/*  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>

static void quicksort(DWORD *const start, DWORD *const stop)
{
    DWORD *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 PDWORD binsearch(PDWORD start, PDWORD stop)
{
    DWORD 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 void update_contribution(PDWORD item, const DWORD mask1, const DWORD mask2)
{
    DWORD 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 void extend_table(PDWORD tbl, PDWORD *end, int bit, int m1, int m2, DWORD 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(PDWORD tbl, PDWORD *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(DWORD *o_head, DWORD *o_tail, DWORD oks,
        DWORD *e_head, DWORD *e_tail, DWORD eks, int rem,
        struct Crypto1State *sl, DWORD in) {
  DWORD *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(DWORD ks2, DWORD in)
{
    struct Crypto1State *statelist;
    DWORD *odd_head = 0, *odd_tail = 0, oks = 0;
    DWORD *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 = (DWORD *) malloc(sizeof(DWORD) << 21);
    even_head = even_tail = (DWORD *) malloc(sizeof(DWORD) << 21);
    statelist = (Crypto1State *)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 DWORD S1[] = {     0x62141, 0x310A0, 0x18850, 0x0C428, 0x06214,
                                   0x0310A, 0x85E30, 0xC69AD, 0x634D6, 0xB5CDE, 0xDE8DA, 0x6F46D, 0xB3C83,
                                   0x59E41, 0xA8995, 0xD027F, 0x6813F, 0x3409F, 0x9E6FA
                             };
static const DWORD S2[] = {  0x3A557B00, 0x5D2ABD80, 0x2E955EC0, 0x174AAF60,
                                0x0BA557B0, 0x05D2ABD8, 0x0449DE68, 0x048464B0, 0x42423258, 0x278192A8,
                                0x156042D0, 0x0AB02168, 0x43F89B30, 0x61FC4D98, 0x765EAD48, 0x7D8FDD20,
                                0x7EC7EE90, 0x7F63F748, 0x79117020
                             };
static const DWORD 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 DWORD 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 DWORD C1[] = { 0x846B5, 0x4235A, 0x211AD};
static const DWORD 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(DWORD ks2, DWORD ks3)
{
    struct Crypto1State *statelist, *sl;
    BYTE oks[32], eks[32], hi[32];
    DWORD low = 0,  win = 0;
    DWORD *tail, table[1 << 16];
    int i, j;

    sl = statelist = (Crypto1State *) 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;
}

BYTE lfsr_rollback_bit(struct Crypto1State *s, DWORD in, int fb);
BYTE lfsr_rollback_byte(struct Crypto1State *s, DWORD in, int fb);
DWORD *lfsr_prefix_ks(BYTE ks[8], int isodd);

/** lfsr_rollback_bit
 * Rollback the shift register in order to get previous states
 */
BYTE lfsr_rollback_bit(struct Crypto1State *s, DWORD in, int fb)
{
  int out;
  BYTE 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
 */
BYTE lfsr_rollback_byte(struct Crypto1State *s, DWORD in, int fb)
{
  int i;
  BYTE 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
 */
DWORD lfsr_rollback_word(struct Crypto1State *s, DWORD in, int fb)
{
  int i;
  DWORD 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 WORD *dist = 0;
int nonce_distance(DWORD from, DWORD to)
{
  WORD x, i;
  if (!dist)
  {
      dist = (WORD *)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 DWORD 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
 */
DWORD *lfsr_prefix_ks(BYTE ks[8], int isodd)
{
    DWORD c, entry, *candidates = (DWORD *)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(DWORD prefix, DWORD rresp, BYTE parities[8][8],
        DWORD odd, DWORD even, struct Crypto1State *sl)
{
    DWORD 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;
}

struct Crypto1State *lfsr_common_prefix(DWORD pfx, DWORD rr, BYTE ks[8], BYTE par[8][8]);
/** 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(DWORD pfx, DWORD rr, BYTE ks[8], BYTE par[8][8])
{
    struct Crypto1State *statelist, *s;
    DWORD *odd, *even, *o, *e, top;

    odd = lfsr_prefix_ks(ks, 1);
    even = lfsr_prefix_ks(ks, 0);

    s = statelist = (Crypto1State *) 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;
}
