ADD: added @piwi's bucketsort to tools/mfkey/crapto1.c and tools/nonce2key/crapto1.c

[proxmark3-svn] / client / nonce2key / crapto1.c

/*  crapto1.c\r
\r
    This program is free software; you can redistribute it and/or\r
    modify it under the terms of the GNU General Public License\r
    as published by the Free Software Foundation; either version 2\r
    of the License, or (at your option) any later version.\r
\r
    This program is distributed in the hope that it will be useful,\r
    but WITHOUT ANY WARRANTY; without even the implied warranty of\r
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\r
    GNU General Public License for more details.\r
\r
    You should have received a copy of the GNU General Public License\r
    along with this program; if not, write to the Free Software\r
    Foundation, Inc., 51 Franklin Street, Fifth Floor,\r
    Boston, MA  02110-1301, US$\r
\r
    Copyright (C) 2008-2014 bla <blapost@gmail.com>\r
*/\r
#include "crapto1.h"\r
#include <stdlib.h>\r
\r
#if !defined LOWMEM && defined __GNUC__\r
static uint8_t filterlut[1 << 20];\r
static void __attribute__((constructor)) fill_lut()\r
{\r
	uint32_t i;\r
	for(i = 0; i < 1 << 20; ++i)\r
			filterlut[i] = filter(i);\r
}\r
#define filter(x) (filterlut[(x) & 0xfffff])\r
#endif\r
\r
\r
\r
typedef struct bucket {\r
	uint32_t *head;\r
	uint32_t *bp;\r
} bucket_t;\r
\r
typedef bucket_t bucket_array_t[2][0x100];\r
\r
typedef struct bucket_info {\r
	struct {\r
		uint32_t *head, *tail;\r
		} bucket_info[2][0x100];\r
		uint32_t numbuckets;\r
	} bucket_info_t;\r
\r
\r
static void bucket_sort_intersect(uint32_t* const estart, uint32_t* const estop,\r
								  uint32_t* const ostart, uint32_t* const ostop,\r
								  bucket_info_t *bucket_info, bucket_array_t bucket)\r
{\r
	uint32_t *p1, *p2;\r
	uint32_t *start[2];\r
	uint32_t *stop[2];\r
\r
	start[0] = estart;\r
	stop[0] = estop;\r
	start[1] = ostart;\r
	stop[1] = ostop;\r
\r
	// init buckets to be empty\r
	for (uint32_t i = 0; i < 2; i++) {\r
		for (uint32_t j = 0x00; j <= 0xff; j++) {\r
			bucket[i][j].bp = bucket[i][j].head;\r
		}\r
	}\r
\r
	// sort the lists into the buckets based on the MSB (contribution bits)\r
	for (uint32_t i = 0; i < 2; i++) {\r
		for (p1 = start[i]; p1 <= stop[i]; p1++) {\r
			uint32_t bucket_index = (*p1 & 0xff000000) >> 24;\r
			*(bucket[i][bucket_index].bp++) = *p1;\r
		}\r
	}\r
\r
\r
	// write back intersecting buckets as sorted list.\r
	// fill in bucket_info with head and tail of the bucket contents in the list and number of non-empty buckets.\r
	uint32_t nonempty_bucket;\r
	for (uint32_t i = 0; i < 2; i++) {\r
		p1 = start[i];\r
		nonempty_bucket = 0;\r
		for (uint32_t j = 0x00; j <= 0xff; j++) {\r
			if (bucket[0][j].bp != bucket[0][j].head && bucket[1][j].bp != bucket[1][j].head) { // non-empty intersecting buckets only\r
				bucket_info->bucket_info[i][nonempty_bucket].head = p1;\r
				for (p2 = bucket[i][j].head; p2 < bucket[i][j].bp; *p1++ = *p2++);\r
				bucket_info->bucket_info[i][nonempty_bucket].tail = p1 - 1;\r
				nonempty_bucket++;\r
			}\r
		}\r
		bucket_info->numbuckets = nonempty_bucket;\r
		}\r
}\r
\r
/** binsearch\r
 * Binary search for the first occurence of *stop's MSB in sorted [start,stop]\r
 */\r
static inline uint32_t* binsearch(uint32_t *start, uint32_t *stop)\r
{\r
	uint32_t mid, val = *stop & 0xff000000;\r
	while(start != stop)\r
		if(start[mid = (stop - start) >> 1] > val)\r
			stop = &start[mid];\r
		else\r
			start += mid + 1;\r
\r
	return start;\r
}\r
\r
/** update_contribution\r
 * helper, calculates the partial linear feedback contributions and puts in MSB\r
 */\r
static inline void\r
update_contribution(uint32_t *item, const uint32_t mask1, const uint32_t mask2)\r
{\r
	uint32_t p = *item >> 25;\r
\r
	p = p << 1 | parity(*item & mask1);\r
	p = p << 1 | parity(*item & mask2);\r
	*item = p << 24 | (*item & 0xffffff);\r
}\r
\r
/** extend_table\r
 * using a bit of the keystream extend the table of possible lfsr states\r
 */\r
static inline void\r
extend_table(uint32_t *tbl, uint32_t **end, int bit, int m1, int m2, uint32_t in)\r
{\r
	in <<= 24;\r
	for(*tbl <<= 1; tbl <= *end; *++tbl <<= 1)\r
		if(filter(*tbl) ^ filter(*tbl | 1)) {\r
			*tbl |= filter(*tbl) ^ bit;\r
			update_contribution(tbl, m1, m2);\r
			*tbl ^= in;\r
		} else if(filter(*tbl) == bit) {\r
			*++*end = tbl[1];\r
			tbl[1] = tbl[0] | 1;\r
			update_contribution(tbl, m1, m2);\r
			*tbl++ ^= in;\r
			update_contribution(tbl, m1, m2);\r
			*tbl ^= in;\r
		} else\r
			*tbl-- = *(*end)--;\r
}\r
/** extend_table_simple\r
 * using a bit of the keystream extend the table of possible lfsr states\r
 */\r
static inline void extend_table_simple(uint32_t *tbl, uint32_t **end, int bit)\r
{\r
	for(*tbl <<= 1; tbl <= *end; *++tbl <<= 1)\r
		if(filter(*tbl) ^ filter(*tbl | 1)) {	// replace\r
			*tbl |= filter(*tbl) ^ bit;\r
		} else if(filter(*tbl) == bit) {		// insert\r
			*++*end = *++tbl;\r
			*tbl = tbl[-1] | 1;\r
		} else									// drop\r
			*tbl-- = *(*end)--;\r
}\r
\r
\r
/** recover\r
 * recursively narrow down the search space, 4 bits of keystream at a time\r
 */\r
static struct Crypto1State*\r
recover(uint32_t *o_head, uint32_t *o_tail, uint32_t oks,\r
	uint32_t *e_head, uint32_t *e_tail, uint32_t eks, int rem,\r
	struct Crypto1State *sl, uint32_t in, bucket_array_t bucket)\r
{\r
	uint32_t *o, *e;\r
	bucket_info_t bucket_info;\r
\r
	if(rem == -1) {\r
		for(e = e_head; e <= e_tail; ++e) {\r
			*e = *e << 1 ^ parity(*e & LF_POLY_EVEN) ^ !!(in & 4);\r
			for(o = o_head; o <= o_tail; ++o, ++sl) {\r
				sl->even = *o;\r
				sl->odd = *e ^ parity(*o & LF_POLY_ODD);\r
				sl[1].odd = sl[1].even = 0;\r
			}\r
		}\r
		return sl;\r
	}\r
\r
	for(uint32_t i = 0; i < 4 && rem--; i++) {\r
		oks >>= 1;\r
		eks >>= 1;\r
		in >>= 2;\r
		extend_table(o_head, &o_tail, oks & 1, LF_POLY_EVEN << 1 | 1,\r
			     LF_POLY_ODD << 1, 0);\r
		if(o_head > o_tail)\r
			return sl;\r
\r
		extend_table(e_head, &e_tail, eks & 1, LF_POLY_ODD,\r
			     LF_POLY_EVEN << 1 | 1, in & 3);\r
		if(e_head > e_tail)\r
			return sl;\r
	}\r
\r
	bucket_sort_intersect(e_head, e_tail, o_head, o_tail, &bucket_info, bucket);\r
\r
	for (int i = bucket_info.numbuckets - 1; i >= 0; i--) {\r
		sl = recover(bucket_info.bucket_info[1][i].head, bucket_info.bucket_info[1][i].tail, oks,\r
					 bucket_info.bucket_info[0][i].head, bucket_info.bucket_info[0][i].tail, eks,\r
					 rem, sl, in, bucket);\r
	}\r
\r
	return sl;\r
}\r
/** lfsr_recovery\r
 * recover the state of the lfsr given 32 bits of the keystream\r
 * additionally you can use the in parameter to specify the value\r
 * that was fed into the lfsr at the time the keystream was generated\r
 */\r
struct Crypto1State* lfsr_recovery32(uint32_t ks2, uint32_t in)\r
{\r
	struct Crypto1State *statelist;\r
	uint32_t *odd_head = 0, *odd_tail = 0, oks = 0;\r
	uint32_t *even_head = 0, *even_tail = 0, eks = 0;\r
	int i;\r
\r
	// split the keystream into an odd and even part\r
	for(i = 31; i >= 0; i -= 2)\r
		oks = oks << 1 | BEBIT(ks2, i);\r
	for(i = 30; i >= 0; i -= 2)\r
 		eks = eks << 1 | BEBIT(ks2, i);\r
\r
	odd_head = odd_tail = malloc(sizeof(uint32_t) << 21);\r
	even_head = even_tail = malloc(sizeof(uint32_t) << 21);\r
	statelist =  malloc(sizeof(struct Crypto1State) << 18);\r
	if(!odd_tail-- || !even_tail-- || !statelist) {\r
		free(statelist);\r
		statelist = 0;\r
		goto out;\r
	}\r
\r
	statelist->odd = statelist->even = 0;\r
\r
	// allocate memory for out of place bucket_sort\r
	bucket_array_t bucket;\r
	for (uint32_t i = 0; i < 2; i++)\r
		for (uint32_t j = 0; j <= 0xff; j++) {\r
			bucket[i][j].head = malloc(sizeof(uint32_t)<<14);\r
			if (!bucket[i][j].head) {\r
				goto out;\r
			}\r
		}\r
\r
\r
	// initialize statelists: add all possible states which would result into the rightmost 2 bits of the keystream\r
	for(i = 1 << 20; i >= 0; --i) {\r
		if(filter(i) == (oks & 1))\r
			*++odd_tail = i;\r
		if(filter(i) == (eks & 1))\r
			*++even_tail = i;\r
	}\r
\r
	// extend the statelists. Look at the next 8 Bits of the keystream (4 Bit each odd and even):\r
	for(i = 0; i < 4; i++) {\r
		extend_table_simple(odd_head,  &odd_tail, (oks >>= 1) & 1);\r
		extend_table_simple(even_head, &even_tail, (eks >>= 1) & 1);\r
	}\r
\r
	// the statelists now contain all states which could have generated the last 10 Bits of the keystream.\r
	// 22 bits to go to recover 32 bits in total. From now on, we need to take the "in"\r
	// parameter into account.\r
	in = (in >> 16 & 0xff) | (in << 16) | (in & 0xff00);		// Byte swapping\r
	recover(odd_head, odd_tail, oks,\r
		even_head, even_tail, eks, 11, statelist, in << 1, bucket);\r
\r
\r
out:\r
	free(odd_head);\r
	free(even_head);\r
	for (uint32_t i = 0; i < 2; i++)\r
		for (uint32_t j = 0; j <= 0xff; j++)\r
			free(bucket[i][j].head);\r
\r
	return statelist;\r
}\r
\r
static const uint32_t S1[] = {     0x62141, 0x310A0, 0x18850, 0x0C428, 0x06214,\r
	0x0310A, 0x85E30, 0xC69AD, 0x634D6, 0xB5CDE, 0xDE8DA, 0x6F46D, 0xB3C83,\r
	0x59E41, 0xA8995, 0xD027F, 0x6813F, 0x3409F, 0x9E6FA};\r
static const uint32_t S2[] = {  0x3A557B00, 0x5D2ABD80, 0x2E955EC0, 0x174AAF60,\r
	0x0BA557B0, 0x05D2ABD8, 0x0449DE68, 0x048464B0, 0x42423258, 0x278192A8,\r
	0x156042D0, 0x0AB02168, 0x43F89B30, 0x61FC4D98, 0x765EAD48, 0x7D8FDD20,\r
	0x7EC7EE90, 0x7F63F748, 0x79117020};\r
static const uint32_t T1[] = {\r
	0x4F37D, 0x279BE, 0x97A6A, 0x4BD35, 0x25E9A, 0x12F4D, 0x097A6, 0x80D66,\r
	0xC4006, 0x62003, 0xB56B4, 0x5AB5A, 0xA9318, 0xD0F39, 0x6879C, 0xB057B,\r
	0x582BD, 0x2C15E, 0x160AF, 0x8F6E2, 0xC3DC4, 0xE5857, 0x72C2B, 0x39615,\r
	0x98DBF, 0xC806A, 0xE0680, 0x70340, 0x381A0, 0x98665, 0x4C332, 0xA272C};\r
static const uint32_t T2[] = {  0x3C88B810, 0x5E445C08, 0x2982A580, 0x14C152C0,\r
	0x4A60A960, 0x253054B0, 0x52982A58, 0x2FEC9EA8, 0x1156C4D0, 0x08AB6268,\r
	0x42F53AB0, 0x217A9D58, 0x161DC528, 0x0DAE6910, 0x46D73488, 0x25CB11C0,\r
	0x52E588E0, 0x6972C470, 0x34B96238, 0x5CFC3A98, 0x28DE96C8, 0x12CFC0E0,\r
	0x4967E070, 0x64B3F038, 0x74F97398, 0x7CDC3248, 0x38CE92A0, 0x1C674950,\r
	0x0E33A4A8, 0x01B959D0, 0x40DCACE8, 0x26CEDDF0};\r
static const uint32_t C1[] = { 0x846B5, 0x4235A, 0x211AD};\r
static const uint32_t C2[] = { 0x1A822E0, 0x21A822E0, 0x21A822E0};\r
/** Reverse 64 bits of keystream into possible cipher states\r
 * Variation mentioned in the paper. Somewhat optimized version\r
 */\r
struct Crypto1State* lfsr_recovery64(uint32_t ks2, uint32_t ks3)\r
{\r
	struct Crypto1State *statelist, *sl;\r
	uint8_t oks[32], eks[32], hi[32];\r
	uint32_t low = 0,  win = 0;\r
	uint32_t *tail, table[1 << 16];\r
	int i, j;\r
\r
	sl = statelist = malloc(sizeof(struct Crypto1State) << 4);\r
	if(!sl)\r
		return 0;\r
	sl->odd = sl->even = 0;\r
\r
	for(i = 30; i >= 0; i -= 2) {\r
		oks[i >> 1] = BEBIT(ks2, i);\r
		oks[16 + (i >> 1)] = BEBIT(ks3, i);\r
	}\r
	for(i = 31; i >= 0; i -= 2) {\r
		eks[i >> 1] = BEBIT(ks2, i);\r
		eks[16 + (i >> 1)] = BEBIT(ks3, i);\r
	}\r
\r
	for(i = 0xfffff; i >= 0; --i) {\r
		if (filter(i) != oks[0])\r
			continue;\r
\r
		*(tail = table) = i;\r
		for(j = 1; tail >= table && j < 29; ++j)\r
			extend_table_simple(table, &tail, oks[j]);\r
\r
		if(tail < table)\r
			continue;\r
\r
		for(j = 0; j < 19; ++j)\r
			low = low << 1 | parity(i & S1[j]);\r
		for(j = 0; j < 32; ++j)\r
			hi[j] = parity(i & T1[j]);\r
\r
		for(; tail >= table; --tail) {\r
			for(j = 0; j < 3; ++j) {\r
				*tail = *tail << 1;\r
				*tail |= parity((i & C1[j]) ^ (*tail & C2[j]));\r
				if(filter(*tail) != oks[29 + j])\r
					goto continue2;\r
			}\r
\r
			for(j = 0; j < 19; ++j)\r
				win = win << 1 | parity(*tail & S2[j]);\r
\r
			win ^= low;\r
			for(j = 0; j < 32; ++j) {\r
				win = win << 1 ^ hi[j] ^ parity(*tail & T2[j]);\r
				if(filter(win) != eks[j])\r
					goto continue2;\r
			}\r
\r
			*tail = *tail << 1 | parity(LF_POLY_EVEN & *tail);\r
			sl->odd = *tail ^ parity(LF_POLY_ODD & win);\r
			sl->even = win;\r
			++sl;\r
			sl->odd = sl->even = 0;\r
			continue2:;\r
		}\r
	}\r
	return statelist;\r
}\r
\r
/** lfsr_rollback_bit\r
 * Rollback the shift register in order to get previous states\r
 */\r
uint8_t lfsr_rollback_bit(struct Crypto1State *s, uint32_t in, int fb)\r
{\r
	int out;\r
	uint8_t ret;\r
	uint32_t t;\r
\r
	s->odd &= 0xffffff;\r
	t = s->odd, s->odd = s->even, s->even = t;\r
\r
	out = s->even & 1;\r
	out ^= LF_POLY_EVEN & (s->even >>= 1);\r
	out ^= LF_POLY_ODD & s->odd;\r
	out ^= !!in;\r
	out ^= (ret = filter(s->odd)) & !!fb;\r
\r
	s->even |= parity(out) << 23;\r
	return ret;\r
}\r
/** lfsr_rollback_byte\r
 * Rollback the shift register in order to get previous states\r
 */\r
uint8_t lfsr_rollback_byte(struct Crypto1State *s, uint32_t in, int fb)\r
{\r
	/*\r
	int i, ret = 0;\r
	for (i = 7; i >= 0; --i)\r
		ret |= lfsr_rollback_bit(s, BIT(in, i), fb) << i;\r
*/\r
// unfold loop 20160112\r
	uint8_t ret = 0;\r
	ret |= lfsr_rollback_bit(s, BIT(in, 7), fb) << 7;\r
	ret |= lfsr_rollback_bit(s, BIT(in, 6), fb) << 6;\r
	ret |= lfsr_rollback_bit(s, BIT(in, 5), fb) << 5;\r
	ret |= lfsr_rollback_bit(s, BIT(in, 4), fb) << 4;\r
	ret |= lfsr_rollback_bit(s, BIT(in, 3), fb) << 3;\r
	ret |= lfsr_rollback_bit(s, BIT(in, 2), fb) << 2;\r
	ret |= lfsr_rollback_bit(s, BIT(in, 1), fb) << 1;\r
	ret |= lfsr_rollback_bit(s, BIT(in, 0), fb) << 0;\r
	return ret;\r
}\r
/** lfsr_rollback_word\r
 * Rollback the shift register in order to get previous states\r
 */\r
uint32_t lfsr_rollback_word(struct Crypto1State *s, uint32_t in, int fb)\r
{\r
	/*\r
	int i;\r
	uint32_t ret = 0;\r
	for (i = 31; i >= 0; --i)\r
		ret |= lfsr_rollback_bit(s, BEBIT(in, i), fb) << (i ^ 24);\r
*/\r
// unfold loop 20160112\r
	uint32_t ret = 0;\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 31), fb) << (31 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 30), fb) << (30 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 29), fb) << (29 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 28), fb) << (28 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 27), fb) << (27 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 26), fb) << (26 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 25), fb) << (25 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 24), fb) << (24 ^ 24);\r
\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 23), fb) << (23 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 22), fb) << (22 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 21), fb) << (21 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 20), fb) << (20 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 19), fb) << (19 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 18), fb) << (18 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 17), fb) << (17 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 16), fb) << (16 ^ 24);\r
	\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 15), fb) << (15 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 14), fb) << (14 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 13), fb) << (13 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 12), fb) << (12 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 11), fb) << (11 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 10), fb) << (10 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 9), fb) << (9 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 8), fb) << (8 ^ 24);\r
	\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 7), fb) << (7 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 6), fb) << (6 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 5), fb) << (5 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 4), fb) << (4 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 3), fb) << (3 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 2), fb) << (2 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 1), fb) << (1 ^ 24);\r
	ret |= lfsr_rollback_bit(s, BEBIT(in, 0), fb) << (0 ^ 24);\r
	return ret;\r
}\r
\r
/** nonce_distance\r
 * x,y valid tag nonces, then prng_successor(x, nonce_distance(x, y)) = y\r
 */\r
static uint16_t *dist = 0;\r
int nonce_distance(uint32_t from, uint32_t to)\r
{\r
	uint16_t x, i;\r
	if(!dist) {\r
		dist = malloc(2 << 16);\r
		if(!dist)\r
			return -1;\r
		for (x = i = 1; i; ++i) {\r
			dist[(x & 0xff) << 8 | x >> 8] = i;\r
			x = x >> 1 | (x ^ x >> 2 ^ x >> 3 ^ x >> 5) << 15;\r
		}\r
	}\r
	return (65535 + dist[to >> 16] - dist[from >> 16]) % 65535;\r
}\r
\r
\r
static uint32_t fastfwd[2][8] = {\r
	{ 0, 0x4BC53, 0xECB1, 0x450E2, 0x25E29, 0x6E27A, 0x2B298, 0x60ECB},\r
	{ 0, 0x1D962, 0x4BC53, 0x56531, 0xECB1, 0x135D3, 0x450E2, 0x58980}};\r
\r
\r
/** lfsr_prefix_ks\r
 *\r
 * Is an exported helper function from the common prefix attack\r
 * Described in the "dark side" paper. It returns an -1 terminated array\r
 * of possible partial(21 bit) secret state.\r
 * The required keystream(ks) needs to contain the keystream that was used to\r
 * encrypt the NACK which is observed when varying only the 3 last bits of Nr\r
 * only correct iff [NR_3] ^ NR_3 does not depend on Nr_3\r
 */\r
uint32_t *lfsr_prefix_ks(uint8_t ks[8], int isodd)\r
{\r
	uint32_t *candidates = malloc(4 << 10);\r
	if(!candidates) return 0;\r
	\r
	uint32_t c,  entry;\r
	int size = 0, i, good;\r
\r
	for(i = 0; i < 1 << 21; ++i) {\r
		for(c = 0, good = 1; good && c < 8; ++c) {\r
			entry = i ^ fastfwd[isodd][c];\r
			good &= (BIT(ks[c], isodd) == filter(entry >> 1));\r
			good &= (BIT(ks[c], isodd + 2) == filter(entry));\r
		}\r
		if(good)\r
			candidates[size++] = i;\r
	}\r
\r
	candidates[size] = -1;\r
\r
	return candidates;\r
}\r
\r
/** check_pfx_parity\r
 * helper function which eliminates possible secret states using parity bits\r
 */\r
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)\r
{\r
	uint32_t ks1, nr, ks2, rr, ks3, c, good = 1;\r
\r
	for(c = 0; good && c < 8; ++c) {\r
		sl->odd = odd ^ fastfwd[1][c];\r
		sl->even = even ^ fastfwd[0][c];\r
\r
		lfsr_rollback_bit(sl, 0, 0);\r
		lfsr_rollback_bit(sl, 0, 0);\r
\r
		ks3 = lfsr_rollback_bit(sl, 0, 0);\r
		ks2 = lfsr_rollback_word(sl, 0, 0);\r
		ks1 = lfsr_rollback_word(sl, prefix | c << 5, 1);\r
\r
		nr = ks1 ^ (prefix | c << 5);\r
		rr = ks2 ^ rresp;\r
\r
		good &= parity(nr & 0x000000ff) ^ parities[c][3] ^ BIT(ks2, 24);\r
		good &= parity(rr & 0xff000000) ^ parities[c][4] ^ BIT(ks2, 16);\r
		good &= parity(rr & 0x00ff0000) ^ parities[c][5] ^ BIT(ks2,  8);\r
		good &= parity(rr & 0x0000ff00) ^ parities[c][6] ^ BIT(ks2,  0);\r
		good &= parity(rr & 0x000000ff) ^ parities[c][7] ^ ks3;\r
	}\r
\r
	return sl + good;\r
}\r
\r
/** lfsr_common_prefix\r
 * Implentation of the common prefix attack.\r
 * Requires the 28 bit constant prefix used as reader nonce (pfx)\r
 * The reader response used (rr)\r
 * The keystream used to encrypt the observed NACK's (ks)\r
 * The parity bits (par)\r
 * It returns a zero terminated list of possible cipher states after the\r
 * tag nonce was fed in\r
 */\r
\r
struct Crypto1State* lfsr_common_prefix(uint32_t pfx, uint32_t rr, uint8_t ks[8], uint8_t par[8][8])\r
{\r
	struct Crypto1State *statelist, *s;\r
	uint32_t *odd, *even, *o, *e, top;\r
\r
	odd = lfsr_prefix_ks(ks, 1);\r
	even = lfsr_prefix_ks(ks, 0);\r
\r
	s = statelist = malloc((sizeof *statelist) << 21);\r
	if(!s || !odd || !even) {\r
		free(statelist);\r
		free(odd);\r
		free(even);\r
		return 0;\r
	}\r
\r
	for(o = odd; *o + 1; ++o)\r
		for(e = even; *e + 1; ++e)\r
			for(top = 0; top < 64; ++top) {\r
				*o += 1 << 21;\r
				*e += (!(top & 7) + 1) << 21;\r
				s = check_pfx_parity(pfx, rr, par, *o, *e, s);\r
			}\r
\r
	s->odd = s->even = 0;\r
\r
	free(odd);\r
	free(even);\r
	return statelist;\r
}