#include "ui.h"
#include "util.h"
#include "nonce2key/crapto1.h"
+#include "parity.h"
// uint32_t test_state_odd = 0;
// uint32_t test_state_even = 0;
-#define CONFIDENCE_THRESHOLD 0.99 // Collect nonces until we are certain enough that the following brute force is successfull
-#define GOOD_BYTES_REQUIRED 25
+#define CONFIDENCE_THRESHOLD 0.95 // Collect nonces until we are certain enough that the following brute force is successfull
+#define GOOD_BYTES_REQUIRED 30
static const float p_K[257] = { // the probability that a random nonce has a Sum Property == K
float Sum8_prob;
bool updated;
noncelistentry_t *first;
+ float score1, score2;
} noncelist_t;
static uint32_t cuid;
static noncelist_t nonces[256];
+static uint8_t best_first_bytes[256];
static uint16_t first_byte_Sum = 0;
static uint16_t first_byte_num = 0;
static uint16_t num_good_first_bytes = 0;
+static uint64_t maximum_states = 0;
+static uint64_t known_target_key;
-#define MAX_BEST_BYTES 40
-static uint8_t best_first_bytes[MAX_BEST_BYTES];
typedef enum {
} statelist_t;
-partial_indexed_statelist_t partial_statelist[17];
-partial_indexed_statelist_t statelist_bitflip;
+static partial_indexed_statelist_t partial_statelist[17];
+static partial_indexed_statelist_t statelist_bitflip;
-statelist_t *candidates = NULL;
+static statelist_t *candidates = NULL;
static int add_nonce(uint32_t nonce_enc, uint8_t par_enc)
if (p1 == NULL) { // first nonce with this 1st byte
first_byte_num++;
- first_byte_Sum += parity((nonce_enc & 0xff000000) | (par_enc & 0x08) | 0x01); // 1st byte sum property. Note: added XOR 1
+ first_byte_Sum += evenparity32((nonce_enc & 0xff000000) | (par_enc & 0x08));
// printf("Adding nonce 0x%08x, par_enc 0x%02x, parity(0x%08x) = %d\n",
// nonce_enc,
// par_enc,
// (nonce_enc & 0xff000000) | (par_enc & 0x08) |0x01,
- // parity((nonce_enc & 0xff000000) | (par_enc & 0x08) | 0x01));
+ // parity((nonce_enc & 0xff000000) | (par_enc & 0x08));
}
while (p1 != NULL && (p1->nonce_enc & 0x00ff0000) < (nonce_enc & 0x00ff0000)) {
p2->par_enc = par_enc;
nonces[first_byte].num++;
- nonces[first_byte].Sum += parity((nonce_enc & 0x00ff0000) | (par_enc & 0x04) | 0x01); // 2nd byte sum property. Note: added XOR 1
+ nonces[first_byte].Sum += evenparity32((nonce_enc & 0x00ff0000) | (par_enc & 0x04));
nonces[first_byte].updated = true; // indicates that we need to recalculate the Sum(a8) probability for this first byte
return (1); // new nonce added
part_sum ^= filter(st);
st = (st << 1) | ((j >> (3-i)) & 0x01) ;
}
+ part_sum ^= 1; // XOR 1 cancelled out for the other 8 bits
} else {
for (uint16_t i = 0; i < 4; i++) {
st = (st << 1) | ((j >> (3-i)) & 0x01) ;
}
-static uint16_t SumProperty(struct Crypto1State *s)
-{
- uint16_t sum_odd = PartialSumProperty(s->odd, ODD_STATE);
- uint16_t sum_even = PartialSumProperty(s->even, EVEN_STATE);
- return (sum_odd*(16-sum_even) + (16-sum_odd)*sum_even);
-}
+// static uint16_t SumProperty(struct Crypto1State *s)
+// {
+ // uint16_t sum_odd = PartialSumProperty(s->odd, ODD_STATE);
+ // uint16_t sum_even = PartialSumProperty(s->even, EVEN_STATE);
+ // return (sum_odd*(16-sum_even) + (16-sum_odd)*sum_even);
+// }
static double p_hypergeometric(uint16_t N, uint16_t K, uint16_t n, uint16_t k)
}
+
+
+static inline uint_fast8_t common_bits(uint_fast8_t bytes_diff)
+{
+ static const uint_fast8_t common_bits_LUT[256] = {
+ 8, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 7, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+ 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
+ };
+
+ return common_bits_LUT[bytes_diff];
+}
+
+
static void Tests()
{
- printf("Tests: Partial Statelist sizes\n");
- for (uint16_t i = 0; i <= 16; i+=2) {
- printf("Partial State List Odd [%2d] has %8d entries\n", i, partial_statelist[i].len[ODD_STATE]);
- }
- for (uint16_t i = 0; i <= 16; i+=2) {
- printf("Partial State List Even [%2d] has %8d entries\n", i, partial_statelist[i].len[EVEN_STATE]);
- }
+ // printf("Tests: Partial Statelist sizes\n");
+ // for (uint16_t i = 0; i <= 16; i+=2) {
+ // printf("Partial State List Odd [%2d] has %8d entries\n", i, partial_statelist[i].len[ODD_STATE]);
+ // }
+ // for (uint16_t i = 0; i <= 16; i+=2) {
+ // printf("Partial State List Even [%2d] has %8d entries\n", i, partial_statelist[i].len[EVEN_STATE]);
+ // }
// #define NUM_STATISTICS 100000
- // uint64_t statistics[257];
// uint32_t statistics_odd[17];
+ // uint64_t statistics[257];
// uint32_t statistics_even[17];
// struct Crypto1State cs;
// time_t time1 = clock();
// printf("p_hypergeometric(256, 1, 1, 1) = %0.8f\n", p_hypergeometric(256, 1, 1, 1));
// printf("p_hypergeometric(256, 1, 1, 0) = %0.8f\n", p_hypergeometric(256, 1, 1, 0));
- struct Crypto1State *pcs;
- pcs = crypto1_create(0xffffffffffff);
- printf("\nTests: for key = 0xffffffffffff:\nSum(a0) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
- SumProperty(pcs), pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
- crypto1_byte(pcs, (cuid >> 24) ^ best_first_bytes[0], true);
- printf("After adding best first byte 0x%02x:\nSum(a8) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
- best_first_bytes[0],
- SumProperty(pcs),
- pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
+ // struct Crypto1State *pcs;
+ // pcs = crypto1_create(0xffffffffffff);
+ // printf("\nTests: for key = 0xffffffffffff:\nSum(a0) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
+ // SumProperty(pcs), pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
+ // crypto1_byte(pcs, (cuid >> 24) ^ best_first_bytes[0], true);
+ // printf("After adding best first byte 0x%02x:\nSum(a8) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
+ // best_first_bytes[0],
+ // SumProperty(pcs),
+ // pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
+ // //test_state_odd = pcs->odd & 0x00ffffff;
+ // //test_state_even = pcs->even & 0x00ffffff;
+ // crypto1_destroy(pcs);
+ // pcs = crypto1_create(0xa0a1a2a3a4a5);
+ // printf("Tests: for key = 0xa0a1a2a3a4a5:\nSum(a0) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
+ // SumProperty(pcs), pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
+ // crypto1_byte(pcs, (cuid >> 24) ^ best_first_bytes[0], true);
+ // printf("After adding best first byte 0x%02x:\nSum(a8) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
+ // best_first_bytes[0],
+ // SumProperty(pcs),
+ // pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
+ // //test_state_odd = pcs->odd & 0x00ffffff;
+ // //test_state_even = pcs->even & 0x00ffffff;
+ // crypto1_destroy(pcs);
+ // pcs = crypto1_create(0xa6b9aa97b955);
+ // printf("Tests: for key = 0xa6b9aa97b955:\nSum(a0) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
+ // SumProperty(pcs), pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
+ // crypto1_byte(pcs, (cuid >> 24) ^ best_first_bytes[0], true);
+ // printf("After adding best first byte 0x%02x:\nSum(a8) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
+ // best_first_bytes[0],
+ // SumProperty(pcs),
+ // pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
//test_state_odd = pcs->odd & 0x00ffffff;
//test_state_even = pcs->even & 0x00ffffff;
- crypto1_destroy(pcs);
- pcs = crypto1_create(0xa0a1a2a3a4a5);
- printf("Tests: for key = 0xa0a1a2a3a4a5:\nSum(a0) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
- SumProperty(pcs), pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
- crypto1_byte(pcs, (cuid >> 24) ^ best_first_bytes[0], true);
- printf("After adding best first byte 0x%02x:\nSum(a8) = %d\nodd_state = 0x%06x\neven_state = 0x%06x\n",
- best_first_bytes[0],
- SumProperty(pcs),
- pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
- // test_state_odd = pcs->odd & 0x00ffffff;
- // test_state_even = pcs->even & 0x00ffffff;
- crypto1_destroy(pcs);
+ // crypto1_destroy(pcs);
- printf("\nTests: number of states with BitFlipProperty: %d, (= %1.3f%% of total states)\n", statelist_bitflip.len[0], 100.0 * statelist_bitflip.len[0] / (1<<20));
+
+ // printf("\nTests: number of states with BitFlipProperty: %d, (= %1.3f%% of total states)\n", statelist_bitflip.len[0], 100.0 * statelist_bitflip.len[0] / (1<<20));
printf("\nTests: Actual BitFlipProperties odd/even:\n");
for (uint16_t i = 0; i < 256; i++) {
- printf("[%3d]:%c%c ", i, nonces[i].BitFlip[ODD_STATE]?'o':' ', nonces[i].BitFlip[EVEN_STATE]?'e':' ');
+ printf("[%02x]:%c ", i, nonces[i].BitFlip[ODD_STATE]?'o':nonces[i].BitFlip[EVEN_STATE]?'e':' ');
if (i % 8 == 7) {
printf("\n");
}
}
- printf("\nTests: Best %d first bytes:\n", MAX_BEST_BYTES);
- for (uint16_t i = 0; i < MAX_BEST_BYTES; i++) {
+ printf("\nTests: Sorted First Bytes:\n");
+ for (uint16_t i = 0; i < 256; i++) {
uint8_t best_byte = best_first_bytes[i];
- uint16_t best_num = nonces[best_byte].num;
- uint16_t best_sum = nonces[best_byte].Sum;
- uint16_t best_sum8 = nonces[best_byte].Sum8_guess;
- float confidence = nonces[best_byte].Sum8_prob;
- printf("Byte: %02x, n = %2d, k = %2d, Sum(a8): %3d, Confidence: %2.1f%%\n", best_byte, best_num, best_sum, best_sum8, confidence*100);
+ printf("#%03d Byte: %02x, n = %3d, k = %3d, Sum(a8): %3d, Confidence: %5.1f%%, Bitflip: %c\n",
+ //printf("#%03d Byte: %02x, n = %3d, k = %3d, Sum(a8): %3d, Confidence: %5.1f%%, Bitflip: %c, score1: %1.5f, score2: %1.0f\n",
+ i, best_byte,
+ nonces[best_byte].num,
+ nonces[best_byte].Sum,
+ nonces[best_byte].Sum8_guess,
+ nonces[best_byte].Sum8_prob * 100,
+ nonces[best_byte].BitFlip[ODD_STATE]?'o':nonces[best_byte].BitFlip[EVEN_STATE]?'e':' '
+ //nonces[best_byte].score1,
+ //nonces[best_byte].score2
+ );
}
+
+ // printf("\nTests: parity performance\n");
+ // time_t time1p = clock();
+ // uint32_t par_sum = 0;
+ // for (uint32_t i = 0; i < 100000000; i++) {
+ // par_sum += parity(i);
+ // }
+ // printf("parsum oldparity = %d, time = %1.5fsec\n", par_sum, (float)(clock() - time1p)/CLOCKS_PER_SEC);
+
+ // time1p = clock();
+ // par_sum = 0;
+ // for (uint32_t i = 0; i < 100000000; i++) {
+ // par_sum += evenparity32(i);
+ // }
+ // printf("parsum newparity = %d, time = %1.5fsec\n", par_sum, (float)(clock() - time1p)/CLOCKS_PER_SEC);
+
+
}
static void sort_best_first_bytes(void)
{
- // find the best choice for the very first byte (b)
- float min_p_K = 1.0;
- float max_prob_min_p_K = 0.0;
- uint8_t best_byte = 0;
+ // sort based on probability for correct guess
for (uint16_t i = 0; i < 256; i++ ) {
+ uint16_t j = 0;
float prob1 = nonces[i].Sum8_prob;
- uint16_t sum8 = nonces[i].Sum8_guess;
- if (p_K[sum8] <= min_p_K && prob1 > CONFIDENCE_THRESHOLD) {
- if (p_K[sum8] < min_p_K) {
- min_p_K = p_K[sum8];
- best_byte = i;
- max_prob_min_p_K = prob1;
- } else if (prob1 > max_prob_min_p_K) {
- max_prob_min_p_K = prob1;
- best_byte = i;
- }
- }
- }
- best_first_bytes[0] = best_byte;
- // printf("Best Byte = 0x%02x, Sum8=%d, prob=%1.3f\n", best_byte, nonces[best_byte].Sum8_guess, nonces[best_byte].Sum8_prob);
-
- // sort the most probable guesses as following bytes (b')
- for (uint16_t i = 0; i < 256; i++ ) {
- if (i == best_first_bytes[0]) {
- continue;
- }
- uint16_t j = 1;
- float prob1 = nonces[i].Sum8_prob;
- float prob2 = nonces[best_first_bytes[1]].Sum8_prob;
- while (prob1 < prob2 && j < MAX_BEST_BYTES-1) {
+ float prob2 = nonces[best_first_bytes[0]].Sum8_prob;
+ while (prob1 < prob2 && j < i) {
prob2 = nonces[best_first_bytes[++j]].Sum8_prob;
}
- if (prob1 >= prob2) {
- for (uint16_t k = MAX_BEST_BYTES-1; k > j; k--) {
+ if (j < i) {
+ for (uint16_t k = i; k > j; k--) {
best_first_bytes[k] = best_first_bytes[k-1];
}
+ }
best_first_bytes[j] = i;
}
+
+ // determine how many are above the CONFIDENCE_THRESHOLD
+ uint16_t num_good_nonces = 0;
+ for (uint16_t i = 0; i < 256; i++) {
+ if (nonces[best_first_bytes[i]].Sum8_prob > CONFIDENCE_THRESHOLD) {
+ ++num_good_nonces;
+ }
}
+
+ uint16_t best_first_byte = 0;
+
+ // select the best possible first byte based on number of common bits with all {b'}
+ // uint16_t max_common_bits = 0;
+ // for (uint16_t i = 0; i < num_good_nonces; i++) {
+ // uint16_t sum_common_bits = 0;
+ // for (uint16_t j = 0; j < num_good_nonces; j++) {
+ // if (i != j) {
+ // sum_common_bits += common_bits(best_first_bytes[i],best_first_bytes[j]);
+ // }
+ // }
+ // if (sum_common_bits > max_common_bits) {
+ // max_common_bits = sum_common_bits;
+ // best_first_byte = i;
+ // }
+ // }
+
+ // select best possible first byte {b} based on least likely sum/bitflip property
+ float min_p_K = 1.0;
+ for (uint16_t i = 0; i < num_good_nonces; i++ ) {
+ uint16_t sum8 = nonces[best_first_bytes[i]].Sum8_guess;
+ float bitflip_prob = 1.0;
+ if (nonces[best_first_bytes[i]].BitFlip[ODD_STATE] || nonces[best_first_bytes[i]].BitFlip[EVEN_STATE]) {
+ bitflip_prob = 0.09375;
+ }
+ nonces[best_first_bytes[i]].score1 = p_K[sum8] * bitflip_prob;
+ if (p_K[sum8] * bitflip_prob <= min_p_K) {
+ min_p_K = p_K[sum8] * bitflip_prob;
+ }
+ }
+
+
+ // use number of commmon bits as a tie breaker
+ uint16_t max_common_bits = 0;
+ for (uint16_t i = 0; i < num_good_nonces; i++) {
+ float bitflip_prob = 1.0;
+ if (nonces[best_first_bytes[i]].BitFlip[ODD_STATE] || nonces[best_first_bytes[i]].BitFlip[EVEN_STATE]) {
+ bitflip_prob = 0.09375;
+ }
+ if (p_K[nonces[best_first_bytes[i]].Sum8_guess] * bitflip_prob == min_p_K) {
+ uint16_t sum_common_bits = 0;
+ for (uint16_t j = 0; j < num_good_nonces; j++) {
+ sum_common_bits += common_bits(best_first_bytes[i] ^ best_first_bytes[j]);
+ }
+ nonces[best_first_bytes[i]].score2 = sum_common_bits;
+ if (sum_common_bits > max_common_bits) {
+ max_common_bits = sum_common_bits;
+ best_first_byte = i;
+ }
+ }
+ }
+
+ // swap best possible first byte to the pole position
+ uint16_t temp = best_first_bytes[0];
+ best_first_bytes[0] = best_first_bytes[best_first_byte];
+ best_first_bytes[best_first_byte] = temp;
+
}
static uint16_t estimate_second_byte_sum(void)
{
- for (uint16_t i = 0; i < MAX_BEST_BYTES; i++) {
- best_first_bytes[i] = 0;
- }
for (uint16_t first_byte = 0; first_byte < 256; first_byte++) {
float Sum8_prob = 0.0;
sort_best_first_bytes();
uint16_t num_good_nonces = 0;
- for (uint16_t i = 0; i < MAX_BEST_BYTES; i++) {
+ for (uint16_t i = 0; i < 256; i++) {
if (nonces[best_first_bytes[i]].Sum8_prob > CONFIDENCE_THRESHOLD) {
++num_good_nonces;
}
}
-int static acquire_nonces(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_t trgBlockNo, uint8_t trgKeyType, bool nonce_file_write, bool slow)
+static void Check_for_FilterFlipProperties(void)
+{
+ printf("Checking for Filter Flip Properties...\n");
+
+ for (uint16_t i = 0; i < 256; i++) {
+ nonces[i].BitFlip[ODD_STATE] = false;
+ nonces[i].BitFlip[EVEN_STATE] = false;
+ }
+
+ for (uint16_t i = 0; i < 256; i++) {
+ uint8_t parity1 = (nonces[i].first->par_enc) >> 3; // parity of first byte
+ uint8_t parity2_odd = (nonces[i^0x80].first->par_enc) >> 3; // XOR 0x80 = last bit flipped
+ uint8_t parity2_even = (nonces[i^0x40].first->par_enc) >> 3; // XOR 0x40 = second last bit flipped
+
+ if (parity1 == parity2_odd) { // has Bit Flip Property for odd bits
+ nonces[i].BitFlip[ODD_STATE] = true;
+ } else if (parity1 == parity2_even) { // has Bit Flip Property for even bits
+ nonces[i].BitFlip[EVEN_STATE] = true;
+ }
+ }
+}
+
+
+static int acquire_nonces(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_t trgBlockNo, uint8_t trgKeyType, bool nonce_file_write, bool slow)
{
clock_t time1 = clock();
bool initialize = true;
bool field_off = false;
bool finished = false;
+ bool filter_flip_checked = false;
uint32_t flags = 0;
uint8_t write_buf[9];
uint32_t total_num_nonces = 0;
if (first_byte_num == 256 ) {
// printf("first_byte_num = %d, first_byte_Sum = %d\n", first_byte_num, first_byte_Sum);
+ if (!filter_flip_checked) {
+ Check_for_FilterFlipProperties();
+ filter_flip_checked = true;
+ }
num_good_first_bytes = estimate_second_byte_sum();
if (total_num_nonces > next_fivehundred) {
next_fivehundred = (total_num_nonces/500+1) * 500;
fclose(fnonces);
}
- PrintAndLog("Acquired a total of %d nonces in %1.1f seconds (%d nonces/minute)",
+ PrintAndLog("Acquired a total of %d nonces in %1.1f seconds (%0.0f nonces/minute)",
total_num_nonces,
((float)clock()-time1)/CLOCKS_PER_SEC,
- total_num_nonces*60*CLOCKS_PER_SEC/(clock()-time1));
+ total_num_nonces*60.0*CLOCKS_PER_SEC/((float)clock()-time1));
return 0;
}
static int init_partial_statelists(void)
{
- const uint32_t sizes_odd[17] = { 125601, 0, 17607, 0, 73421, 0, 182033, 0, 248801, 0, 181737, 0, 74241, 0, 18387, 0, 126757 };
+ const uint32_t sizes_odd[17] = { 126757, 0, 18387, 0, 74241, 0, 181737, 0, 248801, 0, 182033, 0, 73421, 0, 17607, 0, 125601 };
const uint32_t sizes_even[17] = { 125723, 0, 17867, 0, 74305, 0, 178707, 0, 248801, 0, 185063, 0, 73356, 0, 18127, 0, 126634 };
printf("Allocating memory for partial statelists...\n");
}
-static void add_state(statelist_t *sl, uint32_t state, odd_even_t odd_even)
-{
- uint32_t *p;
-
- p = sl->states[odd_even];
- p += sl->len[odd_even];
- *p = state;
- sl->len[odd_even]++;
-}
-
-
-uint32_t *find_first_state(uint32_t state, uint32_t mask, partial_indexed_statelist_t *sl, odd_even_t odd_even)
+static inline uint32_t *find_first_state(uint32_t state, uint32_t mask, partial_indexed_statelist_t *sl, odd_even_t odd_even)
{
uint32_t *p = sl->index[odd_even][(state & mask) >> (20-STATELIST_INDEX_WIDTH)]; // first Bits as index
if (p == NULL) return NULL;
- while ((*p & mask) < (state & mask)) p++;
+ while (*p < (state & mask)) p++;
if (*p == 0xffffffff) return NULL; // reached end of list, no match
if ((*p & mask) == (state & mask)) return p; // found a match.
return NULL; // no match
}
-static bool remaining_bits_match(uint8_t num_common_bits, uint8_t byte1, uint8_t byte2, uint32_t state1, uint32_t state2, odd_even_t odd_even)
+static inline bool /*__attribute__((always_inline))*/ invariant_holds(uint_fast8_t byte_diff, uint_fast32_t state1, uint_fast32_t state2, uint_fast8_t bit, uint_fast8_t state_bit)
{
- uint8_t j = num_common_bits;
- if (odd_even == ODD_STATE) {
- j |= 0x01; // consider the next odd bit
- } else {
- j = (j+1) & 0xfe; // consider the next even bit
- }
-
- while (j <= 7) {
- if (j != num_common_bits) { // this is not the first differing bit, we need first to check if the invariant still holds
- uint32_t bit_diff = ((byte1 ^ byte2) << (17-j)) & 0x00010000; // difference of (j-1)th bit -> bit 16
- uint32_t filter_diff = filter(state1 >> (4-j/2)) ^ filter(state2 >> (4-j/2)); // difference in filter function -> bit 0
- uint32_t mask_y12_y13 = 0x000000c0 >> (j/2);
- uint32_t state_diff = (state1 ^ state2) & mask_y12_y13; // difference in state bits 12 and 13 -> bits 6/7 ... 4/5
- uint32_t all_diff = parity(bit_diff | state_diff | filter_diff); // use parity function to XOR all 4 bits
- if (all_diff) { // invariant doesn't hold any more. Accept this state.
- // if ((odd_even == ODD_STATE && state1 == test_state_odd)
- // || (odd_even == EVEN_STATE && state1 == test_state_even)) {
- // printf("remaining_bits_match(): %s test state: Invariant doesn't hold. Bytes = %02x, %02x, Common Bits=%d, Testing Bit %d, State1=0x%08x, State2=0x%08x\n",
- // odd_even==ODD_STATE?"odd":"even", byte1, byte2, num_common_bits, j, state1, state2);
- // }
- return true;
- }
+ uint_fast8_t j_1_bit_mask = 0x01 << (bit-1);
+ uint_fast8_t bit_diff = byte_diff & j_1_bit_mask; // difference of (j-1)th bit
+ uint_fast8_t filter_diff = filter(state1 >> (4-state_bit)) ^ filter(state2 >> (4-state_bit)); // difference in filter function
+ uint_fast8_t mask_y12_y13 = 0xc0 >> state_bit;
+ uint_fast8_t state_bits_diff = (state1 ^ state2) & mask_y12_y13; // difference in state bits 12 and 13
+ uint_fast8_t all_diff = evenparity8(bit_diff ^ state_bits_diff ^ filter_diff); // use parity function to XOR all bits
+ return !all_diff;
+}
+
+
+static inline bool /*__attribute__((always_inline))*/ invalid_state(uint_fast8_t byte_diff, uint_fast32_t state1, uint_fast32_t state2, uint_fast8_t bit, uint_fast8_t state_bit)
+{
+ uint_fast8_t j_bit_mask = 0x01 << bit;
+ uint_fast8_t bit_diff = byte_diff & j_bit_mask; // difference of jth bit
+ uint_fast8_t mask_y13_y16 = 0x48 >> state_bit;
+ uint_fast8_t state_bits_diff = (state1 ^ state2) & mask_y13_y16; // difference in state bits 13 and 16
+ uint_fast8_t all_diff = evenparity8(bit_diff ^ state_bits_diff); // use parity function to XOR all bits
+ return all_diff;
+}
+
+
+static inline bool remaining_bits_match(uint_fast8_t num_common_bits, uint_fast8_t byte_diff, uint_fast32_t state1, uint_fast32_t state2, odd_even_t odd_even)
+{
+ if (odd_even) {
+ // odd bits
+ switch (num_common_bits) {
+ case 0: if (!invariant_holds(byte_diff, state1, state2, 1, 0)) return true;
+ case 1: if (invalid_state(byte_diff, state1, state2, 1, 0)) return false;
+ case 2: if (!invariant_holds(byte_diff, state1, state2, 3, 1)) return true;
+ case 3: if (invalid_state(byte_diff, state1, state2, 3, 1)) return false;
+ case 4: if (!invariant_holds(byte_diff, state1, state2, 5, 2)) return true;
+ case 5: if (invalid_state(byte_diff, state1, state2, 5, 2)) return false;
+ case 6: if (!invariant_holds(byte_diff, state1, state2, 7, 3)) return true;
+ case 7: if (invalid_state(byte_diff, state1, state2, 7, 3)) return false;
}
- // check for validity of state candidate
- uint32_t bit_diff = ((byte1 ^ byte2) << (16-j)) & 0x00010000; // difference of jth bit -> bit 16
- uint32_t mask_y13_y16 = 0x00000048 >> (j/2);
- uint32_t state_diff = (state1 ^ state2) & mask_y13_y16; // difference in state bits 13 and 16 -> bits 3/6 ... 0/3
- uint32_t all_diff = parity(bit_diff | state_diff); // use parity function to XOR all 3 bits
- if (all_diff) { // not a valid state
- // if ((odd_even == ODD_STATE && state1 == test_state_odd)
- // || (odd_even == EVEN_STATE && state1 == test_state_even)) {
- // printf("remaining_bits_match(): %s test state: Invalid state. Bytes = %02x, %02x, Common Bits=%d, Testing Bit %d, State1=0x%08x, State2=0x%08x\n",
- // odd_even==ODD_STATE?"odd":"even", byte1, byte2, num_common_bits, j, state1, state2);
- // printf(" byte1^byte2: 0x%02x, bit_diff: 0x%08x, state_diff: 0x%08x, all_diff: 0x%08x\n",
- // byte1^byte2, bit_diff, state_diff, all_diff);
- // }
- return false;
+ } else {
+ // even bits
+ switch (num_common_bits) {
+ case 0: if (invalid_state(byte_diff, state1, state2, 0, 0)) return false;
+ case 1: if (!invariant_holds(byte_diff, state1, state2, 2, 1)) return true;
+ case 2: if (invalid_state(byte_diff, state1, state2, 2, 1)) return false;
+ case 3: if (!invariant_holds(byte_diff, state1, state2, 4, 2)) return true;
+ case 4: if (invalid_state(byte_diff, state1, state2, 4, 2)) return false;
+ case 5: if (!invariant_holds(byte_diff, state1, state2, 6, 3)) return true;
+ case 6: if (invalid_state(byte_diff, state1, state2, 6, 3)) return false;
}
- // continue checking for the next bit
- j += 2;
}
return true; // valid state
{
for (uint16_t i = 1; i < num_good_first_bytes; i++) {
uint16_t sum_a8 = nonces[best_first_bytes[i]].Sum8_guess;
- uint8_t j = 0; // number of common bits
- uint8_t common_bits = best_first_bytes[0] ^ best_first_bytes[i];
+ uint_fast8_t bytes_diff = best_first_bytes[0] ^ best_first_bytes[i];
+ uint_fast8_t j = common_bits(bytes_diff);
uint32_t mask = 0xfffffff0;
if (odd_even == ODD_STATE) {
- while ((common_bits & 0x01) == 0 && j < 8) {
- j++;
- common_bits >>= 1;
- if (j % 2 == 0) { // the odd bits
- mask >>= 1;
- }
- }
+ mask >>= j/2;
} else {
- while ((common_bits & 0x01) == 0 && j < 8) {
- j++;
- common_bits >>= 1;
- if (j % 2 == 1) { // the even bits
- mask >>= 1;
- }
- }
+ mask >>= (j+1)/2;
}
mask &= 0x000fffff;
//printf("bytes 0x%02x and 0x%02x: %d common bits, mask = 0x%08x, state = 0x%08x, sum_a8 = %d", best_first_bytes[0], best_first_bytes[i], j, mask, state, sum_a8);
uint32_t *p = find_first_state(state, mask, &partial_statelist[part_sum_a8], odd_even);
if (p != NULL) {
while ((state & mask) == (*p & mask) && (*p != 0xffffffff)) {
- if (remaining_bits_match(j, best_first_bytes[0], best_first_bytes[i], state, (state&0x00fffff0) | *p, odd_even)) {
+ if (remaining_bits_match(j, bytes_diff, state, (state&0x00fffff0) | *p, odd_even)) {
found_match = true;
// if ((odd_even == ODD_STATE && state == test_state_odd)
// || (odd_even == EVEN_STATE && state == test_state_even)) {
}
+static bool all_bit_flips_match(uint32_t state, odd_even_t odd_even)
+{
+ for (uint16_t i = 0; i < 256; i++) {
+ if (nonces[i].BitFlip[odd_even] && i != best_first_bytes[0]) {
+ uint_fast8_t bytes_diff = best_first_bytes[0] ^ i;
+ uint_fast8_t j = common_bits(bytes_diff);
+ uint32_t mask = 0xfffffff0;
+ if (odd_even == ODD_STATE) {
+ mask >>= j/2;
+ } else {
+ mask >>= (j+1)/2;
+ }
+ mask &= 0x000fffff;
+ //printf("bytes 0x%02x and 0x%02x: %d common bits, mask = 0x%08x, state = 0x%08x, sum_a8 = %d", best_first_bytes[0], best_first_bytes[i], j, mask, state, sum_a8);
+ bool found_match = false;
+ uint32_t *p = find_first_state(state, mask, &statelist_bitflip, 0);
+ if (p != NULL) {
+ while ((state & mask) == (*p & mask) && (*p != 0xffffffff)) {
+ if (remaining_bits_match(j, bytes_diff, state, (state&0x00fffff0) | *p, odd_even)) {
+ found_match = true;
+ // if ((odd_even == ODD_STATE && state == test_state_odd)
+ // || (odd_even == EVEN_STATE && state == test_state_even)) {
+ // printf("all_other_first_bytes_match(): %s test state: remaining bits matched. Bytes = %02x, %02x, Common Bits=%d, mask=0x%08x, PartSum(a8)=%d\n",
+ // odd_even==ODD_STATE?"odd":"even", best_first_bytes[0], best_first_bytes[i], j, mask, part_sum_a8);
+ // }
+ break;
+ } else {
+ // if ((odd_even == ODD_STATE && state == test_state_odd)
+ // || (odd_even == EVEN_STATE && state == test_state_even)) {
+ // printf("all_other_first_bytes_match(): %s test state: remaining bits didn't match. Bytes = %02x, %02x, Common Bits=%d, mask=0x%08x, PartSum(a8)=%d\n",
+ // odd_even==ODD_STATE?"odd":"even", best_first_bytes[0], best_first_bytes[i], j, mask, part_sum_a8);
+ // }
+ }
+ p++;
+ }
+ } else {
+ // if ((odd_even == ODD_STATE && state == test_state_odd)
+ // || (odd_even == EVEN_STATE && state == test_state_even)) {
+ // printf("all_other_first_bytes_match(): %s test state: couldn't find a matching state. Bytes = %02x, %02x, Common Bits=%d, mask=0x%08x, PartSum(a8)=%d\n",
+ // odd_even==ODD_STATE?"odd":"even", best_first_bytes[0], best_first_bytes[i], j, mask, part_sum_a8);
+ // }
+ }
+ if (!found_match) {
+ // if ((odd_even == ODD_STATE && state == test_state_odd)
+ // || (odd_even == EVEN_STATE && state == test_state_even)) {
+ // printf("all_other_first_bytes_match(): %s test state: Eliminated. Bytes = %02x, %02x, Common Bits = %d\n", odd_even==ODD_STATE?"odd":"even", best_first_bytes[0], best_first_bytes[i], j);
+ // }
+ return false;
+ }
+ }
+
+ }
+
+ return true;
+}
+
+
+static struct sl_cache_entry {
+ uint32_t *sl;
+ uint32_t len;
+ } sl_cache[17][17][2];
+
+
+static void init_statelist_cache(void)
+{
+
+ for (uint16_t i = 0; i < 17; i+=2) {
+ for (uint16_t j = 0; j < 17; j+=2) {
+ for (uint16_t k = 0; k < 2; k++) {
+ sl_cache[i][j][k].sl = NULL;
+ sl_cache[i][j][k].len = 0;
+ }
+ }
+ }
+}
+
+
static int add_matching_states(statelist_t *candidates, uint16_t part_sum_a0, uint16_t part_sum_a8, odd_even_t odd_even)
{
uint32_t worstcase_size = 1<<20;
+ // check cache for existing results
+ if (sl_cache[part_sum_a0][part_sum_a8][odd_even].sl != NULL) {
+ candidates->states[odd_even] = sl_cache[part_sum_a0][part_sum_a8][odd_even].sl;
+ candidates->len[odd_even] = sl_cache[part_sum_a0][part_sum_a8][odd_even].len;
+ return 0;
+ }
+
candidates->states[odd_even] = (uint32_t *)malloc(sizeof(uint32_t) * worstcase_size);
if (candidates->states[odd_even] == NULL) {
PrintAndLog("Out of memory error.\n");
return 4;
}
+ uint32_t *add_p = candidates->states[odd_even];
for (uint32_t *p1 = partial_statelist[part_sum_a0].states[odd_even]; *p1 != 0xffffffff; p1++) {
uint32_t search_mask = 0x000ffff0;
uint32_t *p2 = find_first_state((*p1 << 4), search_mask, &partial_statelist[part_sum_a8], odd_even);
if (p2 != NULL) {
while (((*p1 << 4) & search_mask) == (*p2 & search_mask) && *p2 != 0xffffffff) {
+ if ((nonces[best_first_bytes[0]].BitFlip[odd_even] && find_first_state((*p1 << 4) | *p2, 0x000fffff, &statelist_bitflip, 0))
+ || !nonces[best_first_bytes[0]].BitFlip[odd_even]) {
if (all_other_first_bytes_match((*p1 << 4) | *p2, odd_even)) {
- add_state(candidates, (*p1 << 4) | *p2, odd_even);
+ if (all_bit_flips_match((*p1 << 4) | *p2, odd_even)) {
+ *add_p++ = (*p1 << 4) | *p2;
+ }
+ }
}
p2++;
}
}
- p2 = candidates->states[odd_even];
- p2 += candidates->len[odd_even];
- *p2 = 0xffffffff;
}
+
+ // set end of list marker and len
+ *add_p = 0xffffffff;
+ candidates->len[odd_even] = add_p - candidates->states[odd_even];
+
candidates->states[odd_even] = realloc(candidates->states[odd_even], sizeof(uint32_t) * (candidates->len[odd_even] + 1));
+ sl_cache[part_sum_a0][part_sum_a8][odd_even].sl = candidates->states[odd_even];
+ sl_cache[part_sum_a0][part_sum_a8][odd_even].len = candidates->len[odd_even];
+
return 0;
}
uint32_t state_odd = pcs->odd & 0x00ffffff;
uint32_t state_even = pcs->even & 0x00ffffff;
- printf("Tests: searching for key %llx after first byte 0x%02x (state_odd = 0x%06x, state_even = 0x%06x) ...\n", key, best_first_bytes[0], state_odd, state_even);
+ //printf("Tests: searching for key %llx after first byte 0x%02x (state_odd = 0x%06x, state_even = 0x%06x) ...\n", key, best_first_bytes[0], state_odd, state_even);
+ uint64_t count = 0;
for (statelist_t *p = candidates; p != NULL; p = p->next) {
+ bool found_odd = false;
+ bool found_even = false;
uint32_t *p_odd = p->states[ODD_STATE];
uint32_t *p_even = p->states[EVEN_STATE];
while (*p_odd != 0xffffffff) {
- if (*p_odd == state_odd) printf("o");
+ if ((*p_odd & 0x00ffffff) == state_odd) {
+ found_odd = true;
+ break;
+ }
p_odd++;
}
while (*p_even != 0xffffffff) {
- if (*p_even == state_even) printf("e");
+ if ((*p_even & 0x00ffffff) == state_even) {
+ found_even = true;
+ }
p_even++;
}
- printf("|");
+ count += (p_odd - p->states[ODD_STATE]) * (p_even - p->states[EVEN_STATE]);
+ if (found_odd && found_even) {
+ PrintAndLog("Key Found after testing %lld (2^%1.1f) out of %lld (2^%1.1f) keys. A brute force would have taken approx %lld minutes.",
+ count, log(count)/log(2),
+ maximum_states, log(maximum_states)/log(2),
+ (count>>23)/60);
+ crypto1_destroy(pcs);
+ return;
+ }
}
- printf("\n");
+
+ printf("Key NOT found!\n");
crypto1_destroy(pcs);
}
statelist_t *current_candidates = NULL;
// estimate maximum candidate states
- uint64_t maximum_states = 0;
+ maximum_states = 0;
for (uint16_t sum_odd = 0; sum_odd <= 16; sum_odd += 2) {
for (uint16_t sum_even = 0; sum_even <= 16; sum_even += 2) {
if (sum_odd*(16-sum_even) + (16-sum_odd)*sum_even == sum_a0) {
}
printf("Number of possible keys with Sum(a0) = %d: %lld (2^%1.1f)\n", sum_a0, maximum_states, log(maximum_states)/log(2.0));
+ init_statelist_cache();
+
for (uint16_t p = 0; p <= 16; p += 2) {
for (uint16_t q = 0; q <= 16; q += 2) {
if (p*(16-q) + (16-p)*q == sum_a0) {
for (uint16_t s = 0; s <= 16; s += 2) {
if (r*(16-s) + (16-r)*s == sum_a8) {
current_candidates = add_more_candidates(current_candidates);
+ // check for the smallest partial statelist. Try this first - it might give 0 candidates
+ // and eliminate the need to calculate the other part
+ if (MIN(partial_statelist[p].len[ODD_STATE], partial_statelist[r].len[ODD_STATE])
+ < MIN(partial_statelist[q].len[EVEN_STATE], partial_statelist[s].len[EVEN_STATE])) {
add_matching_states(current_candidates, p, r, ODD_STATE);
- printf("Odd state candidates: %d (2^%0.1f)\n", current_candidates->len[ODD_STATE], log(current_candidates->len[ODD_STATE])/log(2));
+ if(current_candidates->len[ODD_STATE]) {
add_matching_states(current_candidates, q, s, EVEN_STATE);
- printf("Even state candidates: %d (2^%0.1f)\n", current_candidates->len[EVEN_STATE], log(current_candidates->len[EVEN_STATE])/log(2));
+ } else {
+ current_candidates->len[EVEN_STATE] = 0;
+ uint32_t *p = current_candidates->states[EVEN_STATE] = malloc(sizeof(uint32_t));
+ *p = 0xffffffff;
+ }
+ } else {
+ add_matching_states(current_candidates, q, s, EVEN_STATE);
+ if(current_candidates->len[EVEN_STATE]) {
+ add_matching_states(current_candidates, p, r, ODD_STATE);
+ } else {
+ current_candidates->len[ODD_STATE] = 0;
+ uint32_t *p = current_candidates->states[ODD_STATE] = malloc(sizeof(uint32_t));
+ *p = 0xffffffff;
+ }
+ }
+ printf("Odd state candidates: %6d (2^%0.1f)\n", current_candidates->len[ODD_STATE], log(current_candidates->len[ODD_STATE])/log(2));
+ printf("Even state candidates: %6d (2^%0.1f)\n", current_candidates->len[EVEN_STATE], log(current_candidates->len[EVEN_STATE])/log(2));
}
}
}
}
printf("Number of remaining possible keys: %lld (2^%1.1f)\n", maximum_states, log(maximum_states)/log(2.0));
- TestIfKeyExists(0xffffffffffff);
- TestIfKeyExists(0xa0a1a2a3a4a5);
-
}
-static void Check_for_FilterFlipProperties(void)
+static void brute_force(void)
{
- printf("Checking for Filter Flip Properties...\n");
-
- for (uint16_t i = 0; i < 256; i++) {
- nonces[i].BitFlip[ODD_STATE] = false;
- nonces[i].BitFlip[EVEN_STATE] = false;
- }
-
- for (uint16_t i = 0; i < 256; i++) {
- uint8_t parity1 = (nonces[i].first->par_enc) >> 3; // parity of first byte
- uint8_t parity2_odd = (nonces[i^0x80].first->par_enc) >> 3; // XOR 0x80 = last bit flipped
- uint8_t parity2_even = (nonces[i^0x40].first->par_enc) >> 3; // XOR 0x40 = second last bit flipped
-
- if (parity1 == parity2_odd) { // has Bit Flip Property for odd bits
- nonces[i].BitFlip[ODD_STATE] = true;
- } else if (parity1 == parity2_even) { // has Bit Flip Property for even bits
- nonces[i].BitFlip[EVEN_STATE] = true;
- }
+ if (known_target_key != -1) {
+ PrintAndLog("Looking for known target key in remaining key space...");
+ TestIfKeyExists(known_target_key);
+ } else {
+ PrintAndLog("Brute Force phase is not implemented.");
}
+
}
-int mfnestedhard(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_t trgBlockNo, uint8_t trgKeyType, bool nonce_file_read, bool nonce_file_write, bool slow)
+int mfnestedhard(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_t trgBlockNo, uint8_t trgKeyType, uint8_t *trgkey, bool nonce_file_read, bool nonce_file_write, bool slow)
{
+ if (trgkey != NULL) {
+ known_target_key = bytes_to_num(trgkey, 6);
+ } else {
+ known_target_key = -1;
+ }
// initialize the list of nonces
for (uint16_t i = 0; i < 256; i++) {
if (read_nonce_file() != 0) {
return 3;
}
- num_good_first_bytes = estimate_second_byte_sum();
+ Check_for_FilterFlipProperties();
+ num_good_first_bytes = MIN(estimate_second_byte_sum(), GOOD_BYTES_REQUIRED);
} else { // acquire nonces.
uint16_t is_OK = acquire_nonces(blockNo, keyType, key, trgBlockNo, trgKeyType, nonce_file_write, slow);
if (is_OK != 0) {
}
}
- Check_for_FilterFlipProperties();
Tests();
// best_first_bytes[9] );
PrintAndLog("Number of first bytes with confidence > %2.1f%%: %d", CONFIDENCE_THRESHOLD*100.0, num_good_first_bytes);
+ time_t start_time = clock();
generate_candidates(first_byte_Sum, nonces[best_first_bytes[0]].Sum8_guess);
+ PrintAndLog("Time for generating key candidates list: %1.0f seconds", (float)(clock() - start_time)/CLOCKS_PER_SEC);
- PrintAndLog("Brute force phase not yet implemented");
+ brute_force();
return 0;
}
projects / proxmark3-svn / blobdiff