#include <stdlib.h>
#include <string.h>
#include <pthread.h>
+#include <locale.h>
#include <math.h>
+#include <inttypes.h>
#include "proxmark3.h"
#include "cmdmain.h"
#include "ui.h"
// uint32_t test_state_even = 0;
#define CONFIDENCE_THRESHOLD 0.95 // Collect nonces until we are certain enough that the following brute force is successfull
-#define GOOD_BYTES_REQUIRED 60
+#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 256
-static uint8_t best_first_bytes[MAX_BEST_BYTES];
+static bool write_stats = false;
+static FILE *fstats = NULL;
typedef enum {
}
+static void init_nonce_memory(void)
+{
+ for (uint16_t i = 0; i < 256; i++) {
+ nonces[i].num = 0;
+ nonces[i].Sum = 0;
+ nonces[i].Sum8_guess = 0;
+ nonces[i].Sum8_prob = 0.0;
+ nonces[i].updated = true;
+ nonces[i].first = NULL;
+ }
+ first_byte_num = 0;
+ first_byte_Sum = 0;
+ num_good_first_bytes = 0;
+}
+
+
+static void free_nonce_list(noncelistentry_t *p)
+{
+ if (p == NULL) {
+ return;
+ } else {
+ free_nonce_list(p->next);
+ free(p);
+ }
+}
+
+
+static void free_nonces_memory(void)
+{
+ for (uint16_t i = 0; i < 256; i++) {
+ free_nonce_list(nonces[i].first);
+ }
+}
+
+
static uint16_t PartialSumProperty(uint32_t state, odd_even_t odd_even)
{
uint16_t sum = 0;
}
-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 float sum_probability(uint16_t K, uint16_t n, uint16_t k)
{
const uint16_t N = 256;
-
-
- if (k > K || p_K[K] == 0.0) return 0.0;
+ if (k > K || p_K[K] == 0.0) return 0.0;
- double p_T_is_k_when_S_is_K = p_hypergeometric(N, K, n, k);
- double p_S_is_K = p_K[K];
- double p_T_is_k = 0;
- for (uint16_t i = 0; i <= 256; i++) {
- if (p_K[i] != 0.0) {
- p_T_is_k += p_K[i] * p_hypergeometric(N, i, n, k);
- }
+ double p_T_is_k_when_S_is_K = p_hypergeometric(N, K, n, k);
+ double p_S_is_K = p_K[K];
+ double p_T_is_k = 0;
+ for (uint16_t i = 0; i <= 256; i++) {
+ if (p_K[i] != 0.0) {
+ p_T_is_k += p_K[i] * p_hypergeometric(N, i, n, k);
}
- return(p_T_is_k_when_S_is_K * p_S_is_K / p_T_is_k);
+ }
+ return(p_T_is_k_when_S_is_K * p_S_is_K / p_T_is_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
// uint32_t statistics_odd[17];
// 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);
- //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);
+ // 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);
-
+ // 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("[%02x]:%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("#%03d Byte: %02x, n = %2d, k = %2d, Sum(a8): %3d, Confidence: %2.1f%%\n", i, 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");
// }
// printf("parsum newparity = %d, time = %1.5fsec\n", par_sum, (float)(clock() - time1p)/CLOCKS_PER_SEC);
-}
-
-static int common_bits(uint8_t byte1, uint8_t byte2)
-{
- uint8_t common_bits = byte1 ^ byte2;
- uint8_t j = 0;
- while ((common_bits & 0x01) == 0 && j < 8) {
- j++;
- common_bits >>= 1;
- }
- return j;
}
static void sort_best_first_bytes(void)
{
- // first, sort based on probability for correct guess
+ // 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;
float prob2 = nonces[best_first_bytes[0]].Sum8_prob;
- while (prob1 < prob2 && j < MAX_BEST_BYTES-1) {
+ 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
+ // determine how many are above the CONFIDENCE_THRESHOLD
uint16_t num_good_nonces = 0;
- for (uint16_t i = 0; i < MAX_BEST_BYTES; i++) {
- if (nonces[best_first_bytes[i]].Sum8_prob > CONFIDENCE_THRESHOLD) {
+ for (uint16_t i = 0; i < 256; i++) {
+ if (nonces[best_first_bytes[i]].Sum8_prob >= CONFIDENCE_THRESHOLD) {
++num_good_nonces;
}
}
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;
- best_first_byte = i;
}
}
+
// 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++) {
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]);
+ 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 bytes to the pole position
+ // 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++) {
- if (nonces[best_first_bytes[i]].Sum8_prob > CONFIDENCE_THRESHOLD) {
+ for (uint16_t i = 0; i < 256; i++) {
+ if (nonces[best_first_bytes[i]].Sum8_prob >= CONFIDENCE_THRESHOLD) {
++num_good_nonces;
}
}
}
+static void Check_for_FilterFlipProperties(void)
+{
+ printf("Checking for Filter Flip Properties...\n");
+
+ uint16_t num_bitflips = 0;
+
+ 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;
+ num_bitflips++;
+ } else if (parity1 == parity2_even) { // has Bit Flip Property for even bits
+ nonces[i].BitFlip[EVEN_STATE] = true;
+ num_bitflips++;
+ }
+ }
+
+ if (write_stats) {
+ fprintf(fstats, "%d;", num_bitflips);
+ }
+}
+
+
+static void simulate_MFplus_RNG(uint32_t test_cuid, uint64_t test_key, uint32_t *nt_enc, uint8_t *par_enc)
+{
+ struct Crypto1State sim_cs;
+
+ // init cryptostate with key:
+ for(int8_t i = 47; i > 0; i -= 2) {
+ sim_cs.odd = sim_cs.odd << 1 | BIT(test_key, (i - 1) ^ 7);
+ sim_cs.even = sim_cs.even << 1 | BIT(test_key, i ^ 7);
+ }
+
+ *par_enc = 0;
+ uint32_t nt = (rand() & 0xff) << 24 | (rand() & 0xff) << 16 | (rand() & 0xff) << 8 | (rand() & 0xff);
+ for (int8_t byte_pos = 3; byte_pos >= 0; byte_pos--) {
+ uint8_t nt_byte_dec = (nt >> (8*byte_pos)) & 0xff;
+ uint8_t nt_byte_enc = crypto1_byte(&sim_cs, nt_byte_dec ^ (test_cuid >> (8*byte_pos)), false) ^ nt_byte_dec; // encode the nonce byte
+ *nt_enc = (*nt_enc << 8) | nt_byte_enc;
+ uint8_t ks_par = filter(sim_cs.odd); // the keystream bit to encode/decode the parity bit
+ uint8_t nt_byte_par_enc = ks_par ^ oddparity8(nt_byte_dec); // determine the nt byte's parity and encode it
+ *par_enc = (*par_enc << 1) | nt_byte_par_enc;
+ }
+
+}
+
+
+static void simulate_acquire_nonces()
+{
+ clock_t time1 = clock();
+ bool filter_flip_checked = false;
+ uint32_t total_num_nonces = 0;
+ uint32_t next_fivehundred = 500;
+ uint32_t total_added_nonces = 0;
+
+ cuid = (rand() & 0xff) << 24 | (rand() & 0xff) << 16 | (rand() & 0xff) << 8 | (rand() & 0xff);
+ known_target_key = ((uint64_t)rand() & 0xfff) << 36 | ((uint64_t)rand() & 0xfff) << 24 | ((uint64_t)rand() & 0xfff) << 12 | ((uint64_t)rand() & 0xfff);
+
+ printf("Simulating nonce acquisition for target key %012"llx", cuid %08x ...\n", known_target_key, cuid);
+ fprintf(fstats, "%012"llx";%08x;", known_target_key, cuid);
+
+ do {
+ uint32_t nt_enc = 0;
+ uint8_t par_enc = 0;
+
+ simulate_MFplus_RNG(cuid, known_target_key, &nt_enc, &par_enc);
+ //printf("Simulated RNG: nt_enc1: %08x, nt_enc2: %08x, par_enc: %02x\n", nt_enc1, nt_enc2, par_enc);
+ total_added_nonces += add_nonce(nt_enc, par_enc);
+ total_num_nonces++;
+
+ 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;
+ printf("Acquired %5d nonces (%5d with distinct bytes 0 and 1). Number of bytes with probability for correctly guessed Sum(a8) > %1.1f%%: %d\n",
+ total_num_nonces,
+ total_added_nonces,
+ CONFIDENCE_THRESHOLD * 100.0,
+ num_good_first_bytes);
+ }
+ }
+
+ } while (num_good_first_bytes < GOOD_BYTES_REQUIRED);
+
+ 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*60.0*CLOCKS_PER_SEC/((float)clock()-time1));
+
+ fprintf(fstats, "%d;%d;%d;%1.2f;", total_num_nonces, total_added_nonces, num_good_first_bytes, CONFIDENCE_THRESHOLD);
+
+}
+
+
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;
}
-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]++;
-}
-
-
-static 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 ... 3/4
- 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)) {
{
for (uint16_t i = 0; i < 256; i++) {
if (nonces[i].BitFlip[odd_even] && i != best_first_bytes[0]) {
- uint8_t j = 0; // number of common bits
- uint8_t common_bits = best_first_bytes[0] ^ i;
+ 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) {
- 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, &statelist_bitflip, 0);
if (p != NULL) {
while ((state & mask) == (*p & mask) && (*p != 0xffffffff)) {
- if (remaining_bits_match(j, best_first_bytes[0], 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)) {
}
-#define INVALID_BIT (1<<30)
-#define SET_INVALID(pstate) (*(pstate) |= INVALID_BIT)
-#define IS_INVALID(state) (state & INVALID_BIT)
+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)) {
if (all_bit_flips_match((*p1 << 4) | *p2, odd_even)) {
- add_state(candidates, (*p1 << 4) | *p2, odd_even);
+ *add_p++ = (*p1 << 4) | *p2;
+ }
}
}
p2++;
}
}
- // set end of list marker
- uint32_t *p = candidates->states[odd_even];
- p += candidates->len[odd_even];
- *p = 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;
}
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>>22)/60);
+ (count>>23)/60);
+ if (write_stats) {
+ fprintf(fstats, "1\n");
+ }
crypto1_destroy(pcs);
return;
}
}
printf("Key NOT found!\n");
+ if (write_stats) {
+ fprintf(fstats, "0\n");
+ }
crypto1_destroy(pcs);
}
}
}
}
- printf("Number of possible keys with Sum(a0) = %d: %lld (2^%1.1f)\n", sum_a0, maximum_states, log(maximum_states)/log(2.0));
+ printf("Number of possible keys with Sum(a0) = %d: %"PRIu64" (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) {
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));
}
}
}
for (statelist_t *sl = candidates; sl != NULL; sl = sl->next) {
maximum_states += (uint64_t)sl->len[ODD_STATE] * sl->len[EVEN_STATE];
}
- printf("Number of remaining possible keys: %lld (2^%1.1f)\n", maximum_states, log(maximum_states)/log(2.0));
-
+ printf("Number of remaining possible keys: %"PRIu64" (2^%1.1f)\n", maximum_states, log(maximum_states)/log(2.0));
+ if (write_stats) {
+ if (maximum_states != 0) {
+ fprintf(fstats, "%1.1f;", log(maximum_states)/log(2.0));
+ } else {
+ fprintf(fstats, "%1.1f;", 0.0);
+ }
+ }
}
-static void Check_for_FilterFlipProperties(void)
+static void free_candidates_memory(statelist_t *sl)
{
- 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;
+ if (sl == NULL) {
+ return;
+ } else {
+ free_candidates_memory(sl->next);
+ free(sl);
}
-
- 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 void free_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++) {
+ free(sl_cache[i][j][k].sl);
+ }
}
- }
+ }
}
if (known_target_key != -1) {
PrintAndLog("Looking for known target key in remaining key space...");
TestIfKeyExists(known_target_key);
- return;
} else {
PrintAndLog("Brute Force phase is not implemented.");
- return;
}
-
}
-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)
+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, int tests)
{
+ // initialize Random number generator
+ time_t t;
+ srand((unsigned) time(&t));
+
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++) {
- nonces[i].num = 0;
- nonces[i].Sum = 0;
- nonces[i].Sum8_guess = 0;
- nonces[i].Sum8_prob = 0.0;
- nonces[i].updated = true;
- nonces[i].first = NULL;
- }
- first_byte_num = 0;
- first_byte_Sum = 0;
- num_good_first_bytes = 0;
-
init_partial_statelists();
init_BitFlip_statelist();
+ write_stats = false;
+ if (tests) {
+ // set the correct locale for the stats printing
+ setlocale(LC_ALL, "");
+ write_stats = true;
+ if ((fstats = fopen("hardnested_stats.txt","a")) == NULL) {
+ PrintAndLog("Could not create/open file hardnested_stats.txt");
+ return 3;
+ }
+ for (uint32_t i = 0; i < tests; i++) {
+ init_nonce_memory();
+ simulate_acquire_nonces();
+ Tests();
+ printf("Sum(a0) = %d\n", first_byte_Sum);
+ fprintf(fstats, "%d;", first_byte_Sum);
+ generate_candidates(first_byte_Sum, nonces[best_first_bytes[0]].Sum8_guess);
+ brute_force();
+ free_nonces_memory();
+ free_statelist_cache();
+ free_candidates_memory(candidates);
+ candidates = NULL;
+ }
+ fclose(fstats);
+ } else {
+ init_nonce_memory();
if (nonce_file_read) { // use pre-acquired data from file nonces.bin
if (read_nonce_file() != 0) {
return 3;
}
+ 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);
}
}
- Check_for_FilterFlipProperties();
-
Tests();
PrintAndLog("");
// 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);
brute_force();
+ free_nonces_memory();
+ free_statelist_cache();
+ free_candidates_memory(candidates);
+ candidates = NULL;
+ }
return 0;
}
projects / proxmark3-svn / blobdiff