proxmark3/common/crapto1/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) 2008-2014 bla <blapost@gmail.com>
*/
#include "crapto1.h"

#include "bucketsort.h"

#include <stdlib.h>
#include "parity.h"

#if !defined LOWMEM && defined __GNUC__
static uint8_t filterlut[1 << 20];
static void __attribute__((constructor)) fill_lut() {
    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;
}
/** 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 = 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) {
        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 = malloc(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 = malloc(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;
}

/** 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;
    ret |= lfsr_rollback_bit(s, BEBIT(in, 31), fb) << (31 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 30), fb) << (30 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 29), fb) << (29 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 28), fb) << (28 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 27), fb) << (27 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 26), fb) << (26 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 25), fb) << (25 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 24), fb) << (24 ^ 24);

    ret |= lfsr_rollback_bit(s, BEBIT(in, 23), fb) << (23 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 22), fb) << (22 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 21), fb) << (21 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 20), fb) << (20 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 19), fb) << (19 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 18), fb) << (18 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 17), fb) << (17 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 16), fb) << (16 ^ 24);

    ret |= lfsr_rollback_bit(s, BEBIT(in, 15), fb) << (15 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 14), fb) << (14 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 13), fb) << (13 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 12), fb) << (12 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 11), fb) << (11 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 10), fb) << (10 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 9), fb) << (9 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 8), fb) << (8 ^ 24);

    ret |= lfsr_rollback_bit(s, BEBIT(in, 7), fb) << (7 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 6), fb) << (6 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 5), fb) << (5 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 4), fb) << (4 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 3), fb) << (3 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 2), fb) << (2 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 1), fb) << (1 ^ 24);
    ret |= lfsr_rollback_bit(s, BEBIT(in, 0), fb) << (0 ^ 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) {
    if (!dist) {
        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:
    nonce_distance(nonce, nonce);
    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(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;
}


/** lfsr_common_prefix
 * Implentation 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 = malloc((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;
}