//----------------------------------------------------------------------------- // Copyright (C) 2008-2014 bla // Copyright (C) Proxmark3 contributors. See AUTHORS.md for details. // // This program is free software: you can redistribute it and/or modify // it under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // See LICENSE.txt for the text of the license. //----------------------------------------------------------------------------- #include "crapto1.h" #include "bucketsort.h" #include #include "parity.h" #if !defined LOWMEM && defined __GNUC__ static uint8_t filterlut[1 << 20]; static void __attribute__((constructor)) fill_lut(void) { uint32_t i; for (i = 0; i < 1 << 20; ++i) filterlut[i] = filter(i); } #define filter(x) (filterlut[(x) & 0xfffff]) #endif /** update_contribution * helper, calculates the partial linear feedback contributions and puts in MSB */ static inline void update_contribution(uint32_t *item, const uint32_t mask1, const uint32_t mask2) { uint32_t p = *item >> 25; p = p << 1 | (evenparity32(*item & mask1)); p = p << 1 | (evenparity32(*item & mask2)); *item = p << 24 | (*item & 0xffffff); } /** extend_table * using a bit of the keystream extend the table of possible lfsr states */ static inline void extend_table(uint32_t *tbl, uint32_t **end, int bit, int m1, int m2, uint32_t in) { in <<= 24; for (*tbl <<= 1; tbl <= *end; *++tbl <<= 1) if (filter(*tbl) ^ filter(*tbl | 1)) { *tbl |= filter(*tbl) ^ bit; update_contribution(tbl, m1, m2); *tbl ^= in; } else if (filter(*tbl) == bit) { *++*end = tbl[1]; tbl[1] = tbl[0] | 1; update_contribution(tbl, m1, m2); *tbl++ ^= in; update_contribution(tbl, m1, m2); *tbl ^= in; } else *tbl-- = *(*end)--; } /** extend_table_simple * using a bit of the keystream extend the table of possible lfsr states */ static inline void extend_table_simple(uint32_t *tbl, uint32_t **end, int bit) { for (*tbl <<= 1; tbl <= *end; *++tbl <<= 1) { if (filter(*tbl) ^ filter(*tbl | 1)) { // replace *tbl |= filter(*tbl) ^ bit; } else if (filter(*tbl) == bit) { // insert *++*end = *++tbl; *tbl = tbl[-1] | 1; } else { // drop *tbl-- = *(*end)--; } } } /** recover * recursively narrow down the search space, 4 bits of keystream at a time */ 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) { bucket_info_t bucket_info; if (rem == -1) { for (uint32_t *e = e_head; e <= e_tail; ++e) { *e = *e << 1 ^ (evenparity32(*e & LF_POLY_EVEN)) ^ (!!(in & 4)); for (uint32_t *o = o_head; o <= o_tail; ++o, ++sl) { sl->even = *o; sl->odd = *e ^ (evenparity32(*o & LF_POLY_ODD)); sl[1].odd = sl[1].even = 0; } } return sl; } for (uint32_t i = 0; i < 4 && rem--; i++) { oks >>= 1; eks >>= 1; in >>= 2; extend_table(o_head, &o_tail, oks & 1, LF_POLY_EVEN << 1 | 1, LF_POLY_ODD << 1, 0); if (o_head > o_tail) return sl; extend_table(e_head, &e_tail, eks & 1, LF_POLY_ODD, LF_POLY_EVEN << 1 | 1, in & 3); if (e_head > e_tail) return sl; } bucket_sort_intersect(e_head, e_tail, o_head, o_tail, &bucket_info, bucket); 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, rem, sl, in, bucket); } return sl; } #if !defined(__arm__) || defined(__linux__) || defined(_WIN32) || defined(__APPLE__) // bare metal ARM Proxmark lacks malloc()/free() /** lfsr_recovery * recover the state of the lfsr given 32 bits of the keystream * additionally you can use the in parameter to specify the value * that was fed into the lfsr at the time the keystream was generated */ struct Crypto1State *lfsr_recovery32(uint32_t ks2, uint32_t in) { struct Crypto1State *statelist; uint32_t *odd_head = 0, *odd_tail = 0, oks = 0; uint32_t *even_head = 0, *even_tail = 0, eks = 0; int i; // 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); odd_head = odd_tail = calloc(1, sizeof(uint32_t) << 21); even_head = even_tail = calloc(1, sizeof(uint32_t) << 21); statelist = calloc(1, sizeof(struct Crypto1State) << 18); if (!odd_tail-- || !even_tail-- || !statelist) { free(statelist); statelist = 0; goto out; } statelist->odd = statelist->even = 0; // allocate memory for out of place bucket_sort bucket_array_t bucket; for (i = 0; i < 2; i++) { for (uint32_t j = 0; j <= 0xff; j++) { bucket[i][j].head = calloc(1, sizeof(uint32_t) << 14); if (!bucket[i][j].head) { goto out; } } } // 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)) *++odd_tail = i; if (filter(i) == (eks & 1)) *++even_tail = i; } // 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); } // the statelists now contain all states which could have generated the last 10 Bits of the keystream. // 22 bits to go to recover 32 bits in total. From now on, we need to take the "in" // parameter into account. in = (in >> 16 & 0xff) | (in << 16) | (in & 0xff00); // Byte swapping recover(odd_head, odd_tail, oks, even_head, even_tail, eks, 11, statelist, in << 1, bucket); out: for (i = 0; i < 2; i++) for (uint32_t j = 0; j <= 0xff; j++) free(bucket[i][j].head); free(odd_head); free(even_head); return statelist; } 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 }; 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}; /** Reverse 64 bits of keystream into possible cipher states * Variation mentioned in the paper. Somewhat optimized version */ struct Crypto1State *lfsr_recovery64(uint32_t ks2, uint32_t ks3) { struct Crypto1State *statelist, *sl; uint8_t oks[32], eks[32], hi[32]; uint32_t low = 0, win = 0; uint32_t *tail, table[1 << 16]; int i, j; sl = statelist = calloc(1, sizeof(struct Crypto1State) << 4); if (!sl) return 0; sl->odd = sl->even = 0; for (i = 30; i >= 0; i -= 2) { oks[i >> 1] = BEBIT(ks2, i); oks[16 + (i >> 1)] = BEBIT(ks3, i); } for (i = 31; i >= 0; i -= 2) { eks[i >> 1] = BEBIT(ks2, i); eks[16 + (i >> 1)] = BEBIT(ks3, i); } for (i = 0xfffff; i >= 0; --i) { if (filter(i) != oks[0]) continue; *(tail = table) = i; for (j = 1; tail >= table && j < 29; ++j) extend_table_simple(table, &tail, oks[j]); if (tail < table) continue; for (j = 0; j < 19; ++j) low = low << 1 | (evenparity32(i & S1[j])); for (j = 0; j < 32; ++j) hi[j] = evenparity32(i & T1[j]); for (; tail >= table; --tail) { for (j = 0; j < 3; ++j) { *tail = *tail << 1; *tail |= evenparity32((i & C1[j]) ^ (*tail & C2[j])); if (filter(*tail) != oks[29 + j]) goto continue2; } for (j = 0; j < 19; ++j) win = win << 1 | (evenparity32(*tail & S2[j])); win ^= low; for (j = 0; j < 32; ++j) { win = win << 1 ^ hi[j] ^ (evenparity32(*tail & T2[j])); if (filter(win) != eks[j]) goto continue2; } *tail = *tail << 1 | (evenparity32(LF_POLY_EVEN & *tail)); sl->odd = *tail ^ (evenparity32(LF_POLY_ODD & win)); sl->even = win; ++sl; sl->odd = sl->even = 0; continue2: ; } } return statelist; } #endif /** lfsr_rollback_bit * Rollback the shift register in order to get previous states */ uint8_t lfsr_rollback_bit(struct Crypto1State *s, uint32_t in, int fb) { int out; uint8_t ret; uint32_t t; s->odd &= 0xffffff; t = s->odd, s->odd = s->even, s->even = t; out = s->even & 1; out ^= LF_POLY_EVEN & (s->even >>= 1); out ^= LF_POLY_ODD & s->odd; out ^= !!in; out ^= (ret = filter(s->odd)) & (!!fb); s->even |= (evenparity32(out)) << 23; return ret; } /** lfsr_rollback_byte * Rollback the shift register in order to get previous states */ uint8_t lfsr_rollback_byte(struct Crypto1State *s, uint32_t in, int fb) { uint8_t ret = 0; ret |= lfsr_rollback_bit(s, BIT(in, 7), fb) << 7; ret |= lfsr_rollback_bit(s, BIT(in, 6), fb) << 6; ret |= lfsr_rollback_bit(s, BIT(in, 5), fb) << 5; ret |= lfsr_rollback_bit(s, BIT(in, 4), fb) << 4; ret |= lfsr_rollback_bit(s, BIT(in, 3), fb) << 3; ret |= lfsr_rollback_bit(s, BIT(in, 2), fb) << 2; ret |= lfsr_rollback_bit(s, BIT(in, 1), fb) << 1; ret |= lfsr_rollback_bit(s, BIT(in, 0), fb) << 0; return ret; } /** lfsr_rollback_word * Rollback the shift register in order to get previous states */ uint32_t lfsr_rollback_word(struct Crypto1State *s, uint32_t in, int fb) { uint32_t ret = 0; // note: xor args have been swapped because some compilers emit a warning // for 10^x and 2^x as possible misuses for exponentiation. No comment. ret |= lfsr_rollback_bit(s, BEBIT(in, 31), fb) << (24 ^ 31); ret |= lfsr_rollback_bit(s, BEBIT(in, 30), fb) << (24 ^ 30); ret |= lfsr_rollback_bit(s, BEBIT(in, 29), fb) << (24 ^ 29); ret |= lfsr_rollback_bit(s, BEBIT(in, 28), fb) << (24 ^ 28); ret |= lfsr_rollback_bit(s, BEBIT(in, 27), fb) << (24 ^ 27); ret |= lfsr_rollback_bit(s, BEBIT(in, 26), fb) << (24 ^ 26); ret |= lfsr_rollback_bit(s, BEBIT(in, 25), fb) << (24 ^ 25); ret |= lfsr_rollback_bit(s, BEBIT(in, 24), fb) << (24 ^ 24); ret |= lfsr_rollback_bit(s, BEBIT(in, 23), fb) << (24 ^ 23); ret |= lfsr_rollback_bit(s, BEBIT(in, 22), fb) << (24 ^ 22); ret |= lfsr_rollback_bit(s, BEBIT(in, 21), fb) << (24 ^ 21); ret |= lfsr_rollback_bit(s, BEBIT(in, 20), fb) << (24 ^ 20); ret |= lfsr_rollback_bit(s, BEBIT(in, 19), fb) << (24 ^ 19); ret |= lfsr_rollback_bit(s, BEBIT(in, 18), fb) << (24 ^ 18); ret |= lfsr_rollback_bit(s, BEBIT(in, 17), fb) << (24 ^ 17); ret |= lfsr_rollback_bit(s, BEBIT(in, 16), fb) << (24 ^ 16); ret |= lfsr_rollback_bit(s, BEBIT(in, 15), fb) << (24 ^ 15); ret |= lfsr_rollback_bit(s, BEBIT(in, 14), fb) << (24 ^ 14); ret |= lfsr_rollback_bit(s, BEBIT(in, 13), fb) << (24 ^ 13); ret |= lfsr_rollback_bit(s, BEBIT(in, 12), fb) << (24 ^ 12); ret |= lfsr_rollback_bit(s, BEBIT(in, 11), fb) << (24 ^ 11); ret |= lfsr_rollback_bit(s, BEBIT(in, 10), fb) << (24 ^ 10); ret |= lfsr_rollback_bit(s, BEBIT(in, 9), fb) << (24 ^ 9); ret |= lfsr_rollback_bit(s, BEBIT(in, 8), fb) << (24 ^ 8); ret |= lfsr_rollback_bit(s, BEBIT(in, 7), fb) << (24 ^ 7); ret |= lfsr_rollback_bit(s, BEBIT(in, 6), fb) << (24 ^ 6); ret |= lfsr_rollback_bit(s, BEBIT(in, 5), fb) << (24 ^ 5); ret |= lfsr_rollback_bit(s, BEBIT(in, 4), fb) << (24 ^ 4); ret |= lfsr_rollback_bit(s, BEBIT(in, 3), fb) << (24 ^ 3); ret |= lfsr_rollback_bit(s, BEBIT(in, 2), fb) << (24 ^ 2); ret |= lfsr_rollback_bit(s, BEBIT(in, 1), fb) << (24 ^ 1); ret |= lfsr_rollback_bit(s, BEBIT(in, 0), fb) << (24 ^ 0); return ret; } /** nonce_distance * x,y valid tag nonces, then prng_successor(x, nonce_distance(x, y)) = y */ static uint16_t *dist = 0; int nonce_distance(uint32_t from, uint32_t to) { if (!dist) { // allocation 2bytes * 0xFFFF times. dist = calloc(2 << 16, sizeof(uint8_t)); if (!dist) return -1; uint16_t x = 1; for (uint16_t i = 1; i; ++i) { dist[(x & 0xff) << 8 | x >> 8] = i; x = x >> 1 | (x ^ x >> 2 ^ x >> 3 ^ x >> 5) << 15; } } return (65535 + dist[to >> 16] - dist[from >> 16]) % 65535; } /** validate_prng_nonce * Determine if nonce is deterministic. ie: Suspectable to Darkside attack. * returns * true = weak prng * false = hardend prng */ bool validate_prng_nonce(uint32_t nonce) { // init prng table: if (nonce_distance(nonce, nonce) == -1) return false; return ((65535 - dist[nonce >> 16] + dist[nonce & 0xffff]) % 65535) == 16; } static uint32_t fastfwd[2][8] = { { 0, 0x4BC53, 0xECB1, 0x450E2, 0x25E29, 0x6E27A, 0x2B298, 0x60ECB}, { 0, 0x1D962, 0x4BC53, 0x56531, 0xECB1, 0x135D3, 0x450E2, 0x58980} }; /** lfsr_prefix_ks * * Is an exported helper function from the common prefix attack * Described in the "dark side" paper. It returns an -1 terminated array * of possible partial(21 bit) secret state. * The required keystream(ks) needs to contain the keystream that was used to * encrypt the NACK which is observed when varying only the 3 last bits of Nr * only correct iff [NR_3] ^ NR_3 does not depend on Nr_3 */ uint32_t *lfsr_prefix_ks(const uint8_t ks[8], int isodd) { uint32_t *candidates = calloc(4 << 10, sizeof(uint8_t)); if (!candidates) return 0; int size = 0; for (int i = 0; i < 1 << 21; ++i) { int good = 1; for (uint32_t c = 0; good && c < 8; ++c) { uint32_t entry = i ^ fastfwd[isodd][c]; good &= (BIT(ks[c], isodd) == filter(entry >> 1)); good &= (BIT(ks[c], isodd + 2) == filter(entry)); } if (good) candidates[size++] = i; } candidates[size] = -1; return candidates; } /** check_pfx_parity * helper function which eliminates possible secret states using parity bits */ 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, uint32_t no_par) { uint32_t good = 1; for (uint32_t c = 0; good && c < 8; ++c) { sl->odd = odd ^ fastfwd[1][c]; sl->even = even ^ fastfwd[0][c]; lfsr_rollback_bit(sl, 0, 0); lfsr_rollback_bit(sl, 0, 0); uint32_t ks3 = lfsr_rollback_bit(sl, 0, 0); uint32_t ks2 = lfsr_rollback_word(sl, 0, 0); uint32_t ks1 = lfsr_rollback_word(sl, prefix | c << 5, 1); if (no_par) break; uint32_t nr = ks1 ^ (prefix | c << 5); uint32_t rr = ks2 ^ rresp; good &= evenparity32(nr & 0x000000ff) ^ parities[c][3] ^ BIT(ks2, 24); good &= evenparity32(rr & 0xff000000) ^ parities[c][4] ^ BIT(ks2, 16); good &= evenparity32(rr & 0x00ff0000) ^ parities[c][5] ^ BIT(ks2, 8); good &= evenparity32(rr & 0x0000ff00) ^ parities[c][6] ^ BIT(ks2, 0); good &= evenparity32(rr & 0x000000ff) ^ parities[c][7] ^ ks3; } return sl + good; } #if !defined(__arm__) || defined(__linux__) || defined(_WIN32) || defined(__APPLE__) // bare metal ARM Proxmark lacks malloc()/free() /** lfsr_common_prefix * Implementation of the common prefix attack. * Requires the 28 bit constant prefix used as reader nonce (pfx) * The reader response used (rr) * The keystream used to encrypt the observed NACK's (ks) * The parity bits (par) * It returns a zero terminated list of possible cipher states after the * tag nonce was fed in */ struct Crypto1State *lfsr_common_prefix(uint32_t pfx, uint32_t rr, uint8_t ks[8], uint8_t par[8][8], uint32_t no_par) { struct Crypto1State *statelist, *s; uint32_t *odd, *even, *o, *e, top; odd = lfsr_prefix_ks(ks, 1); even = lfsr_prefix_ks(ks, 0); s = statelist = calloc(1, (sizeof * statelist) << 24); // was << 20. Need more for no_par special attack. Enough??? if (!s || !odd || !even) { free(statelist); statelist = 0; goto out; } 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, no_par); } s->odd = s->even = 0; out: free(odd); free(even); return statelist; } #endif