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proxmark3/client/cmdhfmfhard.c
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//-----------------------------------------------------------------------------
// 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 <stdio.h>
#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"
#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 0.95 // 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
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,
0.0290 };
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;
uint8_t BitFlip[2];
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;
static bool write_stats = false;
static FILE *fstats = NULL;
typedef enum {
EVEN_STATE = 0,
ODD_STATE = 1
} odd_even_t;
#define STATELIST_INDEX_WIDTH 16
#define STATELIST_INDEX_SIZE (1<<STATELIST_INDEX_WIDTH)
typedef struct {
uint32_t *states[2];
uint32_t len[2];
uint32_t *index[2][STATELIST_INDEX_SIZE];
} partial_indexed_statelist_t;
typedef struct {
uint32_t *states[2];
uint32_t len[2];
void* next;
} statelist_t;
static partial_indexed_statelist_t partial_statelist[17];
static partial_indexed_statelist_t statelist_bitflip;
static 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 += 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));
}
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 += 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
}
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;
for (uint16_t j = 0; j < 16; j++) {
uint32_t st = state;
uint16_t part_sum = 0;
if (odd_even == ODD_STATE) {
for (uint16_t i = 0; i < 5; i++) {
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) ;
part_sum ^= filter(st);
}
}
sum += part_sum;
}
return sum;
}
// 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)
{
// 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;
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);
}
}
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]);
// }
// #define NUM_STATISTICS 100000
// uint32_t statistics_odd[17];
// uint64_t statistics[257];
// 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 = PartialSumProperty(cs.even, EVEN_STATE);
// statistics_even[sum_property]++;
// sum_property = PartialSumProperty(cs.odd, ODD_STATE);
// 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[oddsum].len[ODD_STATE] * partial_statelist[evensum].len[EVEN_STATE] * (1<<8);
// num_states += (uint64_t)partial_statelist[oddsum].len[ODD_STATE] * partial_statelist[evensum].len[EVEN_STATE] * (1<<8);
// }
// }
// 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_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);
// 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 ", i, nonces[i].BitFlip[ODD_STATE]?'o':nonces[i].BitFlip[EVEN_STATE]?'e':' ');
if (i % 8 == 7) {
printf("\n");
}
}
printf("\nTests: Sorted First Bytes:\n");
for (uint16_t i = 0; i < 256; i++) {
uint8_t best_byte = best_first_bytes[i];
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)
{
// 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 < i) {
prob2 = nonces[best_first_bytes[++j]].Sum8_prob;
}
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 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;
}
}
sort_best_first_bytes();
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;
}
}
return num_good_nonces;
}
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;
}
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;
uint32_t next_fivehundred = 500;
uint32_t total_added_nonces = 0;
FILE *fnonces = NULL;
UsbCommand resp;
printf("Acquiring nonces...\n");
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);
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);
}
if (num_good_first_bytes >= GOOD_BYTES_REQUIRED) {
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 (%0.0f nonces/minute)",
total_num_nonces,
((float)clock()-time1)/CLOCKS_PER_SEC,
total_num_nonces*60.0*CLOCKS_PER_SEC/((float)clock()-time1));
return 0;
}
static int init_partial_statelists(void)
{
const uint32_t sizes_odd[17] = { 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");
for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
for (uint16_t i = 0; i <= 16; i+=2) {
partial_statelist[i].len[odd_even] = 0;
uint32_t num_of_states = odd_even == ODD_STATE ? sizes_odd[i] : sizes_even[i];
partial_statelist[i].states[odd_even] = malloc(sizeof(uint32_t) * num_of_states);
if (partial_statelist[i].states[odd_even] == NULL) {
PrintAndLog("Cannot allocate enough memory. Aborting");
return 4;
}
for (uint32_t j = 0; j < STATELIST_INDEX_SIZE; j++) {
partial_statelist[i].index[odd_even][j] = NULL;
}
}
}
printf("Generating partial statelists...\n");
for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
uint32_t index = -1;
uint32_t num_of_states = 1<<20;
for (uint32_t state = 0; state < num_of_states; state++) {
uint16_t sum_property = PartialSumProperty(state, odd_even);
uint32_t *p = partial_statelist[sum_property].states[odd_even];
p += partial_statelist[sum_property].len[odd_even];
*p = state;
partial_statelist[sum_property].len[odd_even]++;
uint32_t index_mask = (STATELIST_INDEX_SIZE-1) << (20-STATELIST_INDEX_WIDTH);
if ((state & index_mask) != index) {
index = state & index_mask;
}
if (partial_statelist[sum_property].index[odd_even][index >> (20-STATELIST_INDEX_WIDTH)] == NULL) {
partial_statelist[sum_property].index[odd_even][index >> (20-STATELIST_INDEX_WIDTH)] = p;
}
}
// add End Of List markers
for (uint16_t i = 0; i <= 16; i += 2) {
uint32_t *p = partial_statelist[i].states[odd_even];
p += partial_statelist[i].len[odd_even];
*p = 0xffffffff;
}
}
return 0;
}
static void init_BitFlip_statelist(void)
{
printf("Generating bitflip statelist...\n");
uint32_t *p = statelist_bitflip.states[0] = malloc(sizeof(uint32_t) * 1<<20);
uint32_t index = -1;
uint32_t index_mask = (STATELIST_INDEX_SIZE-1) << (20-STATELIST_INDEX_WIDTH);
for (uint32_t state = 0; state < (1 << 20); state++) {
if (filter(state) != filter(state^1)) {
if ((state & index_mask) != index) {
index = state & index_mask;
}
if (statelist_bitflip.index[0][index >> (20-STATELIST_INDEX_WIDTH)] == NULL) {
statelist_bitflip.index[0][index >> (20-STATELIST_INDEX_WIDTH)] = p;
}
*p++ = state;
}
}
// set len and add End Of List marker
statelist_bitflip.len[0] = p - statelist_bitflip.states[0];
*p = 0xffffffff;
statelist_bitflip.states[0] = realloc(statelist_bitflip.states[0], sizeof(uint32_t) * (statelist_bitflip.len[0] + 1));
}
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 < (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 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)
{
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;
}
} 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;
}
}
return true; // valid state
}
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;
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) {
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;
for (uint16_t r = 0; r <= 16 && !found_match; r += 2) {
for (uint16_t s = 0; s <= 16 && !found_match; s += 2) {
if (r*(16-s) + (16-r)*s == sum_a8) {
//printf("Checking byte 0x%02x for partial sum (%s) %d\n", best_first_bytes[i], odd_even==ODD_STATE?"odd":"even", odd_even==ODD_STATE?r:s);
uint16_t part_sum_a8 = (odd_even == ODD_STATE) ? r : s;
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, 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 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)) {
if (all_bit_flips_match((*p1 << 4) | *p2, odd_even)) {
*add_p++ = (*p1 << 4) | *p2;
}
}
}
p2++;
}
}
}
// 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;
}
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_bytes[0], true);
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);
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 & 0x00ffffff) == state_odd) {
found_odd = true;
break;
}
p_odd++;
}
while (*p_even != 0xffffffff) {
if ((*p_even & 0x00ffffff) == state_even) {
found_even = true;
}
p_even++;
}
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);
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);
}
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
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[sum_odd].len[ODD_STATE] * partial_statelist[sum_even].len[EVEN_STATE] * (1<<8);
}
}
}
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) {
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[p].len[ODD_STATE], partial_statelist[q].len[EVEN_STATE]);
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);
// 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);
if(current_candidates->len[ODD_STATE]) {
add_matching_states(current_candidates, q, s, EVEN_STATE);
} 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));
}
}
}
}
}
}
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];
}
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 free_candidates_memory(statelist_t *sl)
{
if (sl == NULL) {
return;
} else {
free_candidates_memory(sl->next);
free(sl);
}
}
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);
}
}
}
}
static void brute_force(void)
{
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, 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;
}
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);
if (is_OK != 0) {
return is_OK;
}
}
Tests();
PrintAndLog("");
PrintAndLog("Sum(a0) = %d", first_byte_Sum);
// PrintAndLog("Best 10 first bytes: %02x, %02x, %02x, %02x, %02x, %02x, %02x, %02x, %02x, %02x",
// best_first_bytes[0],
// best_first_bytes[1],
// best_first_bytes[2],
// best_first_bytes[3],
// best_first_bytes[4],
// best_first_bytes[5],
// best_first_bytes[6],
// best_first_bytes[7],
// best_first_bytes[8],
// 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;
}
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