proxmark3/tools/nonce2key/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 <stdlib.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



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;
		}
}

/** 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)) {	// 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)
{
	uint32_t *o, *e;
	bucket_info_t bucket_info;

	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(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 (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;
			}
		}
	}

	// 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 (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,
	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 | 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;
}

/** 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 |= 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, ret = 0;
	for (i = 7; i >= 0; --i)
		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
 */
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);
*/
// 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
 * 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 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 << 10);
	if(!candidates) return 0;
	
	uint32_t c,  entry;
	int size = 0, i, good;

	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;

	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 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])
{
	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(pfx, rr, par, *o, *e, s);
			}

	s->odd = s->even = 0;
out:
	free(odd);
	free(even);
	return statelist;
}