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1 /* crapto1.c

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.

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.

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$

19 */

20 #include "crapto1.h"

21 #include <stdlib.h>

23 #if !defined LOWMEM && defined __GNUC__

 static uint8_t filterlut[1 << 20];

 static void __attribute__((constructor)) fill_lut()

26 {

27 uint32_t i;

         for(i = 0; i < 1 << 20; ++i)

                 filterlut[i] = filter(i);

30 }

31 #define filter(x) (filterlut[(x) & 0xfffff])

32 #endif

 static void quicksort(uint32_t* const start, uint32_t* const stop)

35 {

         uint32_t *it = start + 1, *rit = stop;

37 uint32_t tmp;

39 if(it > rit)

40 return;

42 while(it < rit)

43 if(*it <= *start)

44 ++it;

45 else if(*rit > *start)

46 --rit;

47 else {

48 tmp = *it;

49 *it = *rit;

50 *rit = tmp;

51 }

53 if(*rit >= *start)

54 --rit;

55 if(rit != start) {

56 tmp = *rit;

57 *rit = *start;

58 *start = tmp;

59 }

         quicksort(start, rit - 1);

         quicksort(rit + 1, stop);

63 }

64 /** binsearch

65 * Binary search for the first occurence of *stop's MSB in sorted [start,stop]

66 */

 static inline uint32_t* binsearch(uint32_t *start, uint32_t *stop)

68 {

         uint32_t mid, val = *stop & 0xff000000;

70 while(start != stop)

                 if(start[mid = (stop - start) >> 1] > val)

72 stop = &start[mid];

73 else

74 start += mid + 1;

76 return start;

77 }

79 /** update_contribution

80 * helper, calculates the partial linear feedback contributions and puts in MSB

81 */

82 static inline void

 update_contribution(uint32_t *item, const uint32_t mask1, const uint32_t mask2)

84 {

         uint32_t p = *item >> 25;

         p = p << 1 | parity(*item & mask1);

         p = p << 1 | parity(*item & mask2);

         *item = p << 24 | (*item & 0xffffff);

90 }

92 /** extend_table

93 * using a bit of the keystream extend the table of possible lfsr states

94 */

95 static inline void

 extend_table(uint32_t *tbl, uint32_t **end, int bit, int m1, int m2, uint32_t in)

97 {

98 in <<= 24;

         for(*tbl <<= 1; tbl <= *end; *++tbl <<= 1)

                 if(filter(*tbl) ^ filter(*tbl | 1)) {

                         *tbl |= filter(*tbl) ^ bit;

                         update_contribution(tbl, m1, m2);

103 *tbl ^= in;

                 } else if(filter(*tbl) == bit) {

                         *++*end = tbl[1];

                         tbl[1] = tbl[0] | 1;

                         update_contribution(tbl, m1, m2);

108 *tbl++ ^= in;

                         update_contribution(tbl, m1, m2);

110 *tbl ^= in;

111 } else

112 *tbl-- = *(*end)--;

113 }

114 /** extend_table_simple

115 * using a bit of the keystream extend the table of possible lfsr states

116 */

 static inline void extend_table_simple(uint32_t *tbl, uint32_t **end, int bit)

118 {

         for(*tbl <<= 1; tbl <= *end; *++tbl <<= 1)

                 if(filter(*tbl) ^ filter(*tbl | 1))

                         *tbl |= filter(*tbl) ^ bit;

                 else if(filter(*tbl) == bit) {

123 *++*end = *++tbl;

                         *tbl = tbl[-1] | 1;

125 } else

126 *tbl-- = *(*end)--;

127 }

128 /** recover

129 * recursively narrow down the search space, 4 bits of keystream at a time

130 */

131 static struct Crypto1State*

 recover(uint32_t *o_head, uint32_t *o_tail, uint32_t oks,

         uint32_t *e_head, uint32_t *e_tail, uint32_t eks, int rem,

         struct Crypto1State *sl, uint32_t in)

135 {

         uint32_t *o, *e, i;

137

         if(rem == -1) {

                 for(e = e_head; e <= e_tail; ++e) {

                         *e = *e << 1 ^ parity(*e & LF_POLY_EVEN) ^ !!(in & 4);

                         for(o = o_head; o <= o_tail; ++o, ++sl) {

142 sl->even = *o;

                                 sl->odd = *e ^ parity(*o & LF_POLY_ODD);

                                 sl[1].odd = sl[1].even = 0;

145 }

146 }

147 return sl;

148 }

149

         for(i = 0; i < 4 && rem--; i++) {

151 oks >>= 1;

152 eks >>= 1;

153 in >>= 2;

                 extend_table(o_head, &o_tail, oks & 1, LF_POLY_EVEN << 1 | 1,

                                  LF_POLY_ODD << 1, 0);

156 if(o_head > o_tail)

157 return sl;

158

                 extend_table(e_head, &e_tail, eks & 1, LF_POLY_ODD,

                                  LF_POLY_EVEN << 1 | 1, in & 3);

161 if(e_head > e_tail)

162 return sl;

163 }

164

165 quicksort(o_head, o_tail);

166 quicksort(e_head, e_tail);

167

         while(o_tail >= o_head && e_tail >= e_head)

                 if(((*o_tail ^ *e_tail) >> 24) == 0) {

                         o_tail = binsearch(o_head, o = o_tail);

                         e_tail = binsearch(e_head, e = e_tail);

                         sl = recover(o_tail--, o, oks,

                                          e_tail--, e, eks, rem, sl, in);

174 }

175 else if(*o_tail > *e_tail)

                         o_tail = binsearch(o_head, o_tail) - 1;

177 else

                         e_tail = binsearch(e_head, e_tail) - 1;

179

180 return sl;

181 }

182 /** lfsr_recovery

183 * recover the state of the lfsr given 32 bits of the keystream

184 * additionally you can use the in parameter to specify the value

185 * that was fed into the lfsr at the time the keystream was generated

186 */

 struct Crypto1State* lfsr_recovery32(uint32_t ks2, uint32_t in)

188 {

189 struct Crypto1State *statelist;

         uint32_t *odd_head = 0, *odd_tail = 0, oks = 0;

         uint32_t *even_head = 0, *even_tail = 0, eks = 0;

192 int i;

193

         for(i = 31; i >= 0; i -= 2)

                 oks = oks << 1 | BEBIT(ks2, i);

         for(i = 30; i >= 0; i -= 2)

                 eks = eks << 1 | BEBIT(ks2, i);

198

         odd_head = odd_tail = malloc(sizeof(uint32_t) << 21);

         even_head = even_tail = malloc(sizeof(uint32_t) << 21);

         statelist =  malloc(sizeof(struct Crypto1State) << 18);

         if(!odd_tail-- || !even_tail-- || !statelist) {

203 free(statelist);

204 statelist = 0;

205 goto out;

206 }

207

         statelist->odd = statelist->even = 0;

209

         for(i = 1 << 20; i >= 0; --i) {

                 if(filter(i) == (oks & 1))

212 *++odd_tail = i;

                 if(filter(i) == (eks & 1))

214 *++even_tail = i;

215 }

216

         for(i = 0; i < 4; i++) {

                 extend_table_simple(odd_head,  &odd_tail, (oks >>= 1) & 1);

                 extend_table_simple(even_head, &even_tail, (eks >>= 1) & 1);

220 }

221

         in = (in >> 16 & 0xff) | (in << 16) | (in & 0xff00);

         recover(odd_head, odd_tail, oks,

                 even_head, even_tail, eks, 11, statelist, in << 1);

225

226 out:

227 free(odd_head);

228 free(even_head);

229 return statelist;

230 }

231

 static const uint32_t S1[] = {     0x62141, 0x310A0, 0x18850, 0x0C428, 0x06214,

         0x0310A, 0x85E30, 0xC69AD, 0x634D6, 0xB5CDE, 0xDE8DA, 0x6F46D, 0xB3C83,

         0x59E41, 0xA8995, 0xD027F, 0x6813F, 0x3409F, 0x9E6FA};

 static const uint32_t S2[] = {  0x3A557B00, 0x5D2ABD80, 0x2E955EC0, 0x174AAF60,

         0x0BA557B0, 0x05D2ABD8, 0x0449DE68, 0x048464B0, 0x42423258, 0x278192A8,

         0x156042D0, 0x0AB02168, 0x43F89B30, 0x61FC4D98, 0x765EAD48, 0x7D8FDD20,

         0x7EC7EE90, 0x7F63F748, 0x79117020};

239 static const uint32_t T1[] = {

         0x4F37D, 0x279BE, 0x97A6A, 0x4BD35, 0x25E9A, 0x12F4D, 0x097A6, 0x80D66,

         0xC4006, 0x62003, 0xB56B4, 0x5AB5A, 0xA9318, 0xD0F39, 0x6879C, 0xB057B,

         0x582BD, 0x2C15E, 0x160AF, 0x8F6E2, 0xC3DC4, 0xE5857, 0x72C2B, 0x39615,

         0x98DBF, 0xC806A, 0xE0680, 0x70340, 0x381A0, 0x98665, 0x4C332, 0xA272C};

 static const uint32_t T2[] = {  0x3C88B810, 0x5E445C08, 0x2982A580, 0x14C152C0,

         0x4A60A960, 0x253054B0, 0x52982A58, 0x2FEC9EA8, 0x1156C4D0, 0x08AB6268,

         0x42F53AB0, 0x217A9D58, 0x161DC528, 0x0DAE6910, 0x46D73488, 0x25CB11C0,

         0x52E588E0, 0x6972C470, 0x34B96238, 0x5CFC3A98, 0x28DE96C8, 0x12CFC0E0,

         0x4967E070, 0x64B3F038, 0x74F97398, 0x7CDC3248, 0x38CE92A0, 0x1C674950,

         0x0E33A4A8, 0x01B959D0, 0x40DCACE8, 0x26CEDDF0};

 static const uint32_t C1[] = { 0x846B5, 0x4235A, 0x211AD};

 static const uint32_t C2[] = { 0x1A822E0, 0x21A822E0, 0x21A822E0};

252 /** Reverse 64 bits of keystream into possible cipher states

253 * Variation mentioned in the paper. Somewhat optimized version

254 */

 struct Crypto1State* lfsr_recovery64(uint32_t ks2, uint32_t ks3)

256 {

257 struct Crypto1State *statelist, *sl;

         uint8_t oks[32], eks[32], hi[32];

         uint32_t low = 0,  win = 0;

         uint32_t *tail, table[1 << 16];

261 int i, j;

262

         sl = statelist = malloc(sizeof(struct Crypto1State) << 4);

264 if(!sl)

265 return 0;

         sl->odd = sl->even = 0;

267

         for(i = 30; i >= 0; i -= 2) {

                 oks[i >> 1] = BEBIT(ks2, i);

                 oks[16 + (i >> 1)] = BEBIT(ks3, i);

271 }

         for(i = 31; i >= 0; i -= 2) {

                 eks[i >> 1] = BEBIT(ks2, i);

                 eks[16 + (i >> 1)] = BEBIT(ks3, i);

275 }

276

         for(i = 0xfffff; i >= 0; --i) {

                 if (filter(i) != oks[0])

279 continue;

280

281 *(tail = table) = i;

                 for(j = 1; tail >= table && j < 29; ++j)

                         extend_table_simple(table, &tail, oks[j]);

284

285 if(tail < table)

286 continue;

287

                 for(j = 0; j < 19; ++j)

                         low = low << 1 | parity(i & S1[j]);

                 for(j = 0; j < 32; ++j)

                         hi[j] = parity(i & T1[j]);

292

                 for(; tail >= table; --tail) {

                         for(j = 0; j < 3; ++j) {

                                 *tail = *tail << 1;

                                 *tail |= parity((i & C1[j]) ^ (*tail & C2[j]));

                                 if(filter(*tail) != oks[29 + j])

298 goto continue2;

299 }

300

                         for(j = 0; j < 19; ++j)

                                 win = win << 1 | parity(*tail & S2[j]);

303

304 win ^= low;

                         for(j = 0; j < 32; ++j) {

                                 win = win << 1 ^ hi[j] ^ parity(*tail & T2[j]);

                                 if(filter(win) != eks[j])

308 goto continue2;

309 }

310

                         *tail = *tail << 1 | parity(LF_POLY_EVEN & *tail);

                         sl->odd = *tail ^ parity(LF_POLY_ODD & win);

313 sl->even = win;

314 ++sl;

                         sl->odd = sl->even = 0;

316 continue2:;

317 }

318 }

319 return statelist;

320 }

321

322 /** lfsr_rollback_bit

323 * Rollback the shift register in order to get previous states

324 */

 uint8_t lfsr_rollback_bit(struct Crypto1State *s, uint32_t in, int fb)

326 {

327 int out;

328 uint8_t ret;

329 uint32_t tmp;

330

331 s->odd &= 0xffffff;

332 tmp = s->odd;

333 s->odd = s->even;

334 s->even = tmp;

335

         out = s->even & 1;

         out ^= LF_POLY_EVEN & (s->even >>= 1);

338 out ^= LF_POLY_ODD & s->odd;

339 out ^= !!in;

         out ^= (ret = filter(s->odd)) & !!fb;

341

         s->even |= parity(out) << 23;

343 return ret;

344 }

345 /** lfsr_rollback_byte

346 * Rollback the shift register in order to get previous states

347 */

 uint8_t lfsr_rollback_byte(struct Crypto1State *s, uint32_t in, int fb)

349 {

         int i, ret = 0;

         for (i = 7; i >= 0; --i)

                 ret |= lfsr_rollback_bit(s, BIT(in, i), fb) << i;

353 return ret;

354 }

355 /** lfsr_rollback_word

356 * Rollback the shift register in order to get previous states

357 */

 uint32_t lfsr_rollback_word(struct Crypto1State *s, uint32_t in, int fb)

359 {

360 int i;

361 uint32_t ret = 0;

         for (i = 31; i >= 0; --i)

                 ret |= lfsr_rollback_bit(s, BEBIT(in, i), fb) << (i ^ 24);

364 return ret;

365 }

366

367 /** nonce_distance

368 * x,y valid tag nonces, then prng_successor(x, nonce_distance(x, y)) = y

369 */

 static uint16_t *dist = 0;

 int nonce_distance(uint32_t from, uint32_t to)

372 {

373 uint16_t x, i;

374 if(!dist) {

                 dist = malloc(2 << 16);

376 if(!dist)

377 return -1;

                 for (x = i = 1; i; ++i) {

                         dist[(x & 0xff) << 8 | x >> 8] = i;

                         x = x >> 1 | (x ^ x >> 2 ^ x >> 3 ^ x >> 5) << 15;

381 }

382 }

         return (65535 + dist[to >> 16] - dist[from >> 16]) % 65535;

384 }

385

386

 static uint32_t fastfwd[2][8] = {

         { 0, 0x4BC53, 0xECB1, 0x450E2, 0x25E29, 0x6E27A, 0x2B298, 0x60ECB},

         { 0, 0x1D962, 0x4BC53, 0x56531, 0xECB1, 0x135D3, 0x450E2, 0x58980}};

390 /** lfsr_prefix_ks

391 *

392 * Is an exported helper function from the common prefix attack

393 * Described in the "dark side" paper. It returns an -1 terminated array

394 * of possible partial(21 bit) secret state.

395 * The required keystream(ks) needs to contain the keystream that was used to

396 * encrypt the NACK which is observed when varying only the 3 last bits of Nr

397 * only correct iff [NR_3] ^ NR_3 does not depend on Nr_3

398 */

 uint32_t *lfsr_prefix_ks(uint8_t ks[8], int isodd)

400 {

         uint32_t c, entry, *candidates = malloc(4 << 10);

         int i, size = 0, good;

403

404 if(!candidates)

405 return 0;

406

         for(i = 0; i < 1 << 21; ++i) {

                 for(c = 0, good = 1; good && c < 8; ++c) {

                         entry = i ^ fastfwd[isodd][c];

                         good &= (BIT(ks[c], isodd) == filter(entry >> 1));

                         good &= (BIT(ks[c], isodd + 2) == filter(entry));

412 }

413 if(good)

414 candidates[size++] = i;

415 }

416

417 candidates[size] = -1;

418

419 return candidates;

420 }

421

422 /** check_pfx_parity

423 * helper function which eliminates possible secret states using parity bits

424 */

425 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)

428 {

         uint32_t ks1, nr, ks2, rr, ks3, c, good = 1;

430

         for(c = 0; good && c < 8; ++c) {

                 sl->odd = odd ^ fastfwd[1][c];

                 sl->even = even ^ fastfwd[0][c];

434

                 lfsr_rollback_bit(sl, 0, 0);

                 lfsr_rollback_bit(sl, 0, 0);

437

                 ks3 = lfsr_rollback_bit(sl, 0, 0);

                 ks2 = lfsr_rollback_word(sl, 0, 0);

                 ks1 = lfsr_rollback_word(sl, prefix | c << 5, 1);

441

                 nr = ks1 ^ (prefix | c << 5);

443 rr = ks2 ^ rresp;

444

                 good &= parity(nr & 0x000000ff) ^ parities[c][3] ^ BIT(ks2, 24);

                 good &= parity(rr & 0xff000000) ^ parities[c][4] ^ BIT(ks2, 16);

                 good &= parity(rr & 0x00ff0000) ^ parities[c][5] ^ BIT(ks2,  8);

                 good &= parity(rr & 0x0000ff00) ^ parities[c][6] ^ BIT(ks2,  0);

                 good &= parity(rr & 0x000000ff) ^ parities[c][7] ^ ks3;

450 }

451

452 return sl + good;

453 }

454

455

456 /** lfsr_common_prefix

457 * Implentation of the common prefix attack.

458 */

459 struct Crypto1State*

 lfsr_common_prefix(uint32_t pfx, uint32_t rr, uint8_t ks[8], uint8_t par[8][8])

461 {

462 struct Crypto1State *statelist, *s;

         uint32_t *odd, *even, *o, *e, top;

464

         odd = lfsr_prefix_ks(ks, 1);

         even = lfsr_prefix_ks(ks, 0);

467

         s = statelist = malloc((sizeof *statelist) << 20);

         if(!s || !odd || !even) {

470 free(statelist);

471 statelist = 0;

472 goto out;

473 }

474

         for(o = odd; *o + 1; ++o)

                 for(e = even; *e + 1; ++e)

                         for(top = 0; top < 64; ++top) {

                                 *o += 1 << 21;

                                 *e += (!(top & 7) + 1) << 21;

                                 s = check_pfx_parity(pfx, rr, par, *o, *e, s);

481 }

482

         s->odd = s->even = 0;

484 out:

485 free(odd);

486 free(even);

487 return statelist;

488 }