crapto1.c

/*  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 {
      uint32_t x = *it;
      *it = *rit;
      *rit = x;
    }

  if (*rit >= *start)
    --rit;
  if (rit != start) {
    uint32_t x = *it;
    *it = *rit;
    *rit = x;
  }

  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;
  uint32_t x = s->odd;
  s->odd = s->even;
  s->even = x;

  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;
}