+/* crapto1.c\r
+\r
+ This program is free software; you can redistribute it and/or\r
+ modify it under the terms of the GNU General Public License\r
+ as published by the Free Software Foundation; either version 2\r
+ of the License, or (at your option) any later version.\r
+\r
+ This program is distributed in the hope that it will be useful,\r
+ but WITHOUT ANY WARRANTY; without even the implied warranty of\r
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\r
+ GNU General Public License for more details.\r
+\r
+ You should have received a copy of the GNU General Public License\r
+ along with this program; if not, write to the Free Software\r
+ Foundation, Inc., 51 Franklin Street, Fifth Floor,\r
+ Boston, MA 02110-1301, US$\r
+\r
+ Copyright (C) 2008-2008 bla <blapost@gmail.com>\r
+*/\r
+#include "crapto1.h"\r
+#include <stdlib.h>\r
+\r
+#if !defined LOWMEM && defined __GNUC__\r
+static uint8_t filterlut[1 << 20];\r
+static void __attribute__((constructor)) fill_lut()\r
+{\r
+ uint32_t i;\r
+ for(i = 0; i < 1 << 20; ++i)\r
+ filterlut[i] = filter(i);\r
+}\r
+#define filter(x) (filterlut[(x) & 0xfffff])\r
+#endif\r
+\r
+static void quicksort(uint32_t* const start, uint32_t* const stop)\r
+{\r
+ uint32_t *it = start + 1, *rit = stop;\r
+\r
+ if(it > rit)\r
+ return;\r
+\r
+ while(it < rit)\r
+ if(*it <= *start)\r
+ ++it;\r
+ else if(*rit > *start)\r
+ --rit;\r
+ else\r
+ *it ^= (*it ^= *rit, *rit ^= *it);\r
+\r
+ if(*rit >= *start)\r
+ --rit;\r
+ if(rit != start)\r
+ *rit ^= (*rit ^= *start, *start ^= *rit);\r
+\r
+ quicksort(start, rit - 1);\r
+ quicksort(rit + 1, stop);\r
+}\r
+/** binsearch\r
+ * Binary search for the first occurence of *stop's MSB in sorted [start,stop]\r
+ */\r
+static inline uint32_t* binsearch(uint32_t *start, uint32_t *stop)\r
+{\r
+ uint32_t mid, val = *stop & 0xff000000;\r
+ while(start != stop)\r
+ if(start[mid = (stop - start) >> 1] > val)\r
+ stop = &start[mid];\r
+ else\r
+ start += mid + 1;\r
+\r
+ return start;\r
+}\r
+\r
+/** update_contribution\r
+ * helper, calculates the partial linear feedback contributions and puts in MSB\r
+ */\r
+static inline void\r
+update_contribution(uint32_t *item, const uint32_t mask1, const uint32_t mask2)\r
+{\r
+ uint32_t p = *item >> 25;\r
+\r
+ p = p << 1 | parity(*item & mask1);\r
+ p = p << 1 | parity(*item & mask2);\r
+ *item = p << 24 | (*item & 0xffffff);\r
+}\r
+\r
+/** extend_table\r
+ * using a bit of the keystream extend the table of possible lfsr states\r
+ */\r
+static inline void\r
+extend_table(uint32_t *tbl, uint32_t **end, int bit, int m1, int m2, uint32_t in)\r
+{\r
+ in <<= 24;\r
+ for(*tbl <<= 1; tbl <= *end; *++tbl <<= 1)\r
+ if(filter(*tbl) ^ filter(*tbl | 1)) {\r
+ *tbl |= filter(*tbl) ^ bit;\r
+ update_contribution(tbl, m1, m2);\r
+ *tbl ^= in;\r
+ } else if(filter(*tbl) == bit) {\r
+ *++*end = tbl[1];\r
+ tbl[1] = tbl[0] | 1;\r
+ update_contribution(tbl, m1, m2);\r
+ *tbl++ ^= in;\r
+ update_contribution(tbl, m1, m2);\r
+ *tbl ^= in;\r
+ } else\r
+ *tbl-- = *(*end)--;\r
+}\r
+/** extend_table_simple\r
+ * using a bit of the keystream extend the table of possible lfsr states\r
+ */\r
+static inline void extend_table_simple(uint32_t *tbl, uint32_t **end, int bit)\r
+{\r
+ for(*tbl <<= 1; tbl <= *end; *++tbl <<= 1)\r
+ if(filter(*tbl) ^ filter(*tbl | 1))\r
+ *tbl |= filter(*tbl) ^ bit;\r
+ else if(filter(*tbl) == bit) {\r
+ *++*end = *++tbl;\r
+ *tbl = tbl[-1] | 1;\r
+ } else\r
+ *tbl-- = *(*end)--;\r
+}\r
+/** recover\r
+ * recursively narrow down the search space, 4 bits of keystream at a time\r
+ */\r
+static struct Crypto1State*\r
+recover(uint32_t *o_head, uint32_t *o_tail, uint32_t oks,\r
+ uint32_t *e_head, uint32_t *e_tail, uint32_t eks, int rem,\r
+ struct Crypto1State *sl, uint32_t in)\r
+{\r
+ uint32_t *o, *e, i;\r
+\r
+ if(rem == -1) {\r
+ for(e = e_head; e <= e_tail; ++e) {\r
+ *e = *e << 1 ^ parity(*e & LF_POLY_EVEN) ^ !!(in & 4);\r
+ for(o = o_head; o <= o_tail; ++o, ++sl) {\r
+ sl->even = *o;\r
+ sl->odd = *e ^ parity(*o & LF_POLY_ODD);\r
+ sl[1].odd = sl[1].even = 0;\r
+ }\r
+ }\r
+ return sl;\r
+ }\r
+\r
+ for(i = 0; i < 4 && rem--; i++) {\r
+ oks >>= 1;\r
+ eks >>= 1;\r
+ in >>= 2;\r
+ extend_table(o_head, &o_tail, oks & 1, LF_POLY_EVEN << 1 | 1,\r
+ LF_POLY_ODD << 1, 0);\r
+ if(o_head > o_tail)\r
+ return sl;\r
+\r
+ extend_table(e_head, &e_tail, eks & 1, LF_POLY_ODD,\r
+ LF_POLY_EVEN << 1 | 1, in & 3);\r
+ if(e_head > e_tail)\r
+ return sl;\r
+ }\r
+\r
+ quicksort(o_head, o_tail);\r
+ quicksort(e_head, e_tail);\r
+\r
+ while(o_tail >= o_head && e_tail >= e_head)\r
+ if(((*o_tail ^ *e_tail) >> 24) == 0) {\r
+ o_tail = binsearch(o_head, o = o_tail);\r
+ e_tail = binsearch(e_head, e = e_tail);\r
+ sl = recover(o_tail--, o, oks,\r
+ e_tail--, e, eks, rem, sl, in);\r
+ }\r
+ else if(*o_tail > *e_tail)\r
+ o_tail = binsearch(o_head, o_tail) - 1;\r
+ else\r
+ e_tail = binsearch(e_head, e_tail) - 1;\r
+\r
+ return sl;\r
+}\r
+/** lfsr_recovery\r
+ * recover the state of the lfsr given 32 bits of the keystream\r
+ * additionally you can use the in parameter to specify the value\r
+ * that was fed into the lfsr at the time the keystream was generated\r
+ */\r
+struct Crypto1State* lfsr_recovery32(uint32_t ks2, uint32_t in)\r
+{\r
+ struct Crypto1State *statelist;\r
+ uint32_t *odd_head = 0, *odd_tail = 0, oks = 0;\r
+ uint32_t *even_head = 0, *even_tail = 0, eks = 0;\r
+ int i;\r
+\r
+ for(i = 31; i >= 0; i -= 2)\r
+ oks = oks << 1 | BEBIT(ks2, i);\r
+ for(i = 30; i >= 0; i -= 2)\r
+ eks = eks << 1 | BEBIT(ks2, i);\r
+\r
+ odd_head = odd_tail = malloc(sizeof(uint32_t) << 21);\r
+ even_head = even_tail = malloc(sizeof(uint32_t) << 21);\r
+ statelist = malloc(sizeof(struct Crypto1State) << 18);\r
+ if(!odd_tail-- || !even_tail-- || !statelist) {\r
+ free(statelist);\r
+ statelist = 0;\r
+ goto out;\r
+ }\r
+\r
+ statelist->odd = statelist->even = 0;\r
+\r
+ for(i = 1 << 20; i >= 0; --i) {\r
+ if(filter(i) == (oks & 1))\r
+ *++odd_tail = i;\r
+ if(filter(i) == (eks & 1))\r
+ *++even_tail = i;\r
+ }\r
+\r
+ for(i = 0; i < 4; i++) {\r
+ extend_table_simple(odd_head, &odd_tail, (oks >>= 1) & 1);\r
+ extend_table_simple(even_head, &even_tail, (eks >>= 1) & 1);\r
+ }\r
+\r
+ in = (in >> 16 & 0xff) | (in << 16) | (in & 0xff00);\r
+ recover(odd_head, odd_tail, oks,\r
+ even_head, even_tail, eks, 11, statelist, in << 1);\r
+\r
+out:\r
+ free(odd_head);\r
+ free(even_head);\r
+ return statelist;\r
+}\r
+\r
+static const uint32_t S1[] = { 0x62141, 0x310A0, 0x18850, 0x0C428, 0x06214,\r
+ 0x0310A, 0x85E30, 0xC69AD, 0x634D6, 0xB5CDE, 0xDE8DA, 0x6F46D, 0xB3C83,\r
+ 0x59E41, 0xA8995, 0xD027F, 0x6813F, 0x3409F, 0x9E6FA};\r
+static const uint32_t S2[] = { 0x3A557B00, 0x5D2ABD80, 0x2E955EC0, 0x174AAF60,\r
+ 0x0BA557B0, 0x05D2ABD8, 0x0449DE68, 0x048464B0, 0x42423258, 0x278192A8,\r
+ 0x156042D0, 0x0AB02168, 0x43F89B30, 0x61FC4D98, 0x765EAD48, 0x7D8FDD20,\r
+ 0x7EC7EE90, 0x7F63F748, 0x79117020};\r
+static const uint32_t T1[] = {\r
+ 0x4F37D, 0x279BE, 0x97A6A, 0x4BD35, 0x25E9A, 0x12F4D, 0x097A6, 0x80D66,\r
+ 0xC4006, 0x62003, 0xB56B4, 0x5AB5A, 0xA9318, 0xD0F39, 0x6879C, 0xB057B,\r
+ 0x582BD, 0x2C15E, 0x160AF, 0x8F6E2, 0xC3DC4, 0xE5857, 0x72C2B, 0x39615,\r
+ 0x98DBF, 0xC806A, 0xE0680, 0x70340, 0x381A0, 0x98665, 0x4C332, 0xA272C};\r
+static const uint32_t T2[] = { 0x3C88B810, 0x5E445C08, 0x2982A580, 0x14C152C0,\r
+ 0x4A60A960, 0x253054B0, 0x52982A58, 0x2FEC9EA8, 0x1156C4D0, 0x08AB6268,\r
+ 0x42F53AB0, 0x217A9D58, 0x161DC528, 0x0DAE6910, 0x46D73488, 0x25CB11C0,\r
+ 0x52E588E0, 0x6972C470, 0x34B96238, 0x5CFC3A98, 0x28DE96C8, 0x12CFC0E0,\r
+ 0x4967E070, 0x64B3F038, 0x74F97398, 0x7CDC3248, 0x38CE92A0, 0x1C674950,\r
+ 0x0E33A4A8, 0x01B959D0, 0x40DCACE8, 0x26CEDDF0};\r
+static const uint32_t C1[] = { 0x846B5, 0x4235A, 0x211AD};\r
+static const uint32_t C2[] = { 0x1A822E0, 0x21A822E0, 0x21A822E0};\r
+/** Reverse 64 bits of keystream into possible cipher states\r
+ * Variation mentioned in the paper. Somewhat optimized version\r
+ */\r
+struct Crypto1State* lfsr_recovery64(uint32_t ks2, uint32_t ks3)\r
+{\r
+ struct Crypto1State *statelist, *sl;\r
+ uint8_t oks[32], eks[32], hi[32];\r
+ uint32_t low = 0, win = 0;\r
+ uint32_t *tail, table[1 << 16];\r
+ int i, j;\r
+\r
+ sl = statelist = malloc(sizeof(struct Crypto1State) << 4);\r
+ if(!sl)\r
+ return 0;\r
+ sl->odd = sl->even = 0;\r
+\r
+ for(i = 30; i >= 0; i -= 2) {\r
+ oks[i >> 1] = BEBIT(ks2, i);\r
+ oks[16 + (i >> 1)] = BEBIT(ks3, i);\r
+ }\r
+ for(i = 31; i >= 0; i -= 2) {\r
+ eks[i >> 1] = BEBIT(ks2, i);\r
+ eks[16 + (i >> 1)] = BEBIT(ks3, i);\r
+ }\r
+\r
+ for(i = 0xfffff; i >= 0; --i) {\r
+ if (filter(i) != oks[0])\r
+ continue;\r
+\r
+ *(tail = table) = i;\r
+ for(j = 1; tail >= table && j < 29; ++j)\r
+ extend_table_simple(table, &tail, oks[j]);\r
+\r
+ if(tail < table)\r
+ continue;\r
+\r
+ for(j = 0; j < 19; ++j)\r
+ low = low << 1 | parity(i & S1[j]);\r
+ for(j = 0; j < 32; ++j)\r
+ hi[j] = parity(i & T1[j]);\r
+\r
+ for(; tail >= table; --tail) {\r
+ for(j = 0; j < 3; ++j) {\r
+ *tail = *tail << 1;\r
+ *tail |= parity((i & C1[j]) ^ (*tail & C2[j]));\r
+ if(filter(*tail) != oks[29 + j])\r
+ goto continue2;\r
+ }\r
+\r
+ for(j = 0; j < 19; ++j)\r
+ win = win << 1 | parity(*tail & S2[j]);\r
+\r
+ win ^= low;\r
+ for(j = 0; j < 32; ++j) {\r
+ win = win << 1 ^ hi[j] ^ parity(*tail & T2[j]);\r
+ if(filter(win) != eks[j])\r
+ goto continue2;\r
+ }\r
+\r
+ *tail = *tail << 1 | parity(LF_POLY_EVEN & *tail);\r
+ sl->odd = *tail ^ parity(LF_POLY_ODD & win);\r
+ sl->even = win;\r
+ ++sl;\r
+ sl->odd = sl->even = 0;\r
+ continue2:;\r
+ }\r
+ }\r
+ return statelist;\r
+}\r
+\r
+/** lfsr_rollback_bit\r
+ * Rollback the shift register in order to get previous states\r
+ */\r
+uint8_t lfsr_rollback_bit(struct Crypto1State *s, uint32_t in, int fb)\r
+{\r
+ int out;\r
+ uint8_t ret;\r
+\r
+ s->odd &= 0xffffff;\r
+ s->odd ^= (s->odd ^= s->even, s->even ^= s->odd);\r
+\r
+ out = s->even & 1;\r
+ out ^= LF_POLY_EVEN & (s->even >>= 1);\r
+ out ^= LF_POLY_ODD & s->odd;\r
+ out ^= !!in;\r
+ out ^= (ret = filter(s->odd)) & !!fb;\r
+\r
+ s->even |= parity(out) << 23;\r
+ return ret;\r
+}\r
+/** lfsr_rollback_byte\r
+ * Rollback the shift register in order to get previous states\r
+ */\r
+uint8_t lfsr_rollback_byte(struct Crypto1State *s, uint32_t in, int fb)\r
+{\r
+ int i, ret = 0;\r
+ for (i = 7; i >= 0; --i)\r
+ ret |= lfsr_rollback_bit(s, BIT(in, i), fb) << i;\r
+ return ret;\r
+}\r
+/** lfsr_rollback_word\r
+ * Rollback the shift register in order to get previous states\r
+ */\r
+uint32_t lfsr_rollback_word(struct Crypto1State *s, uint32_t in, int fb)\r
+{\r
+ int i;\r
+ uint32_t ret = 0;\r
+ for (i = 31; i >= 0; --i)\r
+ ret |= lfsr_rollback_bit(s, BEBIT(in, i), fb) << (i ^ 24);\r
+ return ret;\r
+}\r
+\r
+/** nonce_distance\r
+ * x,y valid tag nonces, then prng_successor(x, nonce_distance(x, y)) = y\r
+ */\r
+static uint16_t *dist = 0;\r
+int nonce_distance(uint32_t from, uint32_t to)\r
+{\r
+ uint16_t x, i;\r
+ if(!dist) {\r
+ dist = malloc(2 << 16);\r
+ if(!dist)\r
+ return -1;\r
+ for (x = i = 1; i; ++i) {\r
+ dist[(x & 0xff) << 8 | x >> 8] = i;\r
+ x = x >> 1 | (x ^ x >> 2 ^ x >> 3 ^ x >> 5) << 15;\r
+ }\r
+ }\r
+ return (65535 + dist[to >> 16] - dist[from >> 16]) % 65535;\r
+}\r
+\r
+\r
+static uint32_t fastfwd[2][8] = {\r
+ { 0, 0x4BC53, 0xECB1, 0x450E2, 0x25E29, 0x6E27A, 0x2B298, 0x60ECB},\r
+ { 0, 0x1D962, 0x4BC53, 0x56531, 0xECB1, 0x135D3, 0x450E2, 0x58980}};\r
+/** lfsr_prefix_ks\r
+ *\r
+ * Is an exported helper function from the common prefix attack\r
+ * Described in the "dark side" paper. It returns an -1 terminated array\r
+ * of possible partial(21 bit) secret state.\r
+ * The required keystream(ks) needs to contain the keystream that was used to\r
+ * encrypt the NACK which is observed when varying only the 3 last bits of Nr\r
+ * only correct iff [NR_3] ^ NR_3 does not depend on Nr_3\r
+ */\r
+uint32_t *lfsr_prefix_ks(uint8_t ks[8], int isodd)\r
+{\r
+ uint32_t c, entry, *candidates = malloc(4 << 10);\r
+ int i, size = 0, good;\r
+\r
+ if(!candidates)\r
+ return 0;\r
+\r
+ for(i = 0; i < 1 << 21; ++i) {\r
+ for(c = 0, good = 1; good && c < 8; ++c) {\r
+ entry = i ^ fastfwd[isodd][c];\r
+ good &= (BIT(ks[c], isodd) == filter(entry >> 1));\r
+ good &= (BIT(ks[c], isodd + 2) == filter(entry));\r
+ }\r
+ if(good)\r
+ candidates[size++] = i;\r
+ }\r
+\r
+ candidates[size] = -1;\r
+\r
+ return candidates;\r
+}\r
+\r
+/** check_pfx_parity\r
+ * helper function which eliminates possible secret states using parity bits\r
+ */\r
+static struct Crypto1State*\r
+check_pfx_parity(uint32_t prefix, uint32_t rresp, uint8_t parities[8][8],\r
+ uint32_t odd, uint32_t even, struct Crypto1State* sl)\r
+{\r
+ uint32_t ks1, nr, ks2, rr, ks3, c, good = 1;\r
+\r
+ for(c = 0; good && c < 8; ++c) {\r
+ sl->odd = odd ^ fastfwd[1][c];\r
+ sl->even = even ^ fastfwd[0][c];\r
+\r
+ lfsr_rollback_bit(sl, 0, 0);\r
+ lfsr_rollback_bit(sl, 0, 0);\r
+\r
+ ks3 = lfsr_rollback_bit(sl, 0, 0);\r
+ ks2 = lfsr_rollback_word(sl, 0, 0);\r
+ ks1 = lfsr_rollback_word(sl, prefix | c << 5, 1);\r
+\r
+ nr = ks1 ^ (prefix | c << 5);\r
+ rr = ks2 ^ rresp;\r
+\r
+ good &= parity(nr & 0x000000ff) ^ parities[c][3] ^ BIT(ks2, 24);\r
+ good &= parity(rr & 0xff000000) ^ parities[c][4] ^ BIT(ks2, 16);\r
+ good &= parity(rr & 0x00ff0000) ^ parities[c][5] ^ BIT(ks2, 8);\r
+ good &= parity(rr & 0x0000ff00) ^ parities[c][6] ^ BIT(ks2, 0);\r
+ good &= parity(rr & 0x000000ff) ^ parities[c][7] ^ ks3;\r
+ }\r
+\r
+ return sl + good;\r
+} \r
+\r
+\r
+/** lfsr_common_prefix\r
+ * Implentation of the common prefix attack.\r
+ */\r
+struct Crypto1State*\r
+lfsr_common_prefix(uint32_t pfx, uint32_t rr, uint8_t ks[8], uint8_t par[8][8])\r
+{\r
+ struct Crypto1State *statelist, *s;\r
+ uint32_t *odd, *even, *o, *e, top;\r
+\r
+ odd = lfsr_prefix_ks(ks, 1);\r
+ even = lfsr_prefix_ks(ks, 0);\r
+\r
+ s = statelist = malloc((sizeof *statelist) << 20);\r
+ if(!s || !odd || !even) {\r
+ free(statelist);\r
+ statelist = 0;\r
+ goto out;\r
+ }\r
+\r
+ for(o = odd; *o + 1; ++o)\r
+ for(e = even; *e + 1; ++e)\r
+ for(top = 0; top < 64; ++top) {\r
+ *o += 1 << 21;\r
+ *e += (!(top & 7) + 1) << 21;\r
+ s = check_pfx_parity(pfx, rr, par, *o, *e, s);\r
+ }\r
+\r
+ s->odd = s->even = 0;\r
+out:\r
+ free(odd);\r
+ free(even);\r
+ return statelist;\r
+}\r
projects / proxmark3-svn / commitdiff