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- /* crapto1.c
-
- 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 2
- 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.
-
- You should have received a copy of the GNU General Public License
- along with this program; if not, write to the Free Software
- Foundation, Inc., 51 Franklin Street, Fifth Floor,
- Boston, MA 02110-1301, US$
-
- Copyright (C) 2008-2008 bla <blapost@gmail.com>
- */
- #include "crapto1.h"
- #include <stdlib.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
-
- static void quicksort(uint32_t *const start, uint32_t *const stop)
- {
- uint32_t *it = start + 1, *rit = stop;
-
- if (it > rit)
- return;
-
- while (it < rit)
- if (*it <= *start)
- ++it;
- else if (*rit > *start)
- --rit;
- else
- *it ^= (*it ^= *rit, *rit ^= *it);
-
- if (*rit >= *start)
- --rit;
- if (rit != start)
- *rit ^= (*rit ^= *start, *start ^= *rit);
-
- quicksort(start, rit - 1);
- quicksort(rit + 1, stop);
- }
- /** binsearch
- * Binary search for the first occurence of *stop's MSB in sorted [start,stop]
- */
- static inline uint32_t *
- binsearch(uint32_t *start, uint32_t *stop)
- {
- uint32_t mid, val = *stop & 0xff000000;
- while (start != stop)
- if (start[mid = (stop - start) >> 1] > val)
- stop = &start[mid];
- else
- start += mid + 1;
-
- return start;
- }
-
- /** 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 | parity(*item & mask1);
- p = p << 1 | parity(*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)) {
- *tbl |= filter(*tbl) ^ bit;
- } else if (filter(*tbl) == bit) {
- *++*end = *++tbl;
- *tbl = tbl[-1] | 1;
- } else
- *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) {
- uint32_t *o, *e, i;
-
- 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) {
- sl->even = *o;
- sl->odd = *e ^ parity(*o & LF_POLY_ODD);
- sl[1].odd = sl[1].even = 0;
- }
- }
- return sl;
- }
-
- for (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);
- if (o_head > o_tail)
- return sl;
-
- extend_table(e_head, &e_tail, (eks >>= 1) & 1,
- LF_POLY_ODD, LF_POLY_EVEN << 1 | 1, (in >>= 2) & 3);
- if (e_head > e_tail)
- return sl;
- }
-
- quicksort(o_head, o_tail);
- quicksort(e_head, e_tail);
-
- 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);
- } else if (*o_tail > *e_tail)
- o_tail = binsearch(o_head, o_tail) - 1;
- else
- e_tail = binsearch(e_head, e_tail) - 1;
-
- return sl;
- }
- /** 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;
-
- 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 = 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)
- goto out;
-
- statelist->odd = statelist->even = 0;
-
- for (i = 1 << 20; i >= 0; --i) {
- if (filter(i) == (oks & 1))
- *++odd_tail = i;
- if (filter(i) == (eks & 1))
- *++even_tail = i;
- }
-
- 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);
- }
-
- in = (in >> 16 & 0xff) | (in << 16) | (in & 0xff00);
- recover(odd_head, odd_tail, oks,
- even_head, even_tail, eks, 11, statelist, in << 1);
-
- out:
- 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 = malloc(sizeof(struct Crypto1State) << 4);
- if (!sl)
- return 0;
- sl->odd = sl->even = 0;
-
- for (i = 30; i >= 0; i -= 2) {
- oks[i >> 1] = BIT(ks2, i ^ 24);
- oks[16 + (i >> 1)] = BIT(ks3, i ^ 24);
- }
- for (i = 31; i >= 0; i -= 2) {
- eks[i >> 1] = BIT(ks2, i ^ 24);
- eks[16 + (i >> 1)] = BIT(ks3, i ^ 24);
- }
-
- 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 | parity(i & S1[j]);
- for (j = 0; j < 32; ++j)
- hi[j] = parity(i & T1[j]);
-
- 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])
- goto continue2;
- }
-
- for (j = 0; j < 19; ++j)
- win = win << 1 | parity(*tail & S2[j]);
-
- win ^= low;
- for (j = 0; j < 32; ++j) {
- win = win << 1 ^ hi[j] ^ parity(*tail & T2[j]);
- if (filter(win) != eks[j])
- goto continue2;
- }
-
- *tail = *tail << 1 | parity(LF_POLY_EVEN & *tail);
- sl->odd = *tail ^ parity(LF_POLY_ODD & win);
- sl->even = win;
- ++sl;
- sl->odd = sl->even = 0;
- continue2:
- ;
- }
- }
- return statelist;
- }
-
- uint8_t lfsr_rollback_bit(struct Crypto1State *s, uint32_t in, int fb);
- uint8_t lfsr_rollback_byte(struct Crypto1State *s, uint32_t in, int fb);
- uint32_t *lfsr_prefix_ks(uint8_t ks[8], int isodd);
-
- /** 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;
-
- s->odd &= 0xffffff;
- s->odd ^= (s->odd ^= s->even, s->even ^= s->odd);
-
- 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 |= parity(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)
- {
- int i;
- uint8_t ret = 0;
- for (i = 7; i >= 0; --i)
- ret |= lfsr_rollback_bit(s, BIT(in, i), fb) << i;
- 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)
- {
- int i;
- uint32_t ret = 0;
- for (i = 31; i >= 0; --i)
- ret |= lfsr_rollback_bit(s, BEBIT(in, i), fb) << (i ^ 24);
- 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)
- {
- uint16_t x, i;
- if (!dist) {
- dist = malloc(2 << 16);
- if (!dist)
- 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;
- }
- }
- return (65535 + dist[to >> 16] - dist[from >> 16]) % 65535;
- }
-
-
- 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 4 last bits of Nr
- * only correct iff [NR_3] ^ NR_3 does not depend on Nr_3
- */
- uint32_t *lfsr_prefix_ks(uint8_t ks[8], int isodd)
- {
- uint32_t c, entry, *candidates = malloc(4 << 21);
- int i, size = (1 << 21) - 1;
-
- if (!candidates)
- return 0;
-
- for (i = 0; i <= size; ++i)
- candidates[i] = i;
-
- for (c = 0; c < 8; ++c)
- for (i = 0; i <= size; ++i) {
- entry = candidates[i] ^ fastfwd[isodd][c];
-
- if (filter(entry >> 1) != BIT(ks[c], isodd) ||
- filter(entry) != BIT(ks[c], isodd + 2))
- candidates[i--] = candidates[size--];
- }
-
- candidates[size + 1] = -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 ks1, nr, ks2, rr, ks3, c, good = 1;
-
- for (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);
-
- ks3 = lfsr_rollback_bit(sl, 0, 0);
- ks2 = lfsr_rollback_word(sl, 0, 0);
- ks1 = lfsr_rollback_word(sl, prefix | c << 5, 1);
-
- nr = ks1 ^(prefix | c << 5);
- rr = ks2 ^ rresp;
-
- 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;
- }
-
- return sl + good;
- }
-
-
- /** lfsr_common_prefix
- * Implentation of the common prefix attack.
- * Requires the 29 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]) {
- 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 = malloc((sizeof *statelist) << 20);
- if (!s || !odd || !even) {
- free(odd);
- free(even);
- free(statelist);
- return 0;
- }
-
- 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);
- }
-
- s->odd = s->even = 0;
-
- free(odd);
- free(even);
-
- return statelist;
- }
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