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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

36 typedef struct bucket {

37 uint32_t *head;

38 uint32_t *bp;

39 } bucket_t;

 typedef bucket_t bucket_array_t[2][0x100];

43 typedef struct bucket_info {

44 struct {

45 uint32_t *head, *tail;

                 } bucket_info[2][0x100];

47 uint32_t numbuckets;

48 } bucket_info_t;

 static void bucket_sort_intersect(uint32_t* const estart, uint32_t* const estop,

                                                                   uint32_t* const ostart, uint32_t* const ostop,

53 bucket_info_t *bucket_info, bucket_array_t bucket)

54 {

55 uint32_t *p1, *p2;

         uint32_t *start[2];

         uint32_t *stop[2];

59 start[0] = estart;

60 stop[0] = estop;

61 start[1] = ostart;

62 stop[1] = ostop;

64 // init buckets to be empty

         for (uint32_t i = 0; i < 2; i++) {

                 for (uint32_t j = 0x00; j <= 0xff; j++) {

                         bucket[i][j].bp = bucket[i][j].head;

68 }

69 }

71 // sort the lists into the buckets based on the MSB (contribution bits)

         for (uint32_t i = 0; i < 2; i++) { 

                 for (p1 = start[i]; p1 <= stop[i]; p1++) {

                         uint32_t bucket_index = (*p1 & 0xff000000) >> 24;

                         *(bucket[i][bucket_index].bp++) = *p1;

76 }

77 }

80 // write back intersecting buckets as sorted list.

81 // fill in bucket_info with head and tail of the bucket contents in the list and number of non-empty buckets.

82 uint32_t nonempty_bucket;

         for (uint32_t i = 0; i < 2; i++) {

84 p1 = start[i];

85 nonempty_bucket = 0;

                 for (uint32_t j = 0x00; j <= 0xff; j++) {

                         if (bucket[0][j].bp != bucket[0][j].head && bucket[1][j].bp != bucket[1][j].head) { // non-empty intersecting buckets only

                                 bucket_info->bucket_info[i][nonempty_bucket].head = p1;

                                 for (p2 = bucket[i][j].head; p2 < bucket[i][j].bp; *p1++ = *p2++);

                                 bucket_info->bucket_info[i][nonempty_bucket].tail = p1 - 1;

91 nonempty_bucket++;

92 }

93 }

94 bucket_info->numbuckets = nonempty_bucket;

95 }

96 }

98 /** binsearch

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

100 */

101 static inline uint32_t*

 binsearch(uint32_t *start, uint32_t *stop)

103 {

         uint32_t mid, val = *stop & 0xff000000;

105 while(start != stop)

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

107 stop = &start[mid];

108 else

109 start += mid + 1;

110

111 return start;

112 }

113

114 /** update_contribution

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

116 */

117 static inline void

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

119 {

         uint32_t p = *item >> 25;

121

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

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

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

125 }

126

127 /** extend_table

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

129 */

130 static inline void

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

132 {

133 in <<= 24;

134

         for(uint32_t *p = tbl; p <= *end; p++) {

136 *p <<= 1;

                 if(filter(*p) != filter(*p | 1)) {                              // replace

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

                         update_contribution(p, m1, m2);

140 *p ^= in;

                 } else if(filter(*p) == bit) {                                  // insert

                         *++*end = p[1];

                         p[1] = p[0] | 1;

                         update_contribution(p, m1, m2);

145 *p++ ^= in;

                         update_contribution(p, m1, m2);

147 *p ^= in;

148 } else { // drop

149 *p-- = *(*end)--;

150 }

151 }

152

153 }

154

155

156 /** extend_table_simple

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

158 */

159 static inline void

 extend_table_simple(uint32_t *tbl, uint32_t **end, int bit)

161 {

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

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

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

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

166 *++*end = *++tbl;

                         *tbl = tbl[-1] | 1;

168 } else // drop

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

170 }

171

172

173 /** recover

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

175 */

176 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, bucket_array_t bucket)

180 {

181 uint32_t *o, *e;

182 bucket_info_t bucket_info;

183

         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) {

188 sl->even = *o;

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

190 }

191 }

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

193 return sl;

194 }

195

         for(uint32_t i = 0; i < 4 && rem--; i++) {

                 extend_table(o_head, &o_tail, (oks >>= 1) & 1,

                         LF_POLY_EVEN << 1 | 1, LF_POLY_ODD << 1, 0);

199 if(o_head > o_tail)

200 return sl;

201

                 extend_table(e_head, &e_tail, (eks >>= 1) & 1,

                         LF_POLY_ODD, LF_POLY_EVEN << 1 | 1, (in >>= 2) & 3);

204 if(e_head > e_tail)

205 return sl;

206 }

207

         bucket_sort_intersect(e_head, e_tail, o_head, o_tail, &bucket_info, bucket);

209

         for (int i = bucket_info.numbuckets - 1; i >= 0; i--) {

                 sl = recover(bucket_info.bucket_info[1][i].head, bucket_info.bucket_info[1][i].tail, oks,

                                      bucket_info.bucket_info[0][i].head, bucket_info.bucket_info[0][i].tail, eks,

213 rem, sl, in, bucket);

214 }

215

216 return sl;

217 }

218 /** lfsr_recovery

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

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

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

222 */

 struct Crypto1State* lfsr_recovery32(uint32_t ks2, uint32_t in)

224 {

225 struct Crypto1State *statelist;

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

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

228 int i;

229

230 // split the keystream into an odd and even part

         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);

235

         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) {

240 goto out;

241 }

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

243

244 // allocate memory for out of place bucket_sort

245 bucket_array_t bucket;

         for (uint32_t i = 0; i < 2; i++)

                 for (uint32_t j = 0; j <= 0xff; j++) {

                         bucket[i][j].head = malloc(sizeof(uint32_t)<<14);

                         if (!bucket[i][j].head) {

250 goto out;

251 }

252 }

253

254

255 // initialize statelists: add all possible states which would result into the rightmost 2 bits of the keystream

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

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

258 *++odd_tail = i;

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

260 *++even_tail = i;

261 }

262

263 // extend the statelists. Look at the next 8 Bits of the keystream (4 Bit each odd and even):

         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);

267 }

268

269 // the statelists now contain all states which could have generated the last 10 Bits of the keystream.

270 // 22 bits to go to recover 32 bits in total. From now on, we need to take the "in"

271 // parameter into account.

272

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

274

         recover(odd_head, odd_tail, oks,

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

277

278

279 out:

280 free(odd_head);

281 free(even_head);

         for (uint32_t i = 0; i < 2; i++)

                 for (uint32_t j = 0; j <= 0xff; j++)

                         free(bucket[i][j].head);

285

286 return statelist;

287 }

288

 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};

296 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};

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

310 * Variation mentioned in the paper. Somewhat optimized version

311 */

 struct Crypto1State* lfsr_recovery64(uint32_t ks2, uint32_t ks3)

313 {

314 struct Crypto1State *statelist, *sl;

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

         uint32_t low = 0,  win = 0;

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

318 int i, j;

319

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

321 if(!sl)

322 return 0;

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

324

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

                 oks[i >> 1] = BIT(ks2, i ^ 24);

                 oks[16 + (i >> 1)] = BIT(ks3, i ^ 24);

328 }

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

                 eks[i >> 1] = BIT(ks2, i ^ 24);

                 eks[16 + (i >> 1)] = BIT(ks3, i ^ 24);

332 }

333

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

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

336 continue;

337

338 *(tail = table) = i;

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

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

341

342 if(tail < table)

343 continue;

344

                 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]);

349

                 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])

355 goto continue2;

356 }

357

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

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

360

361 win ^= low;

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

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

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

365 goto continue2;

366 }

367

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

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

370 sl->even = win;

371 ++sl;

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

373 continue2:;

374 }

375 }

376 return statelist;

377 }

378

379 /** lfsr_rollback_bit

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

381 */

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

383 {

384 int out;

385

386 s->odd &= 0xffffff;

         s->odd ^= (s->odd ^= s->even, s->even ^= s->odd);

388

         out = s->even & 1;

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

391 out ^= LF_POLY_ODD & s->odd;

392 out ^= !!in;

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

394

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

396 }

397 /** lfsr_rollback_byte

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

399 */

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

401 {

402 int i;

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

                 lfsr_rollback_bit(s, BEBIT(in, i), fb);

405 }

406 /** lfsr_rollback_word

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

408 */

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

410 {

411 int i;

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

                 lfsr_rollback_bit(s, BEBIT(in, i), fb);

414 }

415

416 /** nonce_distance

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

418 */

 static uint16_t *dist = 0;

 int nonce_distance(uint32_t from, uint32_t to)

421 {

422 uint16_t x, i;

423 if(!dist) {

                 dist = malloc(2 << 16);

425 if(!dist)

426 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;

430 }

431 }

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

433 }

434

435

 static uint32_t fastfwd[2][8] = {

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

         { 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 4 last bits of Nr

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

449 */

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

451 {

         uint32_t *candidates = malloc(4 << 21);

453 uint32_t c, entry;

454 int size, i;

455

456 if(!candidates)

457 return 0;

458

         size = (1 << 21) - 1;

         for(i = 0; i <= size; ++i)

461 candidates[i] = i;

462

         for(c = 0;  c < 8; ++c)

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

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

466

                         if(filter(entry >> 1) == BIT(ks[c], isodd))

                                 if(filter(entry) == BIT(ks[c], isodd + 2))

469 continue;

470

471 candidates[i--] = candidates[size--];

472 }

473

         candidates[size + 1] = -1;

475

476 return candidates;

477 }

478

479 /** brute_top

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

481 */

482 static struct Crypto1State*

 brute_top(uint32_t prefix, uint32_t rresp, unsigned char parities[8][8],

           uint32_t odd, uint32_t even, struct Crypto1State* sl, uint8_t no_chk)

485 {

486 struct Crypto1State s;

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

488

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

                 s.odd = odd ^ fastfwd[1][c];

                 s.even = even ^ fastfwd[0][c];

492

                 lfsr_rollback_bit(&s, 0, 0);

                 lfsr_rollback_bit(&s, 0, 0);

                 lfsr_rollback_bit(&s, 0, 0);

496

                 lfsr_rollback_word(&s, 0, 0);

                 lfsr_rollback_word(&s, prefix | c << 5, 1);

499

500 sl->odd = s.odd;

501 sl->even = s.even;

502

503 if (no_chk)

504 break;

505

                 ks1 = crypto1_word(&s, prefix | c << 5, 1);

                 ks2 = crypto1_word(&s,0,0);

                 ks3 = crypto1_word(&s, 0,0);

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

510 rr = ks2 ^ rresp;

511

512 good = 1;

                 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] ^ BIT(ks3, 24);

518

519 if(!good)

520 return sl;

521 }

522

523 return ++sl;

524 }

525

526

527 /** lfsr_common_prefix

528 * Implentation of the common prefix attack.

529 * Requires the 28 bit constant prefix used as reader nonce (pfx)

530 * The reader response used (rr)

531 * The keystream used to encrypt the observed NACK's (ks)

532 * The parity bits (par)

533 * It returns a zero terminated list of possible cipher states after the

534 * tag nonce was fed in

535 */

536 struct Crypto1State*

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

538 {

539 struct Crypto1State *statelist, *s;

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

541

         odd = lfsr_prefix_ks(ks, 1);

         even = lfsr_prefix_ks(ks, 0);

544

         statelist = malloc((sizeof *statelist) << 21);  //how large should be? 

         if(!statelist || !odd || !even)

547 return 0;

548

549 s = statelist;

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

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

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

                                 *o = (*o & 0x1fffff) | (top << 21);

                                 *e = (*e & 0x1fffff) | (top >> 3) << 21;

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

556 }

557

         s->odd = s->even = -1;  

559 //printf("state count = %d\n",s-statelist);

560

561 free(odd);

562 free(even);

563

564 return statelist;

565 }