X-Git-Url: http://cvs.zerfleddert.de/cgi-bin/gitweb.cgi/proxmark3-svn/blobdiff_plain/8ce3e4b4e937f2e3b2fda5b0d5d2c6bd9c6b3ebc..ddb748a973bdcb84c6a0ab21e5fcd2b964e5c2e5:/client/cmdhfmfhard.c diff --git a/client/cmdhfmfhard.c b/client/cmdhfmfhard.c index 6cd5a5b9..6a5c439d 100644 --- a/client/cmdhfmfhard.c +++ b/client/cmdhfmfhard.c @@ -24,12 +24,13 @@ #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 @@ -82,17 +83,19 @@ typedef struct noncelist { 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 { @@ -116,10 +119,10 @@ typedef struct { } 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) @@ -130,12 +133,12 @@ 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)) { @@ -165,7 +168,7 @@ static int add_nonce(uint32_t nonce_enc, uint8_t par_enc) 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 @@ -183,6 +186,7 @@ static uint16_t PartialSumProperty(uint32_t state, odd_even_t odd_even) 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) ; @@ -195,12 +199,12 @@ static uint16_t PartialSumProperty(uint32_t state, odd_even_t odd_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 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) @@ -262,19 +266,46 @@ static float sum_probability(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(); @@ -343,102 +374,176 @@ static void Tests() // 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; @@ -460,7 +565,7 @@ static uint16_t estimate_second_byte_sum(void) 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; } @@ -512,12 +617,36 @@ static int read_nonce_file(void) } -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; @@ -589,6 +718,10 @@ int static acquire_nonces(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_ 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; @@ -617,10 +750,10 @@ int static acquire_nonces(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_ 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; } @@ -628,7 +761,7 @@ int static acquire_nonces(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_ 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"); @@ -701,71 +834,66 @@ static void init_BitFlip_statelist(void) } -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 @@ -776,25 +904,13 @@ static bool all_other_first_bytes_match(uint32_t state, odd_even_t odd_even) { 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); @@ -807,7 +923,7 @@ static bool all_other_first_bytes_match(uint32_t state, odd_even_t odd_even) 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)) { @@ -848,32 +964,127 @@ static bool all_other_first_bytes_match(uint32_t state, odd_even_t odd_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; } @@ -906,22 +1117,39 @@ static void TestIfKeyExists(uint64_t key) 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); } @@ -932,7 +1160,7 @@ static void generate_candidates(uint16_t sum_a0, uint16_t sum_a8) 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) { @@ -942,6 +1170,8 @@ static void generate_candidates(uint16_t sum_a0, uint16_t sum_a8) } 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) { @@ -951,10 +1181,30 @@ static void generate_candidates(uint16_t sum_a0, uint16_t sum_a8) 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)); } } } @@ -969,37 +1219,28 @@ static void generate_candidates(uint16_t sum_a0, uint16_t sum_a8) } 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++) { @@ -1021,7 +1262,8 @@ int mfnestedhard(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_t trgBloc 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) { @@ -1029,7 +1271,6 @@ int mfnestedhard(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_t trgBloc } } - Check_for_FilterFlipProperties(); Tests(); @@ -1048,9 +1289,11 @@ int mfnestedhard(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_t trgBloc // 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; }