i -= 2) {
272 eks[i >> 1] = BEBIT(ks2, i);
273 eks[16 + (i >> 1)] = BEBIT(ks3, i);
274 }
275
276 for(i = 0xfffff; i >= 0; --i) {
277 if (filter(i) != oks[0])
278 continue;
279
280 *(tail = table) = i;
281 for(j = 1; tail >= table && j < 29; ++j)
282 extend_table_simple(table, &tail, oks[j]);
283
284 if(tail < table)
285 continue;
286
287 for(j = 0; j < 19; ++j)
288 low = low << 1 | parity(i & S1[j]);
289 for(j = 0; j < 32; ++j)
290 hi[j] = parity(i & T1[j]);
291
292 for(; tail >= table; --tail) {
293 for(j = 0; j < 3; ++j) {
294 *tail = *tail << 1;
295 *tail |= parity((i & C1[j]) ^ (*tail & C2[j]));
296 if(filter(*tail) != oks[29 + j])
297 goto continue2;
298 }
299
300 for(j = 0; j < 19; ++j)
301 win = win << 1 | parity(*tail & S2[j]);
302
303 win ^= low;
304 for(j = 0; j < 32; ++j) {
305 win = win << 1 ^ hi[j] ^ parity(*tail & T2[j]);
306 if(filter(win) != eks[j])
307 goto continue2;
308 }
309
310 *tail = *tail << 1 | parity(LF_POLY_EVEN & *tail);
311 sl->odd = *tail ^ parity(LF_POLY_ODD & win);
312 sl->even = win;
313 ++sl;
314 sl->odd = sl->even = 0;
315 continue2:;
316 }
317 }
318 return statelist;
319 }
320
321 /** lfsr_rollback_bit
322 * Rollback the shift register in order to get previous states
323 */
324 uint8_t lfsr_rollback_bit(struct Crypto1State *s, uint32_t in, int fb)
325 {
326 int out;
327 uint8_t ret;
328 uint32_t t;
329
330 s->odd &= 0xffffff;
331 t = s->odd, s->odd = s->even, s->even = t;
332
333 out = s->even & 1;
334 out ^= LF_POLY_EVEN & (s->even >>= 1);
335 out ^= LF_POLY_ODD & s->odd;
336 out ^= !!in;
337 out ^= (ret = filter(s->odd)) & !!fb;
338
339 s->even |= parity(out) << 23;
340 return ret;
341 }
342 /** lfsr_rollback_byte
343 * Rollback the shift register in order to get previous states
344 */
345 uint8_t lfsr_rollback_byte(struct Crypto1State *s, uint32_t in, int fb)
346 {
347 /*
348 int i, ret = 0;
349 for (i = 7; i >= 0; --i)
350 ret |= lfsr_rollback_bit(s, BIT(in, i), fb) << i;
351 */
352 // unfold loop 20160112
353 uint8_t ret = 0;
354 ret |= lfsr_rollback_bit(s, BIT(in, 7), fb) << 7;
355 ret |= lfsr_rollback_bit(s, BIT(in, 6), fb) << 6;
356 ret |= lfsr_rollback_bit(s, BIT(in, 5), fb) << 5;
357 ret |= lfsr_rollback_bit(s, BIT(in, 4), fb) << 4;
358 ret |= lfsr_rollback_bit(s, BIT(in, 3), fb) << 3;
359 ret |= lfsr_rollback_bit(s, BIT(in, 2), fb) << 2;
360 ret |= lfsr_rollback_bit(s, BIT(in, 1), fb) << 1;
361 ret |= lfsr_rollback_bit(s, BIT(in, 0), fb) << 0;
362 return ret;
363 }
364 /** lfsr_rollback_word
365 * Rollback the shift register in order to get previous states
366 */
367 uint32_t lfsr_rollback_word(struct Crypto1State *s, uint32_t in, int fb)
368 {
369 /*
370 int i;
371 uint32_t ret = 0;
372 for (i = 31; i >= 0; --i)
373 ret |= lfsr_rollback_bit(s, BEBIT(in, i), fb) << (i ^ 24);
374 */
375 // unfold loop 20160112
376 uint32_t ret = 0;
377 ret |= lfsr_rollback_bit(s, BEBIT(in, 31), fb) << (31 ^ 24);
378 ret |= lfsr_rollback_bit(s, BEBIT(in, 30), fb) << (30 ^ 24);
379 ret |= lfsr_rollback_bit(s, BEBIT(in, 29), fb) << (29 ^ 24);
380 ret |= lfsr_rollback_bit(s, BEBIT(in, 28), fb) << (28 ^ 24);
381 ret |= lfsr_rollback_bit(s, BEBIT(in, 27), fb) << (27 ^ 24);
382 ret |= lfsr_rollback_bit(s, BEBIT(in, 26), fb) << (26 ^ 24);
383 ret |= lfsr_rollback_bit(s, BEBIT(in, 25), fb) << (25 ^ 24);
384 ret |= lfsr_rollback_bit(s, BEBIT(in, 24), fb) << (24 ^ 24);
385
386 ret |= lfsr_rollback_bit(s, BEBIT(in, 23), fb) << (23 ^ 24);
387 ret |= lfsr_rollback_bit(s, BEBIT(in, 22), fb) << (22 ^ 24);
388 ret |= lfsr_rollback_bit(s, BEBIT(in, 21), fb) << (21 ^ 24);
389 ret |= lfsr_rollback_bit(s, BEBIT(in, 20), fb) << (20 ^ 24);
390 ret |= lfsr_rollback_bit(s, BEBIT(in, 19), fb) << (19 ^ 24);
391 ret |= lfsr_rollback_bit(s, BEBIT(in, 18), fb) << (18 ^ 24);
392 ret |= lfsr_rollback_bit(s, BEBIT(in, 17), fb) << (17 ^ 24);
393 ret |= lfsr_rollback_bit(s, BEBIT(in, 16), fb) << (16 ^ 24);
394
395 ret |= lfsr_rollback_bit(s, BEBIT(in, 15), fb) << (15 ^ 24);
396 ret |= lfsr_rollback_bit(s, BEBIT(in, 14), fb) << (14 ^ 24);
397 ret |= lfsr_rollback_bit(s, BEBIT(in, 13), fb) << (13 ^ 24);
398 ret |= lfsr_rollback_bit(s, BEBIT(in, 12), fb) << (12 ^ 24);
399 ret |= lfsr_rollback_bit(s, BEBIT(in, 11), fb) << (11 ^ 24);
400 ret |= lfsr_rollback_bit(s, BEBIT(in, 10), fb) << (10 ^ 24);
401 ret |= lfsr_rollback_bit(s, BEBIT(in, 9), fb) << (9 ^ 24);
402 ret |= lfsr_rollback_bit(s, BEBIT(in, 8), fb) << (8 ^ 24);
403
404 ret |= lfsr_rollback_bit(s, BEBIT(in, 7), fb) << (7 ^ 24);
405 ret |= lfsr_rollback_bit(s, BEBIT(in, 6), fb) << (6 ^ 24);
406 ret |= lfsr_rollback_bit(s, BEBIT(in, 5), fb) << (5 ^ 24);
407 ret |= lfsr_rollback_bit(s, BEBIT(in, 4), fb) << (4 ^ 24);
408 ret |= lfsr_rollback_bit(s, BEBIT(in, 3), fb) << (3 ^ 24);
409 ret |= lfsr_rollback_bit(s, BEBIT(in, 2), fb) << (2 ^ 24);
410 ret |= lfsr_rollback_bit(s, BEBIT(in, 1), fb) << (1 ^ 24);
411 ret |= lfsr_rollback_bit(s, BEBIT(in, 0), fb) << (0 ^ 24);
412 return ret;
413 }
414
415 /** nonce_distance
416 * x,y valid tag nonces, then prng_successor(x, nonce_distance(x, y)) = y
417 */
418 static uint16_t *dist = 0;
419 int nonce_distance(uint32_t from, uint32_t to)
420 {
421 uint16_t x, i;
422 // generate distance lookup table
423 if (!dist) {
424 dist = malloc(2 << 16);
425 if (!dist) return -1;
426
427 for (x = i = 1; i; ++i) {
428 dist[(x & 0xff) << 8 | x >> 8] = i;
429 x = x >> 1 | (x ^ x >> 2 ^ x >> 3 ^ x >> 5) << 15;
430 }
431 }
432 return (65535 + dist[to >> 16] - dist[from >> 16]) % 65535;
433 }
434
435
436 static uint32_t fastfwd[2][8] = {
437 { 0, 0x4BC53, 0xECB1, 0x450E2, 0x25E29, 0x6E27A, 0x2B298, 0x60ECB},
438 { 0, 0x1D962, 0x4BC53, 0x56531, 0xECB1, 0x135D3, 0x450E2, 0x58980}};
439
440
441 /** lfsr_prefix_ks
442 *
443 * Is an exported helper function from the common prefix attack
444 * Described in the "dark side" paper. It returns an -1 terminated array
445 * of possible partial(21 bit) secret state.
446 * The required keystream(ks) needs to contain the keystream that was used to
447 * encrypt the NACK which is observed when varying only the 3 last bits of Nr
448 * only correct iff [NR_3] ^ NR_3 does not depend on Nr_3
449 */
450 uint32_t* lfsr_prefix_ks(uint8_t ks[8], int isodd)
451 {
452 uint32_t *candidates = malloc(4 << 10);
453 if(!candidates) return 0;
454
455 uint32_t c, entry;
456 int size = 0, i, good;
457
458 for(i = 0; i < 1 << 21; ++i) {
459 for(c = 0, good = 1; good && c < 8; ++c) {
460 entry = i ^ fastfwd[isodd][c];
461 good &= (BIT(ks[c], isodd) == filter(entry >> 1));
462 good &= (BIT(ks[c], isodd + 2) == filter(entry));
463 }
464 if(good)
465 candidates[size++] = i;
466 }
467
468 candidates[size] = -1;
469
470 return candidates;
471 }
472
473 /** check_pfx_parity
474 * helper function which eliminates possible secret states using parity bits
475 */
476 static struct Crypto1State* check_pfx_parity(uint32_t prefix, uint32_t rresp, uint8_t parities[8][8], uint32_t odd, uint32_t even, struct Crypto1State* sl)
477 {
478 uint32_t ks1, nr, ks2, rr, ks3, c, good = 1;
479
480 for(c = 0; good && c < 8; ++c) {
481 sl->odd = odd ^ fastfwd[1][c];
482 sl->even = even ^ fastfwd[0][c];
483
484 lfsr_rollback_bit(sl, 0, 0);
485 lfsr_rollback_bit(sl, 0, 0);
486
487 ks3 = lfsr_rollback_bit(sl, 0, 0);
488 ks2 = lfsr_rollback_word(sl, 0, 0);
489 ks1 = lfsr_rollback_word(sl, prefix | c << 5, 1);
490
491 nr = ks1 ^ (prefix | c << 5);
492 rr = ks2 ^ rresp;
493
494 good &= parity(nr & 0x000000ff) ^ parities[c][3] ^ BIT(ks2, 24);
495 good &= parity(rr & 0xff000000) ^ parities[c][4] ^ BIT(ks2, 16);
496 good &= parity(rr & 0x00ff0000) ^ parities[c][5] ^ BIT(ks2, 8);
497 good &= parity(rr & 0x0000ff00) ^ parities[c][6] ^ BIT(ks2, 0);
498 good &= parity(rr & 0x000000ff) ^ parities[c][7] ^ ks3;
499 }
500
501 return sl + good;
502 }
503
504 /** lfsr_common_prefix
505 * Implentation of the common prefix attack.
506 * Requires the 28 bit constant prefix used as reader nonce (pfx)
507 * The reader response used (rr)
508 * The keystream used to encrypt the observed NACK's (ks)
509 * The parity bits (par)
510 * It returns a zero terminated list of possible cipher states after the
511 * tag nonce was fed in
512 */
513 struct Crypto1State* lfsr_common_prefix(uint32_t pfx, uint32_t rr, uint8_t ks[8], uint8_t par[8][8])
514 {
515 struct Crypto1State *statelist, *s;
516 uint32_t *odd, *even, *o, *e, top;
517
518 odd = lfsr_prefix_ks(ks, 1);
519 even = lfsr_prefix_ks(ks, 0);
520
521 s = statelist = malloc((sizeof *statelist) << 21);
522 if(!s || !odd || !even) {
523 free(statelist);
524 statelist = 0;
525 goto out;
526 }
527
528 for(o = odd; *o + 1; ++o)
529 for(e = even; *e + 1; ++e)
530 for(top = 0; top < 64; ++top) {
531 *o += 1 << 21;
532 *e += (!(top & 7) + 1) << 21;
533 s = check_pfx_parity(pfx, rr, par, *o, *e, s);
534 }
535
536 s->odd = s->even = 0;
537 out:
538 free(odd);
539 free(even);
540 return statelist;
541 }
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