X-Git-Url: https://git.zerfleddert.de/cgi-bin/gitweb.cgi/proxmark3-svn/blobdiff_plain/05446d5bc3d9263efc6a12026f6cf84bb421735e..b6e05350b2826c6d43fd8e7363de8a1eeef149a6:/client/nonce2key/crapto1.c?ds=sidebyside diff --git a/client/nonce2key/crapto1.c b/client/nonce2key/crapto1.c index 1d7441c7..9f6f7f6b 100644 --- a/client/nonce2key/crapto1.c +++ b/client/nonce2key/crapto1.c @@ -15,7 +15,7 @@ Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, US$ - Copyright (C) 2008-2008 bla + Copyright (C) 2008-2014 bla */ #include "crapto1.h" #include @@ -24,98 +24,17 @@ 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); + uint32_t i; + for(i = 0; i < 1 << 20; ++i) + filterlut[i] = filter(i); } #define filter(x) (filterlut[(x) & 0xfffff]) #endif - - -typedef struct bucket { - uint32_t *head; - uint32_t *bp; -} bucket_t; - -typedef bucket_t bucket_array_t[2][0x100]; - -typedef struct bucket_info { - struct { - uint32_t *head, *tail; - } bucket_info[2][0x100]; - uint32_t numbuckets; - } bucket_info_t; - - -static void bucket_sort_intersect(uint32_t* const estart, uint32_t* const estop, - uint32_t* const ostart, uint32_t* const ostop, - bucket_info_t *bucket_info, bucket_array_t bucket) -{ - uint32_t *p1, *p2; - uint32_t *start[2]; - uint32_t *stop[2]; - - start[0] = estart; - stop[0] = estop; - start[1] = ostart; - stop[1] = ostop; - - // init buckets to be empty - for (uint32_t i = 0; i < 2; i++) { - for (uint32_t j = 0x00; j <= 0xff; j++) { - bucket[i][j].bp = bucket[i][j].head; - } - } - - // sort the lists into the buckets based on the MSB (contribution bits) - for (uint32_t i = 0; i < 2; i++) { - for (p1 = start[i]; p1 <= stop[i]; p1++) { - uint32_t bucket_index = (*p1 & 0xff000000) >> 24; - *(bucket[i][bucket_index].bp++) = *p1; - } - } - - - // write back intersecting buckets as sorted list. - // fill in bucket_info with head and tail of the bucket contents in the list and number of non-empty buckets. - uint32_t nonempty_bucket; - for (uint32_t i = 0; i < 2; i++) { - p1 = start[i]; - nonempty_bucket = 0; - for (uint32_t j = 0x00; j <= 0xff; j++) { - if (bucket[0][j].bp != bucket[0][j].head && bucket[1][j].bp != bucket[1][j].head) { // non-empty intersecting buckets only - bucket_info->bucket_info[i][nonempty_bucket].head = p1; - for (p2 = bucket[i][j].head; p2 < bucket[i][j].bp; *p1++ = *p2++); - bucket_info->bucket_info[i][nonempty_bucket].tail = p1 - 1; - nonempty_bucket++; - } - } - bucket_info->numbuckets = nonempty_bucket; - } -} - -/** 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) +static inline void update_contribution(uint32_t *item, const uint32_t mask1, const uint32_t mask2) { uint32_t p = *item >> 25; @@ -127,49 +46,40 @@ update_contribution(uint32_t *item, const uint32_t mask1, const uint32_t mask2) /** 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) +static inline void extend_table(uint32_t *tbl, uint32_t **end, int bit, int m1, int m2, uint32_t in) { in <<= 24; - - for(uint32_t *p = tbl; p <= *end; p++) { - *p <<= 1; - if(filter(*p) != filter(*p | 1)) { // replace - *p |= filter(*p) ^ bit; - update_contribution(p, m1, m2); - *p ^= in; - } else if(filter(*p) == bit) { // insert - *++*end = p[1]; - p[1] = p[0] | 1; - update_contribution(p, m1, m2); - *p++ ^= in; - update_contribution(p, m1, m2); - *p ^= in; - } else { // drop - *p-- = *(*end)--; - } - } - + 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) +static inline void extend_table_simple(uint32_t *tbl, uint32_t **end, int bit) { - for(*tbl <<= 1; tbl <= *end; *++tbl <<= 1) + 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 + } else { // drop *tbl-- = *(*end)--; + } + } } - - /** recover * recursively narrow down the search space, 4 bits of keystream at a time */ @@ -187,20 +97,21 @@ recover(uint32_t *o_head, uint32_t *o_tail, uint32_t oks, 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; } } - sl->odd = sl->even = 0; return sl; } for(uint32_t 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); + 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) & 1, - LF_POLY_ODD, LF_POLY_EVEN << 1 | 1, (in >>= 2) & 3); + 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; } @@ -209,7 +120,7 @@ recover(uint32_t *o_head, uint32_t *o_tail, uint32_t oks, 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, + bucket_info.bucket_info[0][i].head, bucket_info.bucket_info[0][i].tail, eks, rem, sl, in, bucket); } @@ -237,20 +148,24 @@ struct Crypto1State* lfsr_recovery32(uint32_t ks2, uint32_t in) 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 (uint32_t i = 0; i < 2; i++) + + for (uint32_t 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; + 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) { @@ -269,24 +184,19 @@ struct Crypto1State* lfsr_recovery32(uint32_t ks2, uint32_t in) // 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); - + recover(odd_head, odd_tail, oks, even_head, even_tail, eks, 11, statelist, in << 1, bucket); out: - free(odd_head); - free(even_head); for (uint32_t 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, +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, @@ -323,12 +233,12 @@ struct Crypto1State* lfsr_recovery64(uint32_t ks2, uint32_t ks3) 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); + oks[i >> 1] = BEBIT(ks2, i); + oks[16 + (i >> 1)] = BEBIT(ks3, i); } for(i = 31; i >= 0; i -= 2) { - eks[i >> 1] = BIT(ks2, i ^ 24); - eks[16 + (i >> 1)] = BIT(ks3, i ^ 24); + eks[i >> 1] = BEBIT(ks2, i); + eks[16 + (i >> 1)] = BEBIT(ks3, i); } for(i = 0xfffff; i >= 0; --i) { @@ -379,41 +289,95 @@ struct Crypto1State* lfsr_recovery64(uint32_t ks2, uint32_t ks3) /** lfsr_rollback_bit * Rollback the shift register in order to get previous states */ -void lfsr_rollback_bit(struct Crypto1State *s, uint32_t in, int fb) +uint8_t lfsr_rollback_bit(struct Crypto1State *s, uint32_t in, int fb) { int out; - uint32_t tmp; + uint8_t ret; + uint32_t t; s->odd &= 0xffffff; - tmp = s->odd; - s->odd = s->even; - s->even = tmp; + 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 ^= filter(s->odd) & !!fb; + 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 */ -void lfsr_rollback_byte(struct Crypto1State *s, uint32_t in, int fb) +uint8_t lfsr_rollback_byte(struct Crypto1State *s, uint32_t in, int fb) { - int i; + /* + int i, ret = 0; for (i = 7; i >= 0; --i) - lfsr_rollback_bit(s, BEBIT(in, i), fb); + ret |= lfsr_rollback_bit(s, BIT(in, i), fb) << i; +*/ +// unfold loop 20160112 + 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 */ -void lfsr_rollback_word(struct Crypto1State *s, uint32_t in, int fb) +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) - lfsr_rollback_bit(s, BEBIT(in, i), fb); + ret |= lfsr_rollback_bit(s, BEBIT(in, i), fb) << (i ^ 24); +*/ +// unfold loop 20160112 + 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 @@ -447,86 +411,78 @@ static uint32_t fastfwd[2][8] = { * 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 + * 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 = malloc(4 << 21); + uint32_t *candidates = malloc(4 << 10); + if(!candidates) return 0; + uint32_t c, entry; - int size, i; - - if(!candidates) - return 0; + int size = 0, i, good; - size = (1 << 21) - 1; - 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)) - if(filter(entry) == BIT(ks[c], isodd + 2)) - continue; - - candidates[i--] = candidates[size--]; + for(i = 0; i < 1 << 21; ++i) { + for(c = 0, good = 1; good && c < 8; ++c) { + 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] = -1; + candidates[size] = -1; return candidates; } -/** brute_top +/** check_pfx_parity * helper function which eliminates possible secret states using parity bits */ -static struct Crypto1State* -brute_top(uint32_t prefix, uint32_t rresp, unsigned char parities[8][8], - uint32_t odd, uint32_t even, struct Crypto1State* sl, uint8_t no_chk) +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) { - struct Crypto1State s; - uint32_t ks1, nr, ks2, rr, ks3, good, c; - - for(c = 0; c < 8; ++c) { - s.odd = odd ^ fastfwd[1][c]; - s.even = even ^ fastfwd[0][c]; + uint32_t ks1, nr, ks2, rr, ks3, c, good = 1; - lfsr_rollback_bit(&s, 0, 0); - lfsr_rollback_bit(&s, 0, 0); - lfsr_rollback_bit(&s, 0, 0); + for(c = 0; good && c < 8; ++c) { + sl->odd = odd ^ fastfwd[1][c]; + sl->even = even ^ fastfwd[0][c]; - lfsr_rollback_word(&s, 0, 0); - lfsr_rollback_word(&s, prefix | c << 5, 1); + lfsr_rollback_bit(sl, 0, 0); + lfsr_rollback_bit(sl, 0, 0); - sl->odd = s.odd; - sl->even = s.even; + ks3 = lfsr_rollback_bit(sl, 0, 0); + ks2 = lfsr_rollback_word(sl, 0, 0); + ks1 = lfsr_rollback_word(sl, prefix | c << 5, 1); - if (no_chk) - break; - - ks1 = crypto1_word(&s, prefix | c << 5, 1); - ks2 = crypto1_word(&s,0,0); - ks3 = crypto1_word(&s, 0,0); nr = ks1 ^ (prefix | c << 5); rr = ks2 ^ rresp; - good = 1; 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] ^ BIT(ks3, 24); - - if(!good) - return sl; + good &= parity(rr & 0x000000ff) ^ parities[c][7] ^ ks3; } + return sl + good; +} +static struct Crypto1State* check_pfx_parity_ex(uint32_t prefix, uint32_t odd, uint32_t even, struct Crypto1State* sl) { + + uint32_t c = 0; + + sl->odd = odd ^ fastfwd[1][c]; + sl->even = even ^ fastfwd[0][c]; + + lfsr_rollback_bit(sl, 0, 0); + lfsr_rollback_bit(sl, 0, 0); + lfsr_rollback_bit(sl, 0, 0); + lfsr_rollback_word(sl, 0, 0); + lfsr_rollback_word(sl, prefix | c << 5, 1); + return ++sl; } - /** lfsr_common_prefix * Implentation of the common prefix attack. * Requires the 28 bit constant prefix used as reader nonce (pfx) @@ -536,8 +492,8 @@ brute_top(uint32_t prefix, uint32_t rresp, unsigned char parities[8][8], * 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], uint8_t no_par) + +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; @@ -545,29 +501,56 @@ lfsr_common_prefix(uint32_t pfx, uint32_t rr, uint8_t ks[8], uint8_t par[8][8], odd = lfsr_prefix_ks(ks, 1); even = lfsr_prefix_ks(ks, 0); - statelist = malloc((sizeof *statelist) << 21); //how large should be? - if(!statelist || !odd || !even) - { - free(statelist); - free(odd); - free(even); - return 0; + s = statelist = malloc((sizeof *statelist) << 20); + if(!s || !odd || !even) { + free(statelist); + statelist = 0; + goto out; } - s = statelist; - for(o = odd; *o != -1; ++o) - for(e = even; *e != -1; ++e) + for(o = odd; *o + 1; ++o) + for(e = even; *e + 1; ++e) for(top = 0; top < 64; ++top) { - *o = (*o & 0x1fffff) | (top << 21); - *e = (*e & 0x1fffff) | (top >> 3) << 21; - s = brute_top(pfx, rr, par, *o, *e, s, no_par); + *o += 1 << 21; + *e += (!(top & 7) + 1) << 21; + s = check_pfx_parity(pfx, rr, par, *o, *e, s); } + s->odd = s->even = 0; +out: + free(odd); + free(even); + return statelist; +} + +struct Crypto1State* lfsr_common_prefix_ex(uint32_t pfx, uint8_t ks[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(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_ex(pfx, *o, *e, s); + } + + // in this version, -1 signifies end of states s->odd = s->even = -1; - //printf("state count = %d\n",s-statelist); +out: free(odd); free(even); - return statelist; -} +} \ No newline at end of file