--- /dev/null
+/* 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>
+#include <stdbool.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;
+ }
+}
+
+/** 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)
+{
+ 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(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)--;
+ }
+ }
+
+}
+
+
+/** 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->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);
+ 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;
+ }
+
+ 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) {
+ 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:
+ 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);
+
+ 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] = 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;
+}
+
+/** 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)
+{
+ int out;
+ uint32_t tmp;
+
+ s->odd &= 0xffffff;
+ tmp = s->odd;
+ s->odd = s->even;
+ s->even = tmp;
+
+ out = s->even & 1;
+ out ^= LF_POLY_EVEN & (s->even >>= 1);
+ out ^= LF_POLY_ODD & s->odd;
+ out ^= !!in;
+ out ^= filter(s->odd) & !!fb;
+
+ s->even |= parity(out) << 23;
+}
+/** 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)
+{
+ int i;
+ for (i = 7; i >= 0; --i)
+ lfsr_rollback_bit(s, BEBIT(in, i), fb);
+}
+/** 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)
+{
+ int i;
+ for (i = 31; i >= 0; --i)
+ lfsr_rollback_bit(s, BEBIT(in, i), fb);
+}
+
+/** 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 4 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 c, entry;
+ int size, i;
+
+ if(!candidates)
+ return 0;
+
+ 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--];
+ }
+
+ candidates[size + 1] = -1;
+
+ return candidates;
+}
+
+/** brute_top
+ * 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)
+{
+ struct Crypto1State s;
+ uint32_t ks1, nr, ks2, rr, ks3, good, c;
+
+ bool no_par = true;
+ for (int i = 0; i < 8; i++) {
+ for (int j = 0; j < 8; j++) {
+ if (parities[i][j] != 0) {
+ no_par = false;
+ break;
+ }
+ }
+ }
+
+ for(c = 0; c < 8; ++c) {
+ s.odd = odd ^ fastfwd[1][c];
+ s.even = even ^ fastfwd[0][c];
+
+ lfsr_rollback_bit(&s, 0, 0);
+ lfsr_rollback_bit(&s, 0, 0);
+ lfsr_rollback_bit(&s, 0, 0);
+
+ lfsr_rollback_word(&s, 0, 0);
+ lfsr_rollback_word(&s, prefix | c << 5, 1);
+
+ sl->odd = s.odd;
+ sl->even = s.even;
+
+ if (no_par)
+ 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;
+ }
+
+ return ++sl;
+}
+
+
+/** 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);
+
+ statelist = malloc((sizeof *statelist) << 21); //how large should be?
+ if(!statelist || !odd || !even)
+ {
+ free(statelist);
+ free(odd);
+ free(even);
+ return 0;
+ }
+
+ s = statelist;
+ 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);
+ }
+
+ s->odd = s->even = -1;
+ //printf("state count = %d\n",s-statelist);
+
+ free(odd);
+ free(even);
+
+ return statelist;
+}
projects / proxmark3-svn / blobdiff