7847961b |
1 | /* crapto1.c\r |
2 | \r |
3 | This program is free software; you can redistribute it and/or\r |
4 | modify it under the terms of the GNU General Public License\r |
5 | as published by the Free Software Foundation; either version 2\r |
6 | of the License, or (at your option) any later version.\r |
7 | \r |
8 | This program is distributed in the hope that it will be useful,\r |
9 | but WITHOUT ANY WARRANTY; without even the implied warranty of\r |
10 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\r |
11 | GNU General Public License for more details.\r |
12 | \r |
13 | You should have received a copy of the GNU General Public License\r |
14 | along with this program; if not, write to the Free Software\r |
15 | Foundation, Inc., 51 Franklin Street, Fifth Floor,\r |
16 | Boston, MA 02110-1301, US$\r |
17 | \r |
18 | Copyright (C) 2008-2008 bla <blapost@gmail.com>\r |
19 | */\r |
20 | #include "crapto1.h"\r |
21 | #include <stdlib.h>\r |
22 | \r |
23 | #if !defined LOWMEM && defined __GNUC__\r |
24 | static uint8_t filterlut[1 << 20];\r |
25 | static void __attribute__((constructor)) fill_lut()\r |
26 | {\r |
27 | uint32_t i;\r |
28 | for(i = 0; i < 1 << 20; ++i)\r |
29 | filterlut[i] = filter(i);\r |
30 | }\r |
31 | #define filter(x) (filterlut[(x) & 0xfffff])\r |
32 | #endif\r |
33 | \r |
34 | static void quicksort(uint32_t* const start, uint32_t* const stop)\r |
35 | {\r |
36 | uint32_t *it = start + 1, *rit = stop;\r |
37 | \r |
38 | if(it > rit)\r |
39 | return;\r |
40 | \r |
41 | while(it < rit)\r |
42 | if(*it <= *start)\r |
43 | ++it;\r |
44 | else if(*rit > *start)\r |
45 | --rit;\r |
46 | else\r |
47 | *it ^= (*it ^= *rit, *rit ^= *it);\r |
48 | \r |
49 | if(*rit >= *start)\r |
50 | --rit;\r |
51 | if(rit != start)\r |
52 | *rit ^= (*rit ^= *start, *start ^= *rit);\r |
53 | \r |
54 | quicksort(start, rit - 1);\r |
55 | quicksort(rit + 1, stop);\r |
56 | }\r |
57 | /** binsearch\r |
58 | * Binary search for the first occurence of *stop's MSB in sorted [start,stop]\r |
59 | */\r |
60 | static inline uint32_t* binsearch(uint32_t *start, uint32_t *stop)\r |
61 | {\r |
62 | uint32_t mid, val = *stop & 0xff000000;\r |
63 | while(start != stop)\r |
64 | if(start[mid = (stop - start) >> 1] > val)\r |
65 | stop = &start[mid];\r |
66 | else\r |
67 | start += mid + 1;\r |
68 | \r |
69 | return start;\r |
70 | }\r |
71 | \r |
72 | /** update_contribution\r |
73 | * helper, calculates the partial linear feedback contributions and puts in MSB\r |
74 | */\r |
75 | static inline void\r |
76 | update_contribution(uint32_t *item, const uint32_t mask1, const uint32_t mask2)\r |
77 | {\r |
78 | uint32_t p = *item >> 25;\r |
79 | \r |
80 | p = p << 1 | parity(*item & mask1);\r |
81 | p = p << 1 | parity(*item & mask2);\r |
82 | *item = p << 24 | (*item & 0xffffff);\r |
83 | }\r |
84 | \r |
85 | /** extend_table\r |
86 | * using a bit of the keystream extend the table of possible lfsr states\r |
87 | */\r |
88 | static inline void\r |
89 | extend_table(uint32_t *tbl, uint32_t **end, int bit, int m1, int m2, uint32_t in)\r |
90 | {\r |
91 | in <<= 24;\r |
92 | for(*tbl <<= 1; tbl <= *end; *++tbl <<= 1)\r |
93 | if(filter(*tbl) ^ filter(*tbl | 1)) {\r |
94 | *tbl |= filter(*tbl) ^ bit;\r |
95 | update_contribution(tbl, m1, m2);\r |
96 | *tbl ^= in;\r |
97 | } else if(filter(*tbl) == bit) {\r |
98 | *++*end = tbl[1];\r |
99 | tbl[1] = tbl[0] | 1;\r |
100 | update_contribution(tbl, m1, m2);\r |
101 | *tbl++ ^= in;\r |
102 | update_contribution(tbl, m1, m2);\r |
103 | *tbl ^= in;\r |
104 | } else\r |
105 | *tbl-- = *(*end)--;\r |
106 | }\r |
107 | /** extend_table_simple\r |
108 | * using a bit of the keystream extend the table of possible lfsr states\r |
109 | */\r |
110 | static inline void extend_table_simple(uint32_t *tbl, uint32_t **end, int bit)\r |
111 | {\r |
112 | for(*tbl <<= 1; tbl <= *end; *++tbl <<= 1)\r |
113 | if(filter(*tbl) ^ filter(*tbl | 1))\r |
114 | *tbl |= filter(*tbl) ^ bit;\r |
115 | else if(filter(*tbl) == bit) {\r |
116 | *++*end = *++tbl;\r |
117 | *tbl = tbl[-1] | 1;\r |
118 | } else\r |
119 | *tbl-- = *(*end)--;\r |
120 | }\r |
121 | /** recover\r |
122 | * recursively narrow down the search space, 4 bits of keystream at a time\r |
123 | */\r |
124 | static struct Crypto1State*\r |
125 | recover(uint32_t *o_head, uint32_t *o_tail, uint32_t oks,\r |
126 | uint32_t *e_head, uint32_t *e_tail, uint32_t eks, int rem,\r |
127 | struct Crypto1State *sl, uint32_t in)\r |
128 | {\r |
129 | uint32_t *o, *e, i;\r |
130 | \r |
131 | if(rem == -1) {\r |
132 | for(e = e_head; e <= e_tail; ++e) {\r |
133 | *e = *e << 1 ^ parity(*e & LF_POLY_EVEN) ^ !!(in & 4);\r |
134 | for(o = o_head; o <= o_tail; ++o, ++sl) {\r |
135 | sl->even = *o;\r |
136 | sl->odd = *e ^ parity(*o & LF_POLY_ODD);\r |
137 | sl[1].odd = sl[1].even = 0;\r |
138 | }\r |
139 | }\r |
140 | return sl;\r |
141 | }\r |
142 | \r |
143 | for(i = 0; i < 4 && rem--; i++) {\r |
144 | oks >>= 1;\r |
145 | eks >>= 1;\r |
146 | in >>= 2;\r |
147 | extend_table(o_head, &o_tail, oks & 1, LF_POLY_EVEN << 1 | 1,\r |
148 | LF_POLY_ODD << 1, 0);\r |
149 | if(o_head > o_tail)\r |
150 | return sl;\r |
151 | \r |
152 | extend_table(e_head, &e_tail, eks & 1, LF_POLY_ODD,\r |
153 | LF_POLY_EVEN << 1 | 1, in & 3);\r |
154 | if(e_head > e_tail)\r |
155 | return sl;\r |
156 | }\r |
157 | \r |
158 | quicksort(o_head, o_tail);\r |
159 | quicksort(e_head, e_tail);\r |
160 | \r |
161 | while(o_tail >= o_head && e_tail >= e_head)\r |
162 | if(((*o_tail ^ *e_tail) >> 24) == 0) {\r |
163 | o_tail = binsearch(o_head, o = o_tail);\r |
164 | e_tail = binsearch(e_head, e = e_tail);\r |
165 | sl = recover(o_tail--, o, oks,\r |
166 | e_tail--, e, eks, rem, sl, in);\r |
167 | }\r |
168 | else if(*o_tail > *e_tail)\r |
169 | o_tail = binsearch(o_head, o_tail) - 1;\r |
170 | else\r |
171 | e_tail = binsearch(e_head, e_tail) - 1;\r |
172 | \r |
173 | return sl;\r |
174 | }\r |
175 | /** lfsr_recovery\r |
176 | * recover the state of the lfsr given 32 bits of the keystream\r |
177 | * additionally you can use the in parameter to specify the value\r |
178 | * that was fed into the lfsr at the time the keystream was generated\r |
179 | */\r |
180 | struct Crypto1State* lfsr_recovery32(uint32_t ks2, uint32_t in)\r |
181 | {\r |
182 | struct Crypto1State *statelist;\r |
183 | uint32_t *odd_head = 0, *odd_tail = 0, oks = 0;\r |
184 | uint32_t *even_head = 0, *even_tail = 0, eks = 0;\r |
185 | int i;\r |
186 | \r |
187 | for(i = 31; i >= 0; i -= 2)\r |
188 | oks = oks << 1 | BEBIT(ks2, i);\r |
189 | for(i = 30; i >= 0; i -= 2)\r |
190 | eks = eks << 1 | BEBIT(ks2, i);\r |
191 | \r |
192 | odd_head = odd_tail = malloc(sizeof(uint32_t) << 21);\r |
193 | even_head = even_tail = malloc(sizeof(uint32_t) << 21);\r |
194 | statelist = malloc(sizeof(struct Crypto1State) << 18);\r |
195 | if(!odd_tail-- || !even_tail-- || !statelist) {\r |
196 | free(statelist);\r |
197 | statelist = 0;\r |
198 | goto out;\r |
199 | }\r |
200 | \r |
201 | statelist->odd = statelist->even = 0;\r |
202 | \r |
203 | for(i = 1 << 20; i >= 0; --i) {\r |
204 | if(filter(i) == (oks & 1))\r |
205 | *++odd_tail = i;\r |
206 | if(filter(i) == (eks & 1))\r |
207 | *++even_tail = i;\r |
208 | }\r |
209 | \r |
210 | for(i = 0; i < 4; i++) {\r |
211 | extend_table_simple(odd_head, &odd_tail, (oks >>= 1) & 1);\r |
212 | extend_table_simple(even_head, &even_tail, (eks >>= 1) & 1);\r |
213 | }\r |
214 | \r |
215 | in = (in >> 16 & 0xff) | (in << 16) | (in & 0xff00);\r |
216 | recover(odd_head, odd_tail, oks,\r |
217 | even_head, even_tail, eks, 11, statelist, in << 1);\r |
218 | \r |
219 | out:\r |
220 | free(odd_head);\r |
221 | free(even_head);\r |
222 | return statelist;\r |
223 | }\r |
224 | \r |
225 | static const uint32_t S1[] = { 0x62141, 0x310A0, 0x18850, 0x0C428, 0x06214,\r |
226 | 0x0310A, 0x85E30, 0xC69AD, 0x634D6, 0xB5CDE, 0xDE8DA, 0x6F46D, 0xB3C83,\r |
227 | 0x59E41, 0xA8995, 0xD027F, 0x6813F, 0x3409F, 0x9E6FA};\r |
228 | static const uint32_t S2[] = { 0x3A557B00, 0x5D2ABD80, 0x2E955EC0, 0x174AAF60,\r |
229 | 0x0BA557B0, 0x05D2ABD8, 0x0449DE68, 0x048464B0, 0x42423258, 0x278192A8,\r |
230 | 0x156042D0, 0x0AB02168, 0x43F89B30, 0x61FC4D98, 0x765EAD48, 0x7D8FDD20,\r |
231 | 0x7EC7EE90, 0x7F63F748, 0x79117020};\r |
232 | static const uint32_t T1[] = {\r |
233 | 0x4F37D, 0x279BE, 0x97A6A, 0x4BD35, 0x25E9A, 0x12F4D, 0x097A6, 0x80D66,\r |
234 | 0xC4006, 0x62003, 0xB56B4, 0x5AB5A, 0xA9318, 0xD0F39, 0x6879C, 0xB057B,\r |
235 | 0x582BD, 0x2C15E, 0x160AF, 0x8F6E2, 0xC3DC4, 0xE5857, 0x72C2B, 0x39615,\r |
236 | 0x98DBF, 0xC806A, 0xE0680, 0x70340, 0x381A0, 0x98665, 0x4C332, 0xA272C};\r |
237 | static const uint32_t T2[] = { 0x3C88B810, 0x5E445C08, 0x2982A580, 0x14C152C0,\r |
238 | 0x4A60A960, 0x253054B0, 0x52982A58, 0x2FEC9EA8, 0x1156C4D0, 0x08AB6268,\r |
239 | 0x42F53AB0, 0x217A9D58, 0x161DC528, 0x0DAE6910, 0x46D73488, 0x25CB11C0,\r |
240 | 0x52E588E0, 0x6972C470, 0x34B96238, 0x5CFC3A98, 0x28DE96C8, 0x12CFC0E0,\r |
241 | 0x4967E070, 0x64B3F038, 0x74F97398, 0x7CDC3248, 0x38CE92A0, 0x1C674950,\r |
242 | 0x0E33A4A8, 0x01B959D0, 0x40DCACE8, 0x26CEDDF0};\r |
243 | static const uint32_t C1[] = { 0x846B5, 0x4235A, 0x211AD};\r |
244 | static const uint32_t C2[] = { 0x1A822E0, 0x21A822E0, 0x21A822E0};\r |
245 | /** Reverse 64 bits of keystream into possible cipher states\r |
246 | * Variation mentioned in the paper. Somewhat optimized version\r |
247 | */\r |
248 | struct Crypto1State* lfsr_recovery64(uint32_t ks2, uint32_t ks3)\r |
249 | {\r |
250 | struct Crypto1State *statelist, *sl;\r |
251 | uint8_t oks[32], eks[32], hi[32];\r |
252 | uint32_t low = 0, win = 0;\r |
253 | uint32_t *tail, table[1 << 16];\r |
254 | int i, j;\r |
255 | \r |
256 | sl = statelist = malloc(sizeof(struct Crypto1State) << 4);\r |
257 | if(!sl)\r |
258 | return 0;\r |
259 | sl->odd = sl->even = 0;\r |
260 | \r |
261 | for(i = 30; i >= 0; i -= 2) {\r |
262 | oks[i >> 1] = BEBIT(ks2, i);\r |
263 | oks[16 + (i >> 1)] = BEBIT(ks3, i);\r |
264 | }\r |
265 | for(i = 31; i >= 0; i -= 2) {\r |
266 | eks[i >> 1] = BEBIT(ks2, i);\r |
267 | eks[16 + (i >> 1)] = BEBIT(ks3, i);\r |
268 | }\r |
269 | \r |
270 | for(i = 0xfffff; i >= 0; --i) {\r |
271 | if (filter(i) != oks[0])\r |
272 | continue;\r |
273 | \r |
274 | *(tail = table) = i;\r |
275 | for(j = 1; tail >= table && j < 29; ++j)\r |
276 | extend_table_simple(table, &tail, oks[j]);\r |
277 | \r |
278 | if(tail < table)\r |
279 | continue;\r |
280 | \r |
281 | for(j = 0; j < 19; ++j)\r |
282 | low = low << 1 | parity(i & S1[j]);\r |
283 | for(j = 0; j < 32; ++j)\r |
284 | hi[j] = parity(i & T1[j]);\r |
285 | \r |
286 | for(; tail >= table; --tail) {\r |
287 | for(j = 0; j < 3; ++j) {\r |
288 | *tail = *tail << 1;\r |
289 | *tail |= parity((i & C1[j]) ^ (*tail & C2[j]));\r |
290 | if(filter(*tail) != oks[29 + j])\r |
291 | goto continue2;\r |
292 | }\r |
293 | \r |
294 | for(j = 0; j < 19; ++j)\r |
295 | win = win << 1 | parity(*tail & S2[j]);\r |
296 | \r |
297 | win ^= low;\r |
298 | for(j = 0; j < 32; ++j) {\r |
299 | win = win << 1 ^ hi[j] ^ parity(*tail & T2[j]);\r |
300 | if(filter(win) != eks[j])\r |
301 | goto continue2;\r |
302 | }\r |
303 | \r |
304 | *tail = *tail << 1 | parity(LF_POLY_EVEN & *tail);\r |
305 | sl->odd = *tail ^ parity(LF_POLY_ODD & win);\r |
306 | sl->even = win;\r |
307 | ++sl;\r |
308 | sl->odd = sl->even = 0;\r |
309 | continue2:;\r |
310 | }\r |
311 | }\r |
312 | return statelist;\r |
313 | }\r |
314 | \r |
315 | /** lfsr_rollback_bit\r |
316 | * Rollback the shift register in order to get previous states\r |
317 | */\r |
318 | uint8_t lfsr_rollback_bit(struct Crypto1State *s, uint32_t in, int fb)\r |
319 | {\r |
320 | int out;\r |
321 | uint8_t ret;\r |
322 | \r |
323 | s->odd &= 0xffffff;\r |
324 | s->odd ^= (s->odd ^= s->even, s->even ^= s->odd);\r |
325 | \r |
326 | out = s->even & 1;\r |
327 | out ^= LF_POLY_EVEN & (s->even >>= 1);\r |
328 | out ^= LF_POLY_ODD & s->odd;\r |
329 | out ^= !!in;\r |
330 | out ^= (ret = filter(s->odd)) & !!fb;\r |
331 | \r |
332 | s->even |= parity(out) << 23;\r |
333 | return ret;\r |
334 | }\r |
335 | /** lfsr_rollback_byte\r |
336 | * Rollback the shift register in order to get previous states\r |
337 | */\r |
338 | uint8_t lfsr_rollback_byte(struct Crypto1State *s, uint32_t in, int fb)\r |
339 | {\r |
340 | int i, ret = 0;\r |
341 | for (i = 7; i >= 0; --i)\r |
342 | ret |= lfsr_rollback_bit(s, BIT(in, i), fb) << i;\r |
343 | return ret;\r |
344 | }\r |
345 | /** lfsr_rollback_word\r |
346 | * Rollback the shift register in order to get previous states\r |
347 | */\r |
348 | uint32_t lfsr_rollback_word(struct Crypto1State *s, uint32_t in, int fb)\r |
349 | {\r |
350 | int i;\r |
351 | uint32_t ret = 0;\r |
352 | for (i = 31; i >= 0; --i)\r |
353 | ret |= lfsr_rollback_bit(s, BEBIT(in, i), fb) << (i ^ 24);\r |
354 | return ret;\r |
355 | }\r |
356 | \r |
357 | /** nonce_distance\r |
358 | * x,y valid tag nonces, then prng_successor(x, nonce_distance(x, y)) = y\r |
359 | */\r |
360 | static uint16_t *dist = 0;\r |
361 | int nonce_distance(uint32_t from, uint32_t to)\r |
362 | {\r |
363 | uint16_t x, i;\r |
364 | if(!dist) {\r |
365 | dist = malloc(2 << 16);\r |
366 | if(!dist)\r |
367 | return -1;\r |
368 | for (x = i = 1; i; ++i) {\r |
369 | dist[(x & 0xff) << 8 | x >> 8] = i;\r |
370 | x = x >> 1 | (x ^ x >> 2 ^ x >> 3 ^ x >> 5) << 15;\r |
371 | }\r |
372 | }\r |
373 | return (65535 + dist[to >> 16] - dist[from >> 16]) % 65535;\r |
374 | }\r |
375 | \r |
376 | \r |
377 | static uint32_t fastfwd[2][8] = {\r |
378 | { 0, 0x4BC53, 0xECB1, 0x450E2, 0x25E29, 0x6E27A, 0x2B298, 0x60ECB},\r |
379 | { 0, 0x1D962, 0x4BC53, 0x56531, 0xECB1, 0x135D3, 0x450E2, 0x58980}};\r |
380 | /** lfsr_prefix_ks\r |
381 | *\r |
382 | * Is an exported helper function from the common prefix attack\r |
383 | * Described in the "dark side" paper. It returns an -1 terminated array\r |
384 | * of possible partial(21 bit) secret state.\r |
385 | * The required keystream(ks) needs to contain the keystream that was used to\r |
386 | * encrypt the NACK which is observed when varying only the 3 last bits of Nr\r |
387 | * only correct iff [NR_3] ^ NR_3 does not depend on Nr_3\r |
388 | */\r |
389 | uint32_t *lfsr_prefix_ks(uint8_t ks[8], int isodd)\r |
390 | {\r |
391 | uint32_t c, entry, *candidates = malloc(4 << 10);\r |
392 | int i, size = 0, good;\r |
393 | \r |
394 | if(!candidates)\r |
395 | return 0;\r |
396 | \r |
397 | for(i = 0; i < 1 << 21; ++i) {\r |
398 | for(c = 0, good = 1; good && c < 8; ++c) {\r |
399 | entry = i ^ fastfwd[isodd][c];\r |
400 | good &= (BIT(ks[c], isodd) == filter(entry >> 1));\r |
401 | good &= (BIT(ks[c], isodd + 2) == filter(entry));\r |
402 | }\r |
403 | if(good)\r |
404 | candidates[size++] = i;\r |
405 | }\r |
406 | \r |
407 | candidates[size] = -1;\r |
408 | \r |
409 | return candidates;\r |
410 | }\r |
411 | \r |
412 | /** check_pfx_parity\r |
413 | * helper function which eliminates possible secret states using parity bits\r |
414 | */\r |
415 | static struct Crypto1State*\r |
416 | check_pfx_parity(uint32_t prefix, uint32_t rresp, uint8_t parities[8][8],\r |
417 | uint32_t odd, uint32_t even, struct Crypto1State* sl)\r |
418 | {\r |
419 | uint32_t ks1, nr, ks2, rr, ks3, c, good = 1;\r |
420 | \r |
421 | for(c = 0; good && c < 8; ++c) {\r |
422 | sl->odd = odd ^ fastfwd[1][c];\r |
423 | sl->even = even ^ fastfwd[0][c];\r |
424 | \r |
425 | lfsr_rollback_bit(sl, 0, 0);\r |
426 | lfsr_rollback_bit(sl, 0, 0);\r |
427 | \r |
428 | ks3 = lfsr_rollback_bit(sl, 0, 0);\r |
429 | ks2 = lfsr_rollback_word(sl, 0, 0);\r |
430 | ks1 = lfsr_rollback_word(sl, prefix | c << 5, 1);\r |
431 | \r |
432 | nr = ks1 ^ (prefix | c << 5);\r |
433 | rr = ks2 ^ rresp;\r |
434 | \r |
435 | good &= parity(nr & 0x000000ff) ^ parities[c][3] ^ BIT(ks2, 24);\r |
436 | good &= parity(rr & 0xff000000) ^ parities[c][4] ^ BIT(ks2, 16);\r |
437 | good &= parity(rr & 0x00ff0000) ^ parities[c][5] ^ BIT(ks2, 8);\r |
438 | good &= parity(rr & 0x0000ff00) ^ parities[c][6] ^ BIT(ks2, 0);\r |
439 | good &= parity(rr & 0x000000ff) ^ parities[c][7] ^ ks3;\r |
440 | }\r |
441 | \r |
442 | return sl + good;\r |
443 | } \r |
444 | \r |
445 | \r |
446 | /** lfsr_common_prefix\r |
447 | * Implentation of the common prefix attack.\r |
448 | */\r |
449 | struct Crypto1State*\r |
450 | lfsr_common_prefix(uint32_t pfx, uint32_t rr, uint8_t ks[8], uint8_t par[8][8])\r |
451 | {\r |
452 | struct Crypto1State *statelist, *s;\r |
453 | uint32_t *odd, *even, *o, *e, top;\r |
454 | \r |
455 | odd = lfsr_prefix_ks(ks, 1);\r |
456 | even = lfsr_prefix_ks(ks, 0);\r |
457 | \r |
458 | s = statelist = malloc((sizeof *statelist) << 20);\r |
459 | if(!s || !odd || !even) {\r |
460 | free(statelist);\r |
461 | statelist = 0;\r |
462 | goto out;\r |
463 | }\r |
464 | \r |
465 | for(o = odd; *o + 1; ++o)\r |
466 | for(e = even; *e + 1; ++e)\r |
467 | for(top = 0; top < 64; ++top) {\r |
468 | *o += 1 << 21;\r |
469 | *e += (!(top & 7) + 1) << 21;\r |
470 | s = check_pfx_parity(pfx, rr, par, *o, *e, s);\r |
471 | }\r |
472 | \r |
473 | s->odd = s->even = 0;\r |
474 | out:\r |
475 | free(odd);\r |
476 | free(even);\r |
477 | return statelist;\r |
478 | }\r |