Update cmdhf14a.c

[proxmark3-svn] / client / cmdhfmfhard.c

//-----------------------------------------------------------------------------
// Copyright (C) 2015, 2016 by 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 "cmdhfmfhard.h"

#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
#include <string.h>
#include <time.h>
#include <pthread.h>
#include <locale.h>
#include <math.h>
#include "proxmark3.h"
#include "cmdmain.h"
#include "ui.h"
#include "util.h"
#include "util_posix.h"
#include "crapto1/crapto1.h"
#include "parity.h"
#include "hardnested/hardnested_bruteforce.h"
#include "hardnested/hardnested_bitarray_core.h"

#define NUM_CHECK_BITFLIPS_THREADS		(num_CPUs())
#define NUM_REDUCTION_WORKING_THREADS	(num_CPUs())

#define IGNORE_BITFLIP_THRESHOLD		0.99	// ignore bitflip arrays which have nearly only valid states

#define STATE_FILES_DIRECTORY			"hardnested/tables/"
#define STATE_FILE_TEMPLATE				"bitflip_%d_%03" PRIx16 "_states.bin"

#define DEBUG_KEY_ELIMINATION
// #define DEBUG_REDUCTION

static uint16_t sums[NUM_SUMS] = {0, 32, 56, 64, 80, 96, 104, 112, 120, 128, 136, 144, 152, 160, 176, 192, 200, 224, 256}; // possible sum property values

#define NUM_PART_SUMS 					9		// number of possible partial sum property values

typedef enum {
	EVEN_STATE = 0,
	ODD_STATE = 1
} odd_even_t;

static uint32_t num_acquired_nonces = 0;
static uint64_t start_time = 0;
static uint16_t effective_bitflip[2][0x400];
static uint16_t num_effective_bitflips[2] = {0, 0};
static uint16_t all_effective_bitflip[0x400];
static uint16_t num_all_effective_bitflips = 0;
static uint16_t num_1st_byte_effective_bitflips = 0;
#define CHECK_1ST_BYTES			0x01
#define CHECK_2ND_BYTES			0x02
static uint8_t hardnested_stage = CHECK_1ST_BYTES;
static uint64_t known_target_key;
static uint32_t test_state[2] = {0,0};
static float brute_force_per_second;


static void get_SIMD_instruction_set(char* instruction_set) {
	#if !defined(__APPLE__) || (defined(__APPLE__) && (__clang_major__ > 8))
		#if (__GNUC__ >= 5) && (__GNUC__ > 5 || __GNUC_MINOR__ > 2)
	if (__builtin_cpu_supports("avx512f")) strcpy(instruction_set, "AVX512F");
	else if (__builtin_cpu_supports("avx2")) strcpy(instruction_set, "AVX2");
		#else 
	if (__builtin_cpu_supports("avx2")) strcpy(instruction_set, "AVX2");
		#endif
	else if (__builtin_cpu_supports("avx")) strcpy(instruction_set, "AVX");
	else if (__builtin_cpu_supports("sse2")) strcpy(instruction_set, "SSE2");
	else if (__builtin_cpu_supports("mmx")) strcpy(instruction_set, "MMX");
	else 
	#endif
		strcpy(instruction_set, "unsupported");
}


static void print_progress_header(void) {
	char progress_text[80];
	char instr_set[12] = "";
	get_SIMD_instruction_set(instr_set);
	sprintf(progress_text, "Start using %d threads and %s SIMD core", num_CPUs(), instr_set);
	PrintAndLog("\n\n");
	PrintAndLog(" time    | #nonces | Activity                                                | expected to brute force");
	PrintAndLog("         |         |                                                         | #states         | time ");
	PrintAndLog("------------------------------------------------------------------------------------------------------");
	PrintAndLog("       0 |       0 | %-55s |                 |", progress_text);
}


void hardnested_print_progress(uint32_t nonces, char *activity, float brute_force, uint64_t min_diff_print_time) {
	static uint64_t last_print_time = 0;
	if (msclock() - last_print_time > min_diff_print_time) {
		last_print_time = msclock();
		uint64_t total_time = msclock() - start_time;
		float brute_force_time = brute_force / brute_force_per_second;
		char brute_force_time_string[20];
		if (brute_force_time < 90) {
			sprintf(brute_force_time_string, "%2.0fs", brute_force_time);
		} else if (brute_force_time < 60 * 90) {
			sprintf(brute_force_time_string, "%2.0fmin", brute_force_time/60);
		} else if (brute_force_time < 60 * 60 * 36) {
			sprintf(brute_force_time_string, "%2.0fh", brute_force_time/(60*60));
		} else {
			sprintf(brute_force_time_string, "%2.0fd", brute_force_time/(60*60*24));
		}
		PrintAndLog(" %7.0f | %7d | %-55s | %15.0f | %5s", (float)total_time/1000.0, nonces, activity, brute_force, brute_force_time_string);
	}
}


//////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// bitarray functions

static inline void clear_bitarray24(uint32_t *bitarray)
{
	memset(bitarray, 0x00, sizeof(uint32_t) * (1<<19));
}


static inline void set_bitarray24(uint32_t *bitarray)
{
	memset(bitarray, 0xff, sizeof(uint32_t) * (1<<19));
}


static inline void set_bit24(uint32_t *bitarray, uint32_t index)
{
	bitarray[index>>5] |= 0x80000000>>(index&0x0000001f);
}


static inline void clear_bit24(uint32_t *bitarray, uint32_t index)
{
	bitarray[index>>5] &= ~(0x80000000>>(index&0x0000001f));
}


static inline uint32_t test_bit24(uint32_t *bitarray, uint32_t index)
{
	return 	bitarray[index>>5] & (0x80000000>>(index&0x0000001f));
}


static inline uint32_t next_state(uint32_t *bitarray, uint32_t state)
{
	if (++state == 1<<24) return 1<<24;
	uint32_t index = state >> 5;
	uint_fast8_t bit = state & 0x1f;
	uint32_t line = bitarray[index] << bit;
	while (bit <= 0x1f) {
		if (line & 0x80000000) return state;
		state++;
		bit++;
		line <<= 1;
	}
	index++;
	while (bitarray[index] == 0x00000000 && state < 1<<24) {
		index++;
		state += 0x20;
	}
	if (state >= 1<<24) return 1<<24;
#if defined __GNUC__
	return state + __builtin_clz(bitarray[index]);
#else
	bit = 0x00;
	line = bitarray[index];
	while (bit <= 0x1f) {
		if (line & 0x80000000) return state;
		state++;
		bit++;
		line <<= 1;
	}
	return 1<<24;
#endif
}


static inline uint32_t next_not_state(uint32_t *bitarray, uint32_t state)
{
	if (++state == 1<<24) return 1<<24;
	uint32_t index = state >> 5;
	uint_fast8_t bit = state & 0x1f;
	uint32_t line = bitarray[index] << bit;
	while (bit <= 0x1f) {
		if ((line & 0x80000000) == 0) return state;
		state++;
		bit++;
		line <<= 1;
	}
	index++;
	while (bitarray[index] == 0xffffffff && state < 1<<24) {
		index++;
		state += 0x20;
	}
	if (state >= 1<<24) return 1<<24;
#if defined __GNUC__
	return state + __builtin_clz(~bitarray[index]);
#else
	bit = 0x00;
	line = bitarray[index];
	while (bit <= 0x1f) {
		if ((line & 0x80000000) == 0) return state;
		state++;
		bit++;
		line <<= 1;
	}
	return 1<<24;
#endif
}




#define BITFLIP_2ND_BYTE				0x0200


//////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// bitflip property bitarrays

static uint32_t *bitflip_bitarrays[2][0x400];
static uint32_t count_bitflip_bitarrays[2][0x400];

static int compare_count_bitflip_bitarrays(const void *b1, const void *b2)
{
	uint64_t count1 = (uint64_t)count_bitflip_bitarrays[ODD_STATE][*(uint16_t *)b1] * count_bitflip_bitarrays[EVEN_STATE][*(uint16_t *)b1];
	uint64_t count2 = (uint64_t)count_bitflip_bitarrays[ODD_STATE][*(uint16_t *)b2] * count_bitflip_bitarrays[EVEN_STATE][*(uint16_t *)b2];
	return (count1 > count2) - (count2 > count1);
}


static void init_bitflip_bitarrays(void)
{
#if defined (DEBUG_REDUCTION)
	uint8_t line = 0;
#endif	

	char state_files_path[strlen(get_my_executable_directory()) + strlen(STATE_FILES_DIRECTORY) + strlen(STATE_FILE_TEMPLATE) + 1];
	char state_file_name[strlen(STATE_FILE_TEMPLATE)+1];
	
	for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
		num_effective_bitflips[odd_even] = 0;
		for (uint16_t bitflip = 0x001; bitflip < 0x400; bitflip++) {
			bitflip_bitarrays[odd_even][bitflip] = NULL;
			count_bitflip_bitarrays[odd_even][bitflip] = 1<<24;
			sprintf(state_file_name, STATE_FILE_TEMPLATE, odd_even, bitflip);
			strcpy(state_files_path, get_my_executable_directory());
			strcat(state_files_path, STATE_FILES_DIRECTORY);
			strcat(state_files_path, state_file_name);
			FILE *statesfile = fopen(state_files_path, "rb");
			if (statesfile == NULL) {
				continue;
			} else {
				uint32_t *bitset = (uint32_t *)malloc_bitarray(sizeof(uint32_t) * (1<<19));
				if (bitset == NULL) {
					printf("Out of memory error in init_bitflip_statelists(). Aborting...\n");
					fclose(statesfile);
					exit(4);
				}
				size_t bytesread = fread(bitset, 1, sizeof(uint32_t) * (1<<19), statesfile);
				if (bytesread != sizeof(uint32_t) * (1<<19)) {
					printf("File read error with %s. Aborting...", state_file_name);
					fclose(statesfile);
					free_bitarray(bitset);
					exit(5);
				}
				fclose(statesfile);
				uint32_t count = count_states(bitset);
				if ((float)count/(1<<24) < IGNORE_BITFLIP_THRESHOLD) {
					effective_bitflip[odd_even][num_effective_bitflips[odd_even]++] = bitflip;
					bitflip_bitarrays[odd_even][bitflip] = bitset;
					count_bitflip_bitarrays[odd_even][bitflip] = count;
#if defined (DEBUG_REDUCTION)
					printf("(%03" PRIx16 " %s:%5.1f%%) ", bitflip, odd_even?"odd ":"even", (float)count/(1<<24)*100.0);
					line++;
					if (line == 8) {
						printf("\n");
						line = 0;
					}
#endif
				} else {
					free_bitarray(bitset);
				}
			}
		}
		effective_bitflip[odd_even][num_effective_bitflips[odd_even]] = 0x400;	// EndOfList marker
	}

	uint16_t i = 0;
	uint16_t j = 0;
	num_all_effective_bitflips = 0;
	num_1st_byte_effective_bitflips = 0;
	while (i < num_effective_bitflips[EVEN_STATE] || j < num_effective_bitflips[ODD_STATE]) {
		if (effective_bitflip[EVEN_STATE][i] < effective_bitflip[ODD_STATE][j]) {
			all_effective_bitflip[num_all_effective_bitflips++] = effective_bitflip[EVEN_STATE][i];
			i++;
		} else if (effective_bitflip[EVEN_STATE][i] > effective_bitflip[ODD_STATE][j]) {
			all_effective_bitflip[num_all_effective_bitflips++] = effective_bitflip[ODD_STATE][j];
			j++;
		} else {
			all_effective_bitflip[num_all_effective_bitflips++] = effective_bitflip[EVEN_STATE][i];
			i++; j++;
		}
		if (!(all_effective_bitflip[num_all_effective_bitflips-1] & BITFLIP_2ND_BYTE)) {
			num_1st_byte_effective_bitflips = num_all_effective_bitflips;
		}
	}
	qsort(all_effective_bitflip, num_1st_byte_effective_bitflips, sizeof(uint16_t), compare_count_bitflip_bitarrays);
#if defined (DEBUG_REDUCTION)
	printf("\n1st byte effective bitflips (%d): \n", num_1st_byte_effective_bitflips);
	for(uint16_t i = 0; i < num_1st_byte_effective_bitflips; i++) {
		printf("%03x ",  all_effective_bitflip[i]);
	}
#endif	
	qsort(all_effective_bitflip+num_1st_byte_effective_bitflips, num_all_effective_bitflips - num_1st_byte_effective_bitflips, sizeof(uint16_t), compare_count_bitflip_bitarrays);
#if defined (DEBUG_REDUCTION)
	printf("\n2nd byte effective bitflips (%d): \n", num_all_effective_bitflips - num_1st_byte_effective_bitflips);
	for(uint16_t i = num_1st_byte_effective_bitflips; i < num_all_effective_bitflips; i++) {
		printf("%03x ",  all_effective_bitflip[i]);
	}
#endif	
	char progress_text[80];
	sprintf(progress_text, "Using %d precalculated bitflip state tables", num_all_effective_bitflips);
	hardnested_print_progress(0, progress_text, (float)(1LL<<47), 0);
}


static void	free_bitflip_bitarrays(void)
{
	for (int16_t bitflip = 0x3ff; bitflip > 0x000; bitflip--) {
		free_bitarray(bitflip_bitarrays[ODD_STATE][bitflip]);
	}
	for (int16_t bitflip = 0x3ff; bitflip > 0x000; bitflip--) {
		free_bitarray(bitflip_bitarrays[EVEN_STATE][bitflip]);
	}
}


//////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// sum property bitarrays

static uint32_t *part_sum_a0_bitarrays[2][NUM_PART_SUMS];
static uint32_t *part_sum_a8_bitarrays[2][NUM_PART_SUMS];
static uint32_t *sum_a0_bitarrays[2][NUM_SUMS];	

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 void init_part_sum_bitarrays(void)
{
	for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
		for (uint16_t part_sum_a0 = 0; part_sum_a0 < NUM_PART_SUMS; part_sum_a0++) {
			part_sum_a0_bitarrays[odd_even][part_sum_a0] = (uint32_t *)malloc_bitarray(sizeof(uint32_t) * (1<<19));
			if (part_sum_a0_bitarrays[odd_even][part_sum_a0] == NULL) {
				printf("Out of memory error in init_part_suma0_statelists(). Aborting...\n");
				exit(4);
			}
			clear_bitarray24(part_sum_a0_bitarrays[odd_even][part_sum_a0]);
		}
	}
	for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
		//printf("(%d, %" PRIu16 ")...", odd_even, part_sum_a0);			
		for (uint32_t state = 0; state < (1<<20); state++) {
			uint16_t part_sum_a0 = PartialSumProperty(state, odd_even) / 2;
			for (uint16_t low_bits = 0; low_bits < 1<<4; low_bits++) {
				set_bit24(part_sum_a0_bitarrays[odd_even][part_sum_a0], state<<4 | low_bits);
			}
		}
	}

	for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
		for (uint16_t part_sum_a8 = 0; part_sum_a8 < NUM_PART_SUMS; part_sum_a8++) {
			part_sum_a8_bitarrays[odd_even][part_sum_a8] = (uint32_t *)malloc_bitarray(sizeof(uint32_t) * (1<<19));
			if (part_sum_a8_bitarrays[odd_even][part_sum_a8] == NULL) {
				printf("Out of memory error in init_part_suma8_statelists(). Aborting...\n");
				exit(4);
			}
			clear_bitarray24(part_sum_a8_bitarrays[odd_even][part_sum_a8]);
		}
	}
	for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
		//printf("(%d, %" PRIu16 ")...", odd_even, part_sum_a8); 
		for (uint32_t state = 0; state < (1<<20); state++) {
			uint16_t part_sum_a8 = PartialSumProperty(state, odd_even) / 2;
			for (uint16_t high_bits = 0; high_bits < 1<<4; high_bits++) {
				set_bit24(part_sum_a8_bitarrays[odd_even][part_sum_a8], state | high_bits<<20);
			}
		}
	}
}


static void free_part_sum_bitarrays(void) 
{
	for (int16_t part_sum_a8 = (NUM_PART_SUMS-1); part_sum_a8 >= 0; part_sum_a8--) {
		free_bitarray(part_sum_a8_bitarrays[ODD_STATE][part_sum_a8]);
	}
	for (int16_t part_sum_a8 = (NUM_PART_SUMS-1); part_sum_a8 >= 0; part_sum_a8--) {
		free_bitarray(part_sum_a8_bitarrays[EVEN_STATE][part_sum_a8]);
	}
	for (int16_t part_sum_a0 = (NUM_PART_SUMS-1); part_sum_a0 >= 0; part_sum_a0--) {
		free_bitarray(part_sum_a0_bitarrays[ODD_STATE][part_sum_a0]);
	}
	for (int16_t part_sum_a0 = (NUM_PART_SUMS-1); part_sum_a0 >= 0; part_sum_a0--) {
		free_bitarray(part_sum_a0_bitarrays[EVEN_STATE][part_sum_a0]);
	}
}


static void init_sum_bitarrays(void)
{
	for (uint16_t sum_a0 = 0; sum_a0 < NUM_SUMS; sum_a0++) {
		for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
			sum_a0_bitarrays[odd_even][sum_a0] = (uint32_t *)malloc_bitarray(sizeof(uint32_t) * (1<<19));
			if (sum_a0_bitarrays[odd_even][sum_a0] == NULL) {
				printf("Out of memory error in init_sum_bitarrays(). Aborting...\n");
				exit(4);
			}
			clear_bitarray24(sum_a0_bitarrays[odd_even][sum_a0]);
		}
	}
	for (uint8_t p = 0; p < NUM_PART_SUMS; p++) {
		for (uint8_t q = 0; q < NUM_PART_SUMS; q++) {
			uint16_t sum_a0 = 2*p*(16-2*q) + (16-2*p)*2*q;
			uint16_t sum_a0_idx = 0;
			while (sums[sum_a0_idx] != sum_a0) sum_a0_idx++;
			bitarray_OR(sum_a0_bitarrays[EVEN_STATE][sum_a0_idx], part_sum_a0_bitarrays[EVEN_STATE][q]);
			bitarray_OR(sum_a0_bitarrays[ODD_STATE][sum_a0_idx], part_sum_a0_bitarrays[ODD_STATE][p]);
		}
	}
	// for (uint16_t sum_a0 = 0; sum_a0 < NUM_SUMS; sum_a0++) {
		// for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
			// uint32_t count = count_states(sum_a0_bitarrays[odd_even][sum_a0]);
			// printf("sum_a0_bitarray[%s][%d] has %d states (%5.2f%%)\n", odd_even==EVEN_STATE?"even":"odd ", sums[sum_a0], count, (float)count/(1<<24)*100.0);
		// }
	// }
}


static void free_sum_bitarrays(void)
{
	for (int8_t sum_a0 = NUM_SUMS-1; sum_a0 >= 0; sum_a0--) {
		free_bitarray(sum_a0_bitarrays[ODD_STATE][sum_a0]);
		free_bitarray(sum_a0_bitarrays[EVEN_STATE][sum_a0]);
	}
}


#ifdef DEBUG_KEY_ELIMINATION
char failstr[250] = "";
#endif

static const float p_K0[NUM_SUMS] = {		// the probability that a random nonce has a Sum Property K 
	0.0290,	0.0083,	0.0006,	0.0339,	0.0048,	0.0934,	0.0119,	0.0489,	0.0602,	0.4180,	0.0602,	0.0489, 0.0119,	0.0934,	0.0048,	0.0339,	0.0006,	0.0083,	0.0290 
	};

static float my_p_K[NUM_SUMS]; 

static const float *p_K;
	
static uint32_t cuid;
static noncelist_t nonces[256];
static uint8_t best_first_bytes[256];
static uint64_t maximum_states = 0;
static uint8_t best_first_byte_smallest_bitarray = 0;
static uint16_t first_byte_Sum = 0;
static uint16_t first_byte_num = 0;
static bool write_stats = false;
static FILE *fstats = NULL;
static uint32_t *all_bitflips_bitarray[2];
static uint32_t num_all_bitflips_bitarray[2];
static bool all_bitflips_bitarray_dirty[2];
static uint64_t last_sample_clock = 0;
static uint64_t sample_period = 0;
static uint64_t num_keys_tested = 0;
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));
	}

	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].sum_a8_guess_dirty = 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].first = NULL;
		for (uint16_t j = 0; j < NUM_SUMS; j++) {
			nonces[i].sum_a8_guess[j].sum_a8_idx = j;
			nonces[i].sum_a8_guess[j].prob = 0.0;
		}
		nonces[i].sum_a8_guess_dirty = false;
		for (uint16_t bitflip = 0x000; bitflip < 0x400; bitflip++) {
			nonces[i].BitFlips[bitflip] = 0;
		}
		nonces[i].states_bitarray[EVEN_STATE] = (uint32_t *)malloc_bitarray(sizeof(uint32_t) * (1<<19));
		if (nonces[i].states_bitarray[EVEN_STATE] == NULL) {
			printf("Out of memory error in init_nonce_memory(). Aborting...\n");
			exit(4);
		}
		set_bitarray24(nonces[i].states_bitarray[EVEN_STATE]);
		nonces[i].num_states_bitarray[EVEN_STATE] = 1 << 24;
		nonces[i].states_bitarray[ODD_STATE] = (uint32_t *)malloc_bitarray(sizeof(uint32_t) * (1<<19));
		if (nonces[i].states_bitarray[ODD_STATE] == NULL) {
			printf("Out of memory error in init_nonce_memory(). Aborting...\n");
			exit(4);
		}
		set_bitarray24(nonces[i].states_bitarray[ODD_STATE]);
		nonces[i].num_states_bitarray[ODD_STATE] = 1 << 24;
		nonces[i].all_bitflips_dirty[EVEN_STATE] = false;
		nonces[i].all_bitflips_dirty[ODD_STATE] = false;
	}
	first_byte_num = 0;
	first_byte_Sum = 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);
	}
	for (int i = 255; i >= 0; i--) {
		free_bitarray(nonces[i].states_bitarray[ODD_STATE]);
		free_bitarray(nonces[i].states_bitarray[EVEN_STATE]);
	}
}


// static double p_hypergeometric_cache[257][NUM_SUMS][257];

// #define CACHE_INVALID -1.0
// static void init_p_hypergeometric_cache(void)
// {
	// for (uint16_t n = 0; n <= 256; n++) {
		// for (uint16_t i_K = 0; i_K < NUM_SUMS; i_K++) {
			// for (uint16_t k = 0; k <= 256; k++) {
				// p_hypergeometric_cache[n][i_K][k] = CACHE_INVALID;
			// }
		// }
	// }
// }


static double p_hypergeometric(uint16_t i_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)

	
	uint16_t const N = 256;
	uint16_t K = sums[i_K];

	// if (p_hypergeometric_cache[n][i_K][k] != CACHE_INVALID) {
		// return p_hypergeometric_cache[n][i_K][k];
	// }
	
	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);
		}
		// p_hypergeometric_cache[n][i_K][k] = exp(log_result);
		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);
			}
			// p_hypergeometric_cache[n][i_K][k] = exp(log_result);
			return exp(log_result);
		} else { 			// recursion
			return (p_hypergeometric(i_K, n, k-1) * (K-k+1) * (n-k+1) / (k * (N-K-n+k)));
		}
	}
}
	
	
static float sum_probability(uint16_t i_K, uint16_t n, uint16_t k)
{
	if (k > sums[i_K]) return 0.0;

	double p_T_is_k_when_S_is_K = p_hypergeometric(i_K, n, k);
	double p_S_is_K = p_K[i_K];
	double p_T_is_k = 0;
	for (uint16_t i = 0; i < NUM_SUMS; i++) {
		p_T_is_k += p_K[i] * p_hypergeometric(i, n, k);
	}
	return(p_T_is_k_when_S_is_K * p_S_is_K / p_T_is_k);
}


static uint32_t part_sum_count[2][NUM_PART_SUMS][NUM_PART_SUMS];

static void init_allbitflips_array(void)
{
	for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
		uint32_t *bitset = all_bitflips_bitarray[odd_even] = (uint32_t *)malloc_bitarray(sizeof(uint32_t) * (1<<19));
		if (bitset == NULL) {
			printf("Out of memory in init_allbitflips_array(). Aborting...");
			exit(4);
		}
		set_bitarray24(bitset);
		all_bitflips_bitarray_dirty[odd_even] = false;
		num_all_bitflips_bitarray[odd_even] = 1<<24;
	}
}


static void update_allbitflips_array(void)
{	
	if (hardnested_stage & CHECK_2ND_BYTES) {
		for (uint16_t i = 0; i < 256; i++) {
			for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
				if (nonces[i].all_bitflips_dirty[odd_even]) {
					uint32_t old_count = num_all_bitflips_bitarray[odd_even];
					num_all_bitflips_bitarray[odd_even] = count_bitarray_low20_AND(all_bitflips_bitarray[odd_even], nonces[i].states_bitarray[odd_even]);
					nonces[i].all_bitflips_dirty[odd_even] = false;
					if (num_all_bitflips_bitarray[odd_even] != old_count) {
						all_bitflips_bitarray_dirty[odd_even] = true;
					}
				}
			}
		}
	}
}

	
static uint32_t estimated_num_states_part_sum_coarse(uint16_t part_sum_a0_idx, uint16_t part_sum_a8_idx, odd_even_t odd_even) 
{
	return part_sum_count[odd_even][part_sum_a0_idx][part_sum_a8_idx];
}


static uint32_t estimated_num_states_part_sum(uint8_t first_byte, uint16_t part_sum_a0_idx, uint16_t part_sum_a8_idx, odd_even_t odd_even) 
{
	if (odd_even == ODD_STATE) {
		return count_bitarray_AND3(part_sum_a0_bitarrays[odd_even][part_sum_a0_idx], 
		                           part_sum_a8_bitarrays[odd_even][part_sum_a8_idx], 
			                       nonces[first_byte].states_bitarray[odd_even]);
	} else {
		return count_bitarray_AND4(part_sum_a0_bitarrays[odd_even][part_sum_a0_idx], 
		                           part_sum_a8_bitarrays[odd_even][part_sum_a8_idx], 
			                       nonces[first_byte].states_bitarray[odd_even],
		                           nonces[first_byte^0x80].states_bitarray[odd_even]);
	}

	// estimate reduction by all_bitflips_match()
	// if (odd_even) {
		// float p_bitflip = (float)nonces[first_byte ^ 0x80].num_states_bitarray[ODD_STATE] / num_all_bitflips_bitarray[ODD_STATE];
		// return (float)count * p_bitflip;		//(p_bitflip - 0.25*p_bitflip*p_bitflip);
	// } else {
		// return count;
	// }
}


static uint64_t estimated_num_states(uint8_t first_byte, uint16_t sum_a0, uint16_t sum_a8)
{
	uint64_t num_states = 0;
	for (uint8_t p = 0; p < NUM_PART_SUMS; p++) {
		for (uint8_t q = 0; q < NUM_PART_SUMS; q++) {
			if (2*p*(16-2*q) + (16-2*p)*2*q == sum_a0) {
				for (uint8_t r = 0; r < NUM_PART_SUMS; r++) {
					for (uint8_t s = 0; s < NUM_PART_SUMS; s++) {
						if (2*r*(16-2*s) + (16-2*r)*2*s == sum_a8) {
							num_states += (uint64_t)estimated_num_states_part_sum(first_byte, p, r, ODD_STATE) 
										* estimated_num_states_part_sum(first_byte, q, s, EVEN_STATE);
						}
					}
				}
			}
		}
	}
	return num_states;
}


static uint64_t estimated_num_states_coarse(uint16_t sum_a0, uint16_t sum_a8)
{
	uint64_t num_states = 0;
	for (uint8_t p = 0; p < NUM_PART_SUMS; p++) {
		for (uint8_t q = 0; q < NUM_PART_SUMS; q++) {
			if (2*p*(16-2*q) + (16-2*p)*2*q == sum_a0) {
				for (uint8_t r = 0; r < NUM_PART_SUMS; r++) {
					for (uint8_t s = 0; s < NUM_PART_SUMS; s++) {
						if (2*r*(16-2*s) + (16-2*r)*2*s == sum_a8) {
							num_states += (uint64_t)estimated_num_states_part_sum_coarse(p, r, ODD_STATE) 
										* estimated_num_states_part_sum_coarse(q, s, EVEN_STATE);
						}
					}
				}
			}
		}
	}
	return num_states;
}


static void update_p_K(void)
{
	if (hardnested_stage & CHECK_2ND_BYTES) {
		uint64_t total_count = 0;
		uint16_t sum_a0 = sums[first_byte_Sum];
		for (uint8_t sum_a8_idx = 0; sum_a8_idx < NUM_SUMS; sum_a8_idx++) {
			uint16_t sum_a8 = sums[sum_a8_idx];
			total_count += estimated_num_states_coarse(sum_a0, sum_a8);
		}
		for (uint8_t sum_a8_idx = 0; sum_a8_idx < NUM_SUMS; sum_a8_idx++) {
			uint16_t sum_a8 = sums[sum_a8_idx];
			my_p_K[sum_a8_idx] = (float)estimated_num_states_coarse(sum_a0, sum_a8) / total_count;
		}
		// printf("my_p_K = [");
		// for (uint8_t sum_a8_idx = 0; sum_a8_idx < NUM_SUMS; sum_a8_idx++) {
			// printf("%7.4f ", my_p_K[sum_a8_idx]);
		// }
		p_K = my_p_K;
	}
}


static void update_sum_bitarrays(odd_even_t odd_even)
{
	if (all_bitflips_bitarray_dirty[odd_even]) {
		for (uint8_t part_sum = 0; part_sum < NUM_PART_SUMS; part_sum++) {
			bitarray_AND(part_sum_a0_bitarrays[odd_even][part_sum], all_bitflips_bitarray[odd_even]);
			bitarray_AND(part_sum_a8_bitarrays[odd_even][part_sum], all_bitflips_bitarray[odd_even]);
		}
		for (uint16_t i = 0; i < 256; i++) {
			nonces[i].num_states_bitarray[odd_even] = count_bitarray_AND(nonces[i].states_bitarray[odd_even], all_bitflips_bitarray[odd_even]);
		}
		for (uint8_t part_sum_a0 = 0; part_sum_a0 < NUM_PART_SUMS; part_sum_a0++) {
			for (uint8_t part_sum_a8 = 0; part_sum_a8 < NUM_PART_SUMS; part_sum_a8++) {
				part_sum_count[odd_even][part_sum_a0][part_sum_a8] 
				    += count_bitarray_AND2(part_sum_a0_bitarrays[odd_even][part_sum_a0], part_sum_a8_bitarrays[odd_even][part_sum_a8]);
			}
		}
		all_bitflips_bitarray_dirty[odd_even] = false;
	}
}


static int compare_expected_num_brute_force(const void *b1, const void *b2)
{
	uint8_t index1 = *(uint8_t *)b1;
	uint8_t index2 = *(uint8_t *)b2;
	float score1 = nonces[index1].expected_num_brute_force;
	float score2 = nonces[index2].expected_num_brute_force;
	return (score1 > score2) - (score1 < score2);
}


static int compare_sum_a8_guess(const void *b1, const void *b2)
{
	float prob1 = ((guess_sum_a8_t *)b1)->prob;
	float prob2 = ((guess_sum_a8_t *)b2)->prob;
	return (prob1 < prob2) - (prob1 > prob2);

}


static float check_smallest_bitflip_bitarrays(void) 
{
	uint32_t num_odd, num_even;
	uint64_t smallest = 1LL << 48;
	// initialize best_first_bytes, do a rough estimation on remaining states
	for (uint16_t i = 0; i < 256; i++) {
		num_odd = nonces[i].num_states_bitarray[ODD_STATE];
		num_even = nonces[i].num_states_bitarray[EVEN_STATE];	// * (float)nonces[i^0x80].num_states_bitarray[EVEN_STATE] / num_all_bitflips_bitarray[EVEN_STATE];
		if ((uint64_t)num_odd * num_even < smallest) {
			smallest = (uint64_t)num_odd * num_even;
			best_first_byte_smallest_bitarray = i;
		}
	}

#if defined (DEBUG_REDUCTION)
	num_odd = nonces[best_first_byte_smallest_bitarray].num_states_bitarray[ODD_STATE];
	num_even = nonces[best_first_byte_smallest_bitarray].num_states_bitarray[EVEN_STATE];	// * (float)nonces[best_first_byte_smallest_bitarray^0x80].num_states_bitarray[EVEN_STATE] / num_all_bitflips_bitarray[EVEN_STATE];
	printf("0x%02x: %8d * %8d = %12" PRIu64 " (2^%1.1f)\n",	best_first_byte_smallest_bitarray, num_odd, num_even, (uint64_t)num_odd * num_even, log((uint64_t)num_odd * num_even)/log(2.0));
#endif
	return (float)smallest/2.0;
}


static void update_expected_brute_force(uint8_t best_byte) {

	float total_prob = 0.0;
	for (uint8_t i = 0; i < NUM_SUMS; i++) {
		total_prob += nonces[best_byte].sum_a8_guess[i].prob;
	}
	// linear adjust probabilities to result in total_prob = 1.0;
	for (uint8_t i = 0; i < NUM_SUMS; i++) {
		nonces[best_byte].sum_a8_guess[i].prob /= total_prob;
	}
	float prob_all_failed = 1.0;
	nonces[best_byte].expected_num_brute_force = 0.0;
	for (uint8_t i = 0; i < NUM_SUMS; i++) {
		nonces[best_byte].expected_num_brute_force += nonces[best_byte].sum_a8_guess[i].prob * (float)nonces[best_byte].sum_a8_guess[i].num_states / 2.0;
		prob_all_failed -= nonces[best_byte].sum_a8_guess[i].prob;
		nonces[best_byte].expected_num_brute_force += prob_all_failed * (float)nonces[best_byte].sum_a8_guess[i].num_states / 2.0;
	}
	return;
}


static float sort_best_first_bytes(void)
{
	
	// initialize best_first_bytes, do a rough estimation on remaining states for each Sum_a8 property
	// and the expected number of states to brute force
	for (uint16_t i = 0; i < 256; i++) {
		best_first_bytes[i] = i;
		float prob_all_failed = 1.0;
		nonces[i].expected_num_brute_force = 0.0;
		for (uint8_t j = 0; j < NUM_SUMS; j++) {
			nonces[i].sum_a8_guess[j].num_states = estimated_num_states_coarse(sums[first_byte_Sum], sums[nonces[i].sum_a8_guess[j].sum_a8_idx]);
			nonces[i].expected_num_brute_force += nonces[i].sum_a8_guess[j].prob * (float)nonces[i].sum_a8_guess[j].num_states / 2.0;
			prob_all_failed -= nonces[i].sum_a8_guess[j].prob;
			nonces[i].expected_num_brute_force += prob_all_failed * (float)nonces[i].sum_a8_guess[j].num_states / 2.0;
		}
	}
	
	// sort based on expected number of states to brute force
	qsort(best_first_bytes, 256, 1, compare_expected_num_brute_force);

	// printf("refine estimations: ");
	#define NUM_REFINES	1
	// refine scores for the best:
	for (uint16_t i = 0; i < NUM_REFINES; i++) {
		// printf("%d...", i);
		uint16_t first_byte = best_first_bytes[i];
		for (uint8_t j = 0; j < NUM_SUMS && nonces[first_byte].sum_a8_guess[j].prob > 0.05; j++) {
			nonces[first_byte].sum_a8_guess[j].num_states = estimated_num_states(first_byte, sums[first_byte_Sum], sums[nonces[first_byte].sum_a8_guess[j].sum_a8_idx]);
		}
		// while (nonces[first_byte].sum_a8_guess[0].num_states == 0
				// || nonces[first_byte].sum_a8_guess[1].num_states == 0
				// || nonces[first_byte].sum_a8_guess[2].num_states == 0) {
			// if (nonces[first_byte].sum_a8_guess[0].num_states == 0) {
				// nonces[first_byte].sum_a8_guess[0].prob = 0.0;
				// printf("(0x%02x,%d)", first_byte, 0);
			// }
			// if (nonces[first_byte].sum_a8_guess[1].num_states == 0) {
				// nonces[first_byte].sum_a8_guess[1].prob = 0.0;
				// printf("(0x%02x,%d)", first_byte, 1);
			// }
			// if (nonces[first_byte].sum_a8_guess[2].num_states == 0) {
				// nonces[first_byte].sum_a8_guess[2].prob = 0.0;
				// printf("(0x%02x,%d)", first_byte, 2);
			// }
			// printf("|");
			// qsort(nonces[first_byte].sum_a8_guess, NUM_SUMS, sizeof(guess_sum_a8_t), compare_sum_a8_guess);
			// for (uint8_t j = 0; j < NUM_SUMS && nonces[first_byte].sum_a8_guess[j].prob > 0.05; j++) {
				// nonces[first_byte].sum_a8_guess[j].num_states = estimated_num_states(first_byte, sums[first_byte_Sum], sums[nonces[first_byte].sum_a8_guess[j].sum_a8_idx]);
			// }
		// }
		// float fix_probs = 0.0;
		// for (uint8_t j = 0; j < NUM_SUMS; j++) {
			// fix_probs += nonces[first_byte].sum_a8_guess[j].prob;
		// }
		// for (uint8_t j = 0; j < NUM_SUMS; j++) {
			// nonces[first_byte].sum_a8_guess[j].prob /= fix_probs;
		// }
		// for (uint8_t j = 0; j < NUM_SUMS && nonces[first_byte].sum_a8_guess[j].prob > 0.05; j++) {
			// nonces[first_byte].sum_a8_guess[j].num_states = estimated_num_states(first_byte, sums[first_byte_Sum], sums[nonces[first_byte].sum_a8_guess[j].sum_a8_idx]);
		// }
		float prob_all_failed = 1.0;
		nonces[first_byte].expected_num_brute_force = 0.0;
		for (uint8_t j = 0; j < NUM_SUMS; j++) {
			nonces[first_byte].expected_num_brute_force += nonces[first_byte].sum_a8_guess[j].prob * (float)nonces[first_byte].sum_a8_guess[j].num_states / 2.0;
			prob_all_failed -= nonces[first_byte].sum_a8_guess[j].prob;
			nonces[first_byte].expected_num_brute_force += prob_all_failed * (float)nonces[first_byte].sum_a8_guess[j].num_states / 2.0;
		}
	}

	// copy best byte to front:
	float least_expected_brute_force = (1LL << 48);
	uint8_t best_byte = 0;
	for (uint16_t i = 0; i < 10; i++) {
		uint16_t first_byte = best_first_bytes[i];
		if (nonces[first_byte].expected_num_brute_force < least_expected_brute_force) {
			least_expected_brute_force = nonces[first_byte].expected_num_brute_force;
			best_byte = i;
		}
	}
	if (best_byte != 0) {
		// printf("0x%02x <-> 0x%02x", best_first_bytes[0], best_first_bytes[best_byte]);
		uint8_t tmp = best_first_bytes[0];
		best_first_bytes[0] = best_first_bytes[best_byte];
		best_first_bytes[best_byte] = tmp;
	}

	return nonces[best_first_bytes[0]].expected_num_brute_force;
}


static float update_reduction_rate(float last, bool init) 
{
#define QUEUE_LEN	4
	static float queue[QUEUE_LEN];
	
	for (uint16_t i = 0; i < QUEUE_LEN-1; i++) {
		if (init) {
			queue[i] = (float)(1LL << 48);
		} else {
			queue[i] = queue[i+1];
		}
	}
	if (init) {
		queue[QUEUE_LEN-1] = (float)(1LL << 48);
	} else {
		queue[QUEUE_LEN-1] = last;
	}
	
	// linear regression
	float avg_y = 0.0;
	float avg_x = 0.0;
	for (uint16_t i = 0; i < QUEUE_LEN; i++) {
		avg_x += i;
		avg_y += queue[i];
	}
	avg_x /= QUEUE_LEN;
	avg_y /= QUEUE_LEN;
	
	float dev_xy = 0.0;
	float dev_x2 = 0.0;
	for (uint16_t i = 0; i < QUEUE_LEN; i++) {
		dev_xy += (i - avg_x)*(queue[i] - avg_y);
		dev_x2 += (i - avg_x)*(i - avg_x);
	}

	float reduction_rate = -1.0 * dev_xy / dev_x2;  // the negative slope of the linear regression

#if defined (DEBUG_REDUCTION)	
	printf("update_reduction_rate(%1.0f) = %1.0f per sample, brute_force_per_sample = %1.0f\n", last, reduction_rate, brute_force_per_second * (float)sample_period / 1000.0);
#endif	
	return reduction_rate;
}


static bool shrink_key_space(float *brute_forces)
{
#if defined(DEBUG_REDUCTION)
	printf("shrink_key_space() with stage = 0x%02x\n", hardnested_stage);
#endif
	float brute_forces1 = check_smallest_bitflip_bitarrays();
	float brute_forces2 = (float)(1LL << 47);
	if (hardnested_stage & CHECK_2ND_BYTES) {
		brute_forces2 = sort_best_first_bytes();
	}
	*brute_forces = MIN(brute_forces1, brute_forces2);
	float reduction_rate = update_reduction_rate(*brute_forces, false);
	return ((hardnested_stage & CHECK_2ND_BYTES) 
		&& reduction_rate >= 0.0 && reduction_rate < brute_force_per_second * sample_period / 1000.0);
}

	
static void estimate_sum_a8(void) 
{
	if (first_byte_num == 256) {
		for (uint16_t i = 0; i < 256; i++) {
			if (nonces[i].sum_a8_guess_dirty) {
				for (uint16_t j = 0; j < NUM_SUMS; j++ ) {
					uint16_t sum_a8_idx = nonces[i].sum_a8_guess[j].sum_a8_idx;
					nonces[i].sum_a8_guess[j].prob = sum_probability(sum_a8_idx, nonces[i].num, nonces[i].Sum);
				}
				qsort(nonces[i].sum_a8_guess, NUM_SUMS, sizeof(guess_sum_a8_t), compare_sum_a8_guess);
				nonces[i].sum_a8_guess_dirty = false;
			}
		}
	}
}	


static int read_nonce_file(void)
{
	FILE *fnonces = NULL;
	size_t bytes_read;
	uint8_t trgBlockNo;
	uint8_t trgKeyType;
	uint8_t read_buf[9];
	uint32_t nt_enc1, nt_enc2;
	uint8_t par_enc;
	
	num_acquired_nonces = 0;
	if ((fnonces = fopen("nonces.bin","rb")) == NULL) { 
		PrintAndLog("Could not open file nonces.bin");
		return 1;
	}

	hardnested_print_progress(0, "Reading nonces from file nonces.bin...", (float)(1LL<<47), 0);
	bytes_read = fread(read_buf, 1, 6, fnonces);
	if (bytes_read != 6) {
		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);

	bytes_read = fread(read_buf, 1, 9, fnonces);
	while (bytes_read == 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);
		add_nonce(nt_enc1, par_enc >> 4);
		add_nonce(nt_enc2, par_enc & 0x0f);
		num_acquired_nonces += 2;
		bytes_read = fread(read_buf, 1, 9, fnonces);
	}
	fclose(fnonces);
	
	char progress_string[80];
	sprintf(progress_string, "Read %d nonces from file. cuid=%08x", num_acquired_nonces, cuid); 
	hardnested_print_progress(num_acquired_nonces, progress_string, (float)(1LL<<47), 0);
	sprintf(progress_string, "Target Block=%d, Keytype=%c", trgBlockNo, trgKeyType==0?'A':'B');
	hardnested_print_progress(num_acquired_nonces, progress_string, (float)(1LL<<47), 0);

	for (uint16_t i = 0; i < NUM_SUMS; i++) {
		if (first_byte_Sum == sums[i]) {
			first_byte_Sum = i;
			break;
		}
	}
	
	return 0;
}


noncelistentry_t *SearchFor2ndByte(uint8_t b1, uint8_t b2)
{
	noncelistentry_t *p = nonces[b1].first;
	while (p != NULL) {
		if ((p->nonce_enc >> 16 & 0xff) == b2) {
			return p;
		}
		p = p->next;
	}
	return NULL;
}


static bool timeout(void)
{
	return (msclock() > last_sample_clock + sample_period);
}


static void *check_for_BitFlipProperties_thread(void *args)
{
	uint8_t first_byte = ((uint8_t *)args)[0];
	uint8_t last_byte = ((uint8_t *)args)[1];
	uint8_t time_budget = ((uint8_t *)args)[2];
	
	if (hardnested_stage & CHECK_1ST_BYTES) {
		// for (uint16_t bitflip = 0x001; bitflip < 0x200; bitflip++) {
		for (uint16_t bitflip_idx = 0; bitflip_idx < num_1st_byte_effective_bitflips; bitflip_idx++) {
			uint16_t bitflip = all_effective_bitflip[bitflip_idx];
			if (time_budget & timeout()) {
#if defined (DEBUG_REDUCTION)				
				printf("break at bitflip_idx %d...", bitflip_idx);
#endif				
				return NULL;
			}
			for (uint16_t i = first_byte; i <= last_byte; i++) {
				if (nonces[i].BitFlips[bitflip] == 0 && nonces[i].BitFlips[bitflip ^ 0x100] == 0
					&& nonces[i].first != NULL && nonces[i^(bitflip&0xff)].first != NULL) {
					uint8_t parity1 = (nonces[i].first->par_enc) >> 3;					// parity of first byte
					uint8_t parity2 = (nonces[i^(bitflip&0xff)].first->par_enc) >> 3; 	// parity of nonce with bits flipped
					if ((parity1 == parity2 && !(bitflip & 0x100)) 			// bitflip
						|| (parity1 != parity2 && (bitflip & 0x100))) {		// not bitflip
						nonces[i].BitFlips[bitflip] = 1;
						for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
							if (bitflip_bitarrays[odd_even][bitflip] != NULL) {
								uint32_t old_count = nonces[i].num_states_bitarray[odd_even];
								nonces[i].num_states_bitarray[odd_even] = count_bitarray_AND(nonces[i].states_bitarray[odd_even], bitflip_bitarrays[odd_even][bitflip]);
								if (nonces[i].num_states_bitarray[odd_even] != old_count) {
									nonces[i].all_bitflips_dirty[odd_even] = true;
								}
								// printf("bitflip: %d old: %d, new: %d ", bitflip, old_count, nonces[i].num_states_bitarray[odd_even]);
							}
						}
					}
				}
			}
			((uint8_t *)args)[1] = num_1st_byte_effective_bitflips - bitflip_idx - 1;  // bitflips still to go in stage 1
		}
	}

	((uint8_t *)args)[1] = 0;  // stage 1 definitely completed

	if (hardnested_stage & CHECK_2ND_BYTES) {
		for (uint16_t bitflip_idx = num_1st_byte_effective_bitflips; bitflip_idx < num_all_effective_bitflips; bitflip_idx++) {
			uint16_t bitflip = all_effective_bitflip[bitflip_idx];
			if (time_budget & timeout()) {
#if defined (DEBUG_REDUCTION)
				printf("break at bitflip_idx %d...", bitflip_idx);
#endif
				return NULL;
			}
			for (uint16_t i = first_byte; i <= last_byte; i++) {
				// Check for Bit Flip Property of 2nd bytes
				if (nonces[i].BitFlips[bitflip] == 0) {
					for (uint16_t j = 0; j < 256; j++) { 	// for each 2nd Byte
						noncelistentry_t *byte1 = SearchFor2ndByte(i, j);
						noncelistentry_t *byte2 = SearchFor2ndByte(i, j^(bitflip&0xff));
						if (byte1 != NULL && byte2 != NULL) {
							uint8_t parity1 = byte1->par_enc >> 2 & 0x01;	// parity of 2nd byte
							uint8_t parity2 = byte2->par_enc >> 2 & 0x01; 	// parity of 2nd byte with bits flipped
							if ((parity1 == parity2 && !(bitflip&0x100)) 		// bitflip
								|| (parity1 != parity2 && (bitflip&0x100))) { // not bitflip
								nonces[i].BitFlips[bitflip] = 1;
								for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
									if (bitflip_bitarrays[odd_even][bitflip] != NULL) {
										uint32_t old_count = nonces[i].num_states_bitarray[odd_even];
										nonces[i].num_states_bitarray[odd_even] = count_bitarray_AND(nonces[i].states_bitarray[odd_even], bitflip_bitarrays[odd_even][bitflip]);
										if (nonces[i].num_states_bitarray[odd_even] != old_count) {
											nonces[i].all_bitflips_dirty[odd_even] = true;
										}
									}
								}
								break;
							}
						}
					}
				}
				// printf("states_bitarray[0][%" PRIu16 "] contains %d ones.\n", i, count_states(nonces[i].states_bitarray[EVEN_STATE]));
				// printf("states_bitarray[1][%" PRIu16 "] contains %d ones.\n", i, count_states(nonces[i].states_bitarray[ODD_STATE]));
			}
		}
	}

	return NULL;
}


static void check_for_BitFlipProperties(bool time_budget)
{
	// create and run worker threads
	pthread_t thread_id[NUM_CHECK_BITFLIPS_THREADS];
		
	uint8_t args[NUM_CHECK_BITFLIPS_THREADS][3];
	uint16_t bytes_per_thread = (256 + (NUM_CHECK_BITFLIPS_THREADS/2)) / NUM_CHECK_BITFLIPS_THREADS; 
	for (uint8_t i = 0; i < NUM_CHECK_BITFLIPS_THREADS; i++) {
		args[i][0] = i * bytes_per_thread;
		args[i][1] = MIN(args[i][0]+bytes_per_thread-1, 255);
		args[i][2] = time_budget;
	}
	args[NUM_CHECK_BITFLIPS_THREADS-1][1] = MAX(args[NUM_CHECK_BITFLIPS_THREADS-1][1], 255);
	
	// start threads
	for (uint8_t i = 0; i < NUM_CHECK_BITFLIPS_THREADS; i++) {
		pthread_create(&thread_id[i], NULL, check_for_BitFlipProperties_thread, args[i]);
	}
	
	// wait for threads to terminate:
	for (uint8_t i = 0; i < NUM_CHECK_BITFLIPS_THREADS; i++) {
		pthread_join(thread_id[i], NULL);
	}
	
	if (hardnested_stage & CHECK_2ND_BYTES) {
		hardnested_stage &= ~CHECK_1ST_BYTES;	// we are done with 1st stage, except...
		for (uint16_t i = 0; i < NUM_CHECK_BITFLIPS_THREADS; i++) {
			if (args[i][1] != 0) {
				hardnested_stage |= CHECK_1ST_BYTES;  // ... when any of the threads didn't complete in time
				break;
			}
		}
	}
#if defined (DEBUG_REDUCTION)	
	if (hardnested_stage & CHECK_1ST_BYTES) printf("stage 1 not completed yet\n");
#endif
}


static void update_nonce_data(bool time_budget)
{
	check_for_BitFlipProperties(time_budget);
	update_allbitflips_array();
	update_sum_bitarrays(EVEN_STATE);
	update_sum_bitarrays(ODD_STATE);
	update_p_K();
	estimate_sum_a8();
}


static void apply_sum_a0(void)
{
	uint32_t old_count = num_all_bitflips_bitarray[EVEN_STATE];
	num_all_bitflips_bitarray[EVEN_STATE] = count_bitarray_AND(all_bitflips_bitarray[EVEN_STATE], sum_a0_bitarrays[EVEN_STATE][first_byte_Sum]);
	if (num_all_bitflips_bitarray[EVEN_STATE] != old_count) {
		all_bitflips_bitarray_dirty[EVEN_STATE] = true;
	}
	old_count = num_all_bitflips_bitarray[ODD_STATE];
	num_all_bitflips_bitarray[ODD_STATE] = count_bitarray_AND(all_bitflips_bitarray[ODD_STATE], sum_a0_bitarrays[ODD_STATE][first_byte_Sum]);
	if (num_all_bitflips_bitarray[ODD_STATE] != old_count) {
		all_bitflips_bitarray_dirty[ODD_STATE] = true;
	}
}


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()
{
	time_t time1 = time(NULL);
	last_sample_clock = 0;
	sample_period = 1000;		// for simulation
	hardnested_stage = CHECK_1ST_BYTES;
	bool acquisition_completed = false;
	uint32_t total_num_nonces = 0;
	float brute_force;
	bool reported_suma8 = false;
	
	cuid = (rand() & 0xff) << 24 | (rand() & 0xff) << 16 | (rand() & 0xff) << 8 | (rand() & 0xff);
	if (known_target_key == -1) {
		known_target_key = ((uint64_t)rand() & 0xfff) << 36 | ((uint64_t)rand() & 0xfff) << 24 | ((uint64_t)rand() & 0xfff) << 12 | ((uint64_t)rand() & 0xfff);
	}

	char progress_text[80];
	sprintf(progress_text, "Simulating key %012" PRIx64 ", cuid %08" PRIx32 " ...", known_target_key, cuid);
	hardnested_print_progress(0, progress_text, (float)(1LL<<47), 0);
	fprintf(fstats, "%012" PRIx64 ";%" PRIx32 ";", known_target_key, cuid);

	num_acquired_nonces = 0;
	
	do {
		uint32_t nt_enc = 0;
		uint8_t par_enc = 0;

		for (uint16_t i = 0; i < 113; i++) {
			simulate_MFplus_RNG(cuid, known_target_key, &nt_enc, &par_enc);
			num_acquired_nonces += add_nonce(nt_enc, par_enc);
			total_num_nonces++;
		}

		last_sample_clock = msclock();
	
		if (first_byte_num == 256 ) {
			if (hardnested_stage == CHECK_1ST_BYTES) {
				for (uint16_t i = 0; i < NUM_SUMS; i++) {
					if (first_byte_Sum == sums[i]) {
						first_byte_Sum = i;
						break;
					}
				}
				hardnested_stage |= CHECK_2ND_BYTES;
				apply_sum_a0();
			} 
			update_nonce_data(true);
			acquisition_completed = shrink_key_space(&brute_force);
			if (!reported_suma8) {
				char progress_string[80];
				sprintf(progress_string, "Apply Sum property. Sum(a0) = %d", sums[first_byte_Sum]);
				hardnested_print_progress(num_acquired_nonces, progress_string, brute_force, 0);
				reported_suma8 = true;
			} else {
				hardnested_print_progress(num_acquired_nonces, "Apply bit flip properties", brute_force, 0);
			}
		} else {
			update_nonce_data(true);
			acquisition_completed = shrink_key_space(&brute_force);
			hardnested_print_progress(num_acquired_nonces, "Apply bit flip properties", brute_force, 0);
		}
	} while (!acquisition_completed);

	time_t end_time = time(NULL);
	// PrintAndLog("Acquired a total of %" PRId32" nonces in %1.0f seconds (%1.0f nonces/minute)", 
		// num_acquired_nonces, 
		// difftime(end_time, time1), 
		// difftime(end_time, time1)!=0.0?(float)total_num_nonces*60.0/difftime(end_time, time1):INFINITY
		// );

	fprintf(fstats, "%" PRId32 ";%" PRId32 ";%1.0f;", total_num_nonces, num_acquired_nonces, difftime(end_time,time1));
		
}


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)
{
	last_sample_clock = msclock();
	sample_period = 2000;	// initial rough estimate. Will be refined.
	bool initialize = true;
	bool field_off = false;
	hardnested_stage = CHECK_1ST_BYTES;
	bool acquisition_completed = false;
	uint32_t flags = 0;
	uint8_t write_buf[9];
	uint32_t total_num_nonces = 0;
	float brute_force;
	bool reported_suma8 = false;
	FILE *fnonces = NULL;
	UsbCommand resp;

	num_acquired_nonces = 0;
	
	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) break;
		
		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;
				}
				hardnested_print_progress(0, "Writing acquired nonces to binary file nonces.bin", (float)(1LL<<47), 0);
				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_sampled_nonces = resp.arg[2];
			uint8_t *bufp = resp.d.asBytes;
			for (uint16_t i = 0; i < num_sampled_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);
				num_acquired_nonces += add_nonce(nt_enc1, par_enc >> 4);
				//printf("Encrypted nonce: %08x, encrypted_parity: %02x\n", nt_enc2, par_enc & 0x0f);
				num_acquired_nonces += add_nonce(nt_enc2, par_enc & 0x0f);

				if (nonce_file_write) {
					fwrite(bufp, 1, 9, fnonces);
				}
				bufp += 9;
			}
			total_num_nonces += num_sampled_nonces;
		
			if (first_byte_num == 256 ) {
				if (hardnested_stage == CHECK_1ST_BYTES) {
					for (uint16_t i = 0; i < NUM_SUMS; i++) {
						if (first_byte_Sum == sums[i]) {
							first_byte_Sum = i;
							break;
						}
					}
					hardnested_stage |= CHECK_2ND_BYTES;
					apply_sum_a0();
				}
				update_nonce_data(true);
				acquisition_completed = shrink_key_space(&brute_force);
				if (!reported_suma8) {
					char progress_string[80];
					sprintf(progress_string, "Apply Sum property. Sum(a0) = %d", sums[first_byte_Sum]);
					hardnested_print_progress(num_acquired_nonces, progress_string, brute_force, 0);
					reported_suma8 = true;
				} else {
					hardnested_print_progress(num_acquired_nonces, "Apply bit flip properties", brute_force, 0);
				}
			} else {
				update_nonce_data(true);
				acquisition_completed = shrink_key_space(&brute_force);
				hardnested_print_progress(num_acquired_nonces, "Apply bit flip properties", brute_force, 0);
			}
		}
		
		if (acquisition_completed) {
			field_off = true;	// switch off field with next SendCommand and then finish
		}

		if (!initialize) {
			if (!WaitForResponseTimeout(CMD_ACK, &resp, 3000)) {
				if (nonce_file_write) {
					fclose(fnonces);
				}
				return 1;
			}
			if (resp.arg[0]) {
				if (nonce_file_write) {
					fclose(fnonces);
				}
				return resp.arg[0];  // error during nested_hard
			}
		}

		initialize = false;

		if (msclock() - last_sample_clock < sample_period) {
			sample_period = msclock() - last_sample_clock;
		}
		last_sample_clock = msclock();

	} while (!acquisition_completed || field_off);

	if (nonce_file_write) {
		fclose(fnonces);
	}
	
	// PrintAndLog("Sampled a total of %d nonces in %d seconds (%0.0f nonces/minute)", 
		// total_num_nonces, 
		// time(NULL)-time1, 
		// (float)total_num_nonces*60.0/(time(NULL)-time1));
	
	return 0;
}


static inline bool 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 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 pthread_mutex_t statelist_cache_mutex;
static pthread_mutex_t book_of_work_mutex;


typedef enum {
	TO_BE_DONE,
	WORK_IN_PROGRESS,
	COMPLETED
} work_status_t;

static struct sl_cache_entry {
	uint32_t *sl;
	uint32_t len;
	work_status_t cache_status;
	} sl_cache[NUM_PART_SUMS][NUM_PART_SUMS][2];


static void init_statelist_cache(void)
{
	pthread_mutex_lock(&statelist_cache_mutex);
	for (uint16_t i = 0; i < NUM_PART_SUMS; i++) {
		for (uint16_t j = 0; j < NUM_PART_SUMS; j++) {
			for (uint16_t k = 0; k < 2; k++) {
				sl_cache[i][j][k].sl = NULL;
				sl_cache[i][j][k].len = 0;
				sl_cache[i][j][k].cache_status = TO_BE_DONE;
			}
		}
	}		
	pthread_mutex_unlock(&statelist_cache_mutex);
}


static void free_statelist_cache(void)
{
	pthread_mutex_lock(&statelist_cache_mutex);
	for (uint16_t i = 0; i < NUM_PART_SUMS; i++) {
		for (uint16_t j = 0; j < NUM_PART_SUMS; j++) {
			for (uint16_t k = 0; k < 2; k++) {
				free(sl_cache[i][j][k].sl);
			}
		}
	}		
	pthread_mutex_unlock(&statelist_cache_mutex);
}


#ifdef DEBUG_KEY_ELIMINATION
static inline bool bitflips_match(uint8_t byte, uint32_t state, odd_even_t odd_even, bool quiet)
#else
static inline bool bitflips_match(uint8_t byte, uint32_t state, odd_even_t odd_even)
#endif	
{
	uint32_t *bitset = nonces[byte].states_bitarray[odd_even];
	bool possible = test_bit24(bitset, state);
	if (!possible) {
#ifdef DEBUG_KEY_ELIMINATION
		if (!quiet && known_target_key != -1 && state == test_state[odd_even]) {
			printf("Initial state lists: %s test state eliminated by bitflip property.\n", odd_even==EVEN_STATE?"even":"odd");
			sprintf(failstr, "Initial %s Byte Bitflip property", odd_even==EVEN_STATE?"even":"odd");
		}
#endif
		return false;
	} else {
		return true;
	}
}
	
	
static uint_fast8_t reverse(uint_fast8_t byte)
{
	uint_fast8_t rev_byte = 0;
	
	for (uint8_t i = 0; i < 8; i++) {
		rev_byte <<= 1;
		rev_byte |= (byte >> i) & 0x01;
	}
	
	return rev_byte;
}


static bool all_bitflips_match(uint8_t byte, uint32_t state, odd_even_t odd_even) 
{
	uint32_t masks[2][8] = {{0x00fffff0, 0x00fffff8, 0x00fffff8, 0x00fffffc, 0x00fffffc, 0x00fffffe, 0x00fffffe, 0x00ffffff},
							{0x00fffff0, 0x00fffff0, 0x00fffff8, 0x00fffff8, 0x00fffffc, 0x00fffffc, 0x00fffffe, 0x00fffffe} };
	
	for (uint16_t i = 1; i < 256; i++) {
		uint_fast8_t bytes_diff = reverse(i);	// start with most common bits
		uint_fast8_t byte2 = byte ^ bytes_diff;
		uint_fast8_t num_common = trailing_zeros(bytes_diff);
		uint32_t mask = masks[odd_even][num_common];
		bool found_match = false;
		for (uint8_t remaining_bits = 0; remaining_bits <= (~mask & 0xff); remaining_bits++) {
			if (remaining_bits_match(num_common, bytes_diff, state, (state & mask) | remaining_bits, odd_even)) {
#ifdef DEBUG_KEY_ELIMINATION
				if (bitflips_match(byte2, (state & mask) | remaining_bits, odd_even, true)) {
#else
				if (bitflips_match(byte2, (state & mask) | remaining_bits, odd_even)) {
#endif						
					found_match = true;
					break;
				}
			}
		}
		if (!found_match) {
#ifdef DEBUG_KEY_ELIMINATION				
			if (known_target_key != -1 && state == test_state[odd_even]) {
				printf("all_bitflips_match() 1st Byte: %s test state (0x%06x): Eliminated. Bytes = %02x, %02x, Common Bits = %d\n", 
					odd_even==ODD_STATE?"odd":"even",
					test_state[odd_even],
					byte, byte2, num_common);
				if (failstr[0] == '\0') {
					sprintf(failstr, "Other 1st Byte %s, all_bitflips_match(), no match", odd_even?"odd":"even");
				}
			}
#endif
			return false;
		}
	}

	return true;
}


static void	bitarray_to_list(uint8_t byte, uint32_t *bitarray, uint32_t *state_list, uint32_t *len, odd_even_t odd_even)
{
	uint32_t *p = state_list;
	for (uint32_t state = next_state(bitarray, -1L); state < (1<<24); state = next_state(bitarray, state)) {
		if (all_bitflips_match(byte, state, odd_even)) {
			*p++ = state;
		}
	}
	// add End Of List marker
	*p = 0xffffffff;
	*len = p - state_list;
}


static void add_cached_states(statelist_t *candidates, uint16_t part_sum_a0, uint16_t part_sum_a8, odd_even_t odd_even)
{
	candidates->states[odd_even] = sl_cache[part_sum_a0/2][part_sum_a8/2][odd_even].sl;
	candidates->len[odd_even] = sl_cache[part_sum_a0/2][part_sum_a8/2][odd_even].len;
	return;
}


static void add_matching_states(statelist_t *candidates, uint8_t part_sum_a0, uint8_t part_sum_a8, odd_even_t odd_even)
{
	uint32_t worstcase_size = 1<<20;
	candidates->states[odd_even] = (uint32_t *)malloc(sizeof(uint32_t) * worstcase_size);
	if (candidates->states[odd_even] == NULL) {
		PrintAndLog("Out of memory error in add_matching_states() - statelist.\n");
		exit(4);
	}
	uint32_t *candidates_bitarray = (uint32_t *)malloc_bitarray(sizeof(uint32_t) * (1<<19));
	if (candidates_bitarray == NULL) {
		PrintAndLog("Out of memory error in add_matching_states() - bitarray.\n");
		free(candidates->states[odd_even]);
		exit(4);
	}
	
	uint32_t *bitarray_a0 = part_sum_a0_bitarrays[odd_even][part_sum_a0/2];
	uint32_t *bitarray_a8 = part_sum_a8_bitarrays[odd_even][part_sum_a8/2];
	uint32_t *bitarray_bitflips = nonces[best_first_bytes[0]].states_bitarray[odd_even];

	// for (uint32_t i = 0; i < (1<<19); i++) {
		// candidates_bitarray[i] = bitarray_a0[i] & bitarray_a8[i] & bitarray_bitflips[i];
	// }
	bitarray_AND4(candidates_bitarray, bitarray_a0, bitarray_a8, bitarray_bitflips);
	
	bitarray_to_list(best_first_bytes[0], candidates_bitarray, candidates->states[odd_even], &(candidates->len[odd_even]), odd_even);
	if (candidates->len[odd_even] == 0) {
		free(candidates->states[odd_even]);
		candidates->states[odd_even] = NULL;
	} else if (candidates->len[odd_even] + 1 < worstcase_size) {
		candidates->states[odd_even] = realloc(candidates->states[odd_even], sizeof(uint32_t) * (candidates->len[odd_even] + 1));
	}
	free_bitarray(candidates_bitarray);


	pthread_mutex_lock(&statelist_cache_mutex);
	sl_cache[part_sum_a0/2][part_sum_a8/2][odd_even].sl = candidates->states[odd_even];
	sl_cache[part_sum_a0/2][part_sum_a8/2][odd_even].len = candidates->len[odd_even];
	sl_cache[part_sum_a0/2][part_sum_a8/2][odd_even].cache_status = COMPLETED;
	pthread_mutex_unlock(&statelist_cache_mutex);

	return;
}


static statelist_t *add_more_candidates(void)
{
	statelist_t *new_candidates = candidates;
	if (candidates == NULL) {
		candidates = (statelist_t *)malloc(sizeof(statelist_t));
		new_candidates = candidates;
	} else {
		new_candidates = candidates;
		while (new_candidates->next != NULL) {
			new_candidates = new_candidates->next;
		}
		new_candidates = new_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 add_bitflip_candidates(uint8_t byte)
{
	statelist_t *candidates = add_more_candidates();

	for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
		uint32_t worstcase_size = nonces[byte].num_states_bitarray[odd_even] + 1;
		candidates->states[odd_even] = (uint32_t *)malloc(sizeof(uint32_t) * worstcase_size);
		if (candidates->states[odd_even] == NULL) {
			PrintAndLog("Out of memory error in add_bitflip_candidates().\n");
			exit(4);
		}
	
		bitarray_to_list(byte, nonces[byte].states_bitarray[odd_even], candidates->states[odd_even], &(candidates->len[odd_even]), odd_even);

		if (candidates->len[odd_even] + 1 < worstcase_size) {
			candidates->states[odd_even] = realloc(candidates->states[odd_even], sizeof(uint32_t) * (candidates->len[odd_even] + 1));
		}
	}
	return;
}


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;
	
	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];
		if (p_odd != NULL && p_even != NULL) {
			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 += (uint64_t)(p_odd - p->states[ODD_STATE]) * (uint64_t)(p_even - p->states[EVEN_STATE]);
		}
		if (found_odd && found_even) {
			num_keys_tested += count;
			hardnested_print_progress(num_acquired_nonces, "(Test: Key found)", 0.0, 0);
			crypto1_destroy(pcs);
			return true;
		}
	}

	num_keys_tested += count;
	hardnested_print_progress(num_acquired_nonces, "(Test: Key NOT found)", 0.0, 0);

	crypto1_destroy(pcs);
	return false;
}


static work_status_t book_of_work[NUM_PART_SUMS][NUM_PART_SUMS][NUM_PART_SUMS][NUM_PART_SUMS];


static void init_book_of_work(void)
{
	for (uint8_t p = 0; p < NUM_PART_SUMS; p++) {
		for (uint8_t q = 0; q < NUM_PART_SUMS; q++) {
			for (uint8_t r = 0; r < NUM_PART_SUMS; r++) {
				for (uint8_t s = 0; s < NUM_PART_SUMS; s++) {
					book_of_work[p][q][r][s] = TO_BE_DONE;
				}
			}
		}
	}
}


static void *generate_candidates_worker_thread(void *args)
{
	uint16_t *sum_args = (uint16_t *)args;
	uint16_t sum_a0 = sums[sum_args[0]];
	uint16_t sum_a8 = sums[sum_args[1]];
	// uint16_t my_thread_number = sums[2];
	
	bool there_might_be_more_work = true;
	do {
		there_might_be_more_work = false;
		for (uint8_t p = 0; p < NUM_PART_SUMS; p++) {
			for (uint8_t q = 0; q < NUM_PART_SUMS; q++) {
				if (2*p*(16-2*q) + (16-2*p)*2*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 (uint8_t r = 0; r < NUM_PART_SUMS; r++) {
						for (uint8_t s = 0; s < NUM_PART_SUMS; s++) {
							if (2*r*(16-2*s) + (16-2*r)*2*s == sum_a8) {
								pthread_mutex_lock(&book_of_work_mutex);
								if (book_of_work[p][q][r][s] != TO_BE_DONE) {  // this has been done or is currently been done by another thread. Look for some other work.
									pthread_mutex_unlock(&book_of_work_mutex);
									continue;
								}

								pthread_mutex_lock(&statelist_cache_mutex);
								if (sl_cache[p][r][ODD_STATE].cache_status == WORK_IN_PROGRESS
									|| sl_cache[q][s][EVEN_STATE].cache_status == WORK_IN_PROGRESS) { // defer until not blocked by another thread.
									pthread_mutex_unlock(&statelist_cache_mutex);
									pthread_mutex_unlock(&book_of_work_mutex);
									there_might_be_more_work = true;
									continue;
								}

								// we finally can do some work.
								book_of_work[p][q][r][s] = WORK_IN_PROGRESS;
								statelist_t *current_candidates = add_more_candidates();

								// Check for cached results and add them first
								bool odd_completed = false;
								if (sl_cache[p][r][ODD_STATE].cache_status == COMPLETED) {
									add_cached_states(current_candidates, 2*p, 2*r, ODD_STATE);
									odd_completed = true;
								}
								bool even_completed = false;
								if (sl_cache[q][s][EVEN_STATE].cache_status == COMPLETED) {
									add_cached_states(current_candidates, 2*q, 2*s, EVEN_STATE);
									even_completed = true;
								}
								
								bool work_required = true;

								// if there had been two cached results, there is no more work to do
								if (even_completed && odd_completed) {
									work_required = false;
								}	

								// if there had been one cached empty result, there is no need to calculate the other part:
								if (work_required) {
									if (even_completed && !current_candidates->len[EVEN_STATE]) {
										current_candidates->len[ODD_STATE] = 0;
										current_candidates->states[ODD_STATE] = NULL;
										work_required = false;
									}									
									if (odd_completed && !current_candidates->len[ODD_STATE]) {
										current_candidates->len[EVEN_STATE] = 0;
										current_candidates->states[EVEN_STATE] = NULL;
										work_required = false;
									}
								}

								if (!work_required) {
									pthread_mutex_unlock(&statelist_cache_mutex);
									pthread_mutex_unlock(&book_of_work_mutex);
								} else {
									// we really need to calculate something
									if (even_completed) { // we had one cache hit with non-zero even states
										// printf("Thread #%u: start working on  odd states p=%2d, r=%2d...\n", my_thread_number, p, r);
										sl_cache[p][r][ODD_STATE].cache_status = WORK_IN_PROGRESS;
										pthread_mutex_unlock(&statelist_cache_mutex);
										pthread_mutex_unlock(&book_of_work_mutex);
										add_matching_states(current_candidates, 2*p, 2*r, ODD_STATE);
										work_required = false;
									} else if (odd_completed) { // we had one cache hit with non-zero odd_states
										// printf("Thread #%u: start working on even states q=%2d, s=%2d...\n", my_thread_number, q, s);
										sl_cache[q][s][EVEN_STATE].cache_status = WORK_IN_PROGRESS;
										pthread_mutex_unlock(&statelist_cache_mutex);
										pthread_mutex_unlock(&book_of_work_mutex);
										add_matching_states(current_candidates, 2*q, 2*s, EVEN_STATE);
										work_required = false;
									}
								}
									
								if (work_required) { // we had no cached result. Need to calculate both odd and even
									sl_cache[p][r][ODD_STATE].cache_status = WORK_IN_PROGRESS;
									sl_cache[q][s][EVEN_STATE].cache_status = WORK_IN_PROGRESS;
									pthread_mutex_unlock(&statelist_cache_mutex);
									pthread_mutex_unlock(&book_of_work_mutex);

									add_matching_states(current_candidates, 2*p, 2*r, ODD_STATE);
									if(current_candidates->len[ODD_STATE]) {
										// printf("Thread #%u: start working on even states q=%2d, s=%2d...\n", my_thread_number, q, s);
										add_matching_states(current_candidates, 2*q, 2*s, EVEN_STATE);
									} else { // no need to calculate even states yet
										pthread_mutex_lock(&statelist_cache_mutex);
										sl_cache[q][s][EVEN_STATE].cache_status = TO_BE_DONE;
										pthread_mutex_unlock(&statelist_cache_mutex);
										current_candidates->len[EVEN_STATE] = 0;
										current_candidates->states[EVEN_STATE] = NULL;
									}
								}

								// update book of work
								pthread_mutex_lock(&book_of_work_mutex);
								book_of_work[p][q][r][s] = COMPLETED;
								pthread_mutex_unlock(&book_of_work_mutex);

								// if ((uint64_t)current_candidates->len[ODD_STATE] * current_candidates->len[EVEN_STATE]) {
									// printf("Candidates for p=%2u, q=%2u, r=%2u, s=%2u: %" PRIu32 " * %" PRIu32 " = %" PRIu64 " (2^%0.1f)\n",
										// 2*p, 2*q, 2*r, 2*s, current_candidates->len[ODD_STATE], current_candidates->len[EVEN_STATE],
										// (uint64_t)current_candidates->len[ODD_STATE] * current_candidates->len[EVEN_STATE],
										// log((uint64_t)current_candidates->len[ODD_STATE] * current_candidates->len[EVEN_STATE])/log(2));
									// uint32_t estimated_odd = estimated_num_states_part_sum(best_first_bytes[0], p, r, ODD_STATE);
									// uint32_t estimated_even= estimated_num_states_part_sum(best_first_bytes[0], q, s, EVEN_STATE);
									// uint64_t estimated_total = (uint64_t)estimated_odd * estimated_even; 
									// printf("Estimated: %" PRIu32 " * %" PRIu32 " = %" PRIu64 " (2^%0.1f)\n", estimated_odd, estimated_even, estimated_total, log(estimated_total) / log(2));
									// if (estimated_odd < current_candidates->len[ODD_STATE] || estimated_even < current_candidates->len[EVEN_STATE]) {
										// printf("############################################################################ERROR! ESTIMATED < REAL !!!\n"); 
										// //exit(2);
										// }
								// }
							}
						}
					}
				}
			}
		}
	} while (there_might_be_more_work);
	
	return NULL;
}


static void generate_candidates(uint8_t sum_a0_idx, uint8_t sum_a8_idx)
{
	// printf("Generating crypto1 state candidates... \n");
	
	// 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)count_states(part_sum_a0_bitarrays[EVEN_STATE][sum_even/2]) 
								// * count_states(part_sum_a0_bitarrays[ODD_STATE][sum_odd/2]);
			// }
		// }
	// }
	// 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();
	init_book_of_work();

	// create mutexes for accessing the statelist cache and our "book of work"
	pthread_mutex_init(&statelist_cache_mutex, NULL);
	pthread_mutex_init(&book_of_work_mutex, NULL);

	// create and run worker threads
	pthread_t thread_id[NUM_REDUCTION_WORKING_THREADS];
		
	uint16_t sums[NUM_REDUCTION_WORKING_THREADS][3];
	for (uint16_t i = 0; i < NUM_REDUCTION_WORKING_THREADS; i++) {
		sums[i][0] = sum_a0_idx;
		sums[i][1] = sum_a8_idx;
		sums[i][2] = i+1;
		pthread_create(thread_id + i, NULL, generate_candidates_worker_thread, sums[i]);
	}
	
	// wait for threads to terminate:
	for (uint16_t i = 0; i < NUM_REDUCTION_WORKING_THREADS; i++) {
		pthread_join(thread_id[i], NULL);
	}

	// clean up mutex
	pthread_mutex_destroy(&statelist_cache_mutex);
	
	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];
	}

	for (uint8_t i = 0; i < NUM_SUMS; i++) {
		if (nonces[best_first_bytes[0]].sum_a8_guess[i].sum_a8_idx == sum_a8_idx) {
			nonces[best_first_bytes[0]].sum_a8_guess[i].num_states = maximum_states;
			break;
		}
	}
	update_expected_brute_force(best_first_bytes[0]);

	hardnested_print_progress(num_acquired_nonces, "Apply Sum(a8) and all bytes bitflip properties", nonces[best_first_bytes[0]].expected_num_brute_force, 0);
}


static void	free_candidates_memory(statelist_t *sl)
{
	if (sl == NULL) {
		return;
	} else {
		free_candidates_memory(sl->next);
		free(sl);
	}
}


static void pre_XOR_nonces(void)
{
	// prepare acquired nonces for faster brute forcing. 
	
	// XOR the cryptoUID and its parity
	for (uint16_t i = 0; i < 256; i++) {
		noncelistentry_t *test_nonce = nonces[i].first;
		while (test_nonce != NULL) {
			test_nonce->nonce_enc ^= cuid;
			test_nonce->par_enc ^= oddparity8(cuid >>  0 & 0xff) << 0;
			test_nonce->par_enc ^= oddparity8(cuid >>  8 & 0xff) << 1;
			test_nonce->par_enc ^= oddparity8(cuid >> 16 & 0xff) << 2;
			test_nonce->par_enc ^= oddparity8(cuid >> 24 & 0xff) << 3;
			test_nonce = test_nonce->next;
		}
	}
}
	

static bool brute_force(void)
{
	if (known_target_key != -1) {
		TestIfKeyExists(known_target_key);
	}
	return brute_force_bs(NULL, candidates, cuid, num_acquired_nonces, maximum_states, nonces, best_first_bytes);
}


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 void Tests()
{

/*  	#define NUM_STATISTICS 100000
	uint32_t statistics_odd[17];
	uint64_t statistics[257];
	uint32_t statistics_even[17];
	struct Crypto1State cs;
	uint64_t time1 = msclock();

	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)msclock() - time1)/1000.0, NUM_STATISTICS/((float)msclock() - time1)*1000.0);
	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);
		}
	}
 */

/*    	#define NUM_STATISTICS 100000000LL
	uint64_t statistics_a0[257];
	uint64_t statistics_a8[257][257];
	struct Crypto1State cs;
	uint64_t time1 = msclock();

	for (uint16_t i = 0; i < 257; i++) {
		statistics_a0[i] = 0;
		for (uint16_t j = 0; j < 257; j++) {
			statistics_a8[i][j] = 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_a0 = SumProperty(&cs);
		statistics_a0[sum_property_a0]++;
		uint8_t first_byte = rand() & 0xff;
		crypto1_byte(&cs, first_byte, true);
		uint16_t sum_property_a8 = SumProperty(&cs);
		statistics_a8[sum_property_a0][sum_property_a8] += 1;
		if (i%(NUM_STATISTICS/100) == 0) printf("."); 
	}
	
	printf("\nTests: Probability Distribution of a8 depending on a0:\n");
	printf("\n      ");
	for (uint16_t i = 0; i < NUM_SUMS; i++) {
		printf("%7d ", sums[i]);
	}
	printf("\n-------------------------------------------------------------------------------------------------------------------------------------------\n");
	printf("a0:   ");
	for (uint16_t i = 0; i < NUM_SUMS; i++) {
		printf("%7.5f ", (float)statistics_a0[sums[i]] / NUM_STATISTICS);
	}
	printf("\n");
	for (uint16_t i = 0; i < NUM_SUMS; i++) {
		printf("%3d   ", sums[i]);
		for (uint16_t j = 0; j < NUM_SUMS; j++) {
			printf("%7.5f ", (float)statistics_a8[sums[i]][sums[j]] / statistics_a0[sums[i]]);
			}
		printf("\n");
	}
	printf("\nTests: Calculated %"lld" Sum properties in %0.3f seconds (%0.0f calcs/second)\n", NUM_STATISTICS, ((float)msclock() - time1)/1000.0, NUM_STATISTICS/((float)msclock() - time1)*1000.0);
 */		
 
/*   	#define NUM_STATISTICS 100000LL
	uint64_t statistics_a8[257];
	struct Crypto1State cs;
	uint64_t time1 = msclock();

	printf("\nTests: Probability Distribution of a8 depending on first byte:\n");
	printf("\n      ");
	for (uint16_t i = 0; i < NUM_SUMS; i++) {
		printf("%7d ", sums[i]);
	}
	printf("\n-------------------------------------------------------------------------------------------------------------------------------------------\n");
	for (uint16_t first_byte = 0; first_byte < 256; first_byte++) {
		for (uint16_t i = 0; i < 257; i++) {
			statistics_a8[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);
			crypto1_byte(&cs, first_byte, true);
			uint16_t sum_property_a8 = SumProperty(&cs);
			statistics_a8[sum_property_a8] += 1;
		}
		printf("%03x   ", first_byte);
		for (uint16_t j = 0; j < NUM_SUMS; j++) {
			printf("%7.5f ", (float)statistics_a8[sums[j]] / NUM_STATISTICS);
		}
		printf("\n");
	}
	printf("\nTests: Calculated %"lld" Sum properties in %0.3f seconds (%0.0f calcs/second)\n", NUM_STATISTICS, ((float)msclock() - time1)/1000.0, NUM_STATISTICS/((float)msclock() - time1)*1000.0);
*/	

/* 	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);
		}
	}
 */	

/* 	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: Sorted First Bytes:\n");
	// for (uint16_t i = 0; i < 20; i++) {
		// uint8_t best_byte = best_first_bytes[i];
		// //printf("#%03d Byte: %02x, n = %3d, k = %3d, Sum(a8): %3d, Confidence: %5.1f%%\n", 
		// printf("#%03d Byte: %02x, n = %3d, k = %3d, Sum(a8) = ", i, best_byte, nonces[best_byte].num, nonces[best_byte].Sum);
		// for (uint16_t j = 0; j < 3; j++) {
			// printf("%3d @ %4.1f%%, ", sums[nonces[best_byte].sum_a8_guess[j].sum_a8_idx], nonces[best_byte].sum_a8_guess[j].prob * 100.0);
		// }
		// printf(" %12" PRIu64 ", %12" PRIu64 ", %12" PRIu64 ", exp_brute: %12.0f\n", 
			// nonces[best_byte].sum_a8_guess[0].num_states, 
			// nonces[best_byte].sum_a8_guess[1].num_states,
			// nonces[best_byte].sum_a8_guess[2].num_states,
			// nonces[best_byte].expected_num_brute_force);
	// }

 	// printf("\nTests: Actual BitFlipProperties of best byte:\n");
	// printf("[%02x]:", best_first_bytes[0]);
	// for (uint16_t bitflip_idx = 0; bitflip_idx < num_all_effective_bitflips; bitflip_idx++) {
		// uint16_t bitflip_prop = all_effective_bitflip[bitflip_idx];
		// if (nonces[best_first_bytes[0]].BitFlips[bitflip_prop]) {
			// printf(" %03" PRIx16 , bitflip_prop);
		// }
	// }
	// printf("\n");
	
 	// printf("\nTests2: Actual BitFlipProperties of first_byte_smallest_bitarray:\n");
	// printf("[%02x]:", best_first_byte_smallest_bitarray);
	// for (uint16_t bitflip_idx = 0; bitflip_idx < num_all_effective_bitflips; bitflip_idx++) {
		// uint16_t bitflip_prop = all_effective_bitflip[bitflip_idx];
		// if (nonces[best_first_byte_smallest_bitarray].BitFlips[bitflip_prop]) {
			// printf(" %03" PRIx16 , bitflip_prop);
		// }
	// }
	// printf("\n");

	if (known_target_key != -1) {
		for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
			uint32_t *bitset = nonces[best_first_bytes[0]].states_bitarray[odd_even];
			if (!test_bit24(bitset, test_state[odd_even])) {
				printf("\nBUG: known target key's %s state is not member of first nonce byte's (0x%02x) states_bitarray!\n", 
					odd_even==EVEN_STATE?"even":"odd ", 
					best_first_bytes[0]);
			}
		}
	}

	if (known_target_key != -1) {
		for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
			uint32_t *bitset = all_bitflips_bitarray[odd_even];
			if (!test_bit24(bitset, test_state[odd_even])) {
				printf("\nBUG: known target key's %s state is not member of all_bitflips_bitarray!\n", 
					odd_even==EVEN_STATE?"even":"odd ");
			}
		}
	}	

 	// if (known_target_key != -1) {
		// int16_t p = -1, q = -1, r = -1, s = -1;

		// printf("\nTests: known target key is member of these partial sum_a0 bitsets:\n");
		// for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
			// printf("%s", odd_even==EVEN_STATE?"even:":"odd: ");
			// for (uint16_t i = 0; i < NUM_PART_SUMS; i++) {
				// uint32_t *bitset = part_sum_a0_bitarrays[odd_even][i];
				// if (test_bit24(bitset, test_state[odd_even])) {
					// printf("%d ", i);
					// if (odd_even == ODD_STATE) {
						// p = 2*i;
					// } else {
						// q = 2*i;
					// }
				// }
			// }
			// printf("\n");
		// }

		// printf("\nTests: known target key is member of these partial sum_a8 bitsets:\n");
		// for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
			// printf("%s", odd_even==EVEN_STATE?"even:":"odd: ");
			// for (uint16_t i = 0; i < NUM_PART_SUMS; i++) {
				// uint32_t *bitset = part_sum_a8_bitarrays[odd_even][i];
				// if (test_bit24(bitset, test_state[odd_even])) {
					// printf("%d ", i);
					// if (odd_even == ODD_STATE) {
						// r = 2*i;
					// } else {
						// s = 2*i;
					// }
				// }
			// }
			// printf("\n");
		// }

		// printf("Sum(a0) = p*(16-q) + (16-p)*q = %d*(16-%d) + (16-%d)*%d = %d\n", p, q, p, q, p*(16-q)+(16-p)*q);
		// printf("Sum(a8) = r*(16-s) + (16-r)*s = %d*(16-%d) + (16-%d)*%d = %d\n", r, s, r, s, r*(16-s)+(16-r)*s);
	// }
	
	/* 	printf("\nTests: parity performance\n");
	uint64_t time1p = msclock();
	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)(msclock() - time1p)/1000.0);

	time1p = msclock();
	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)(msclock() - time1p)/1000.0);
 */

}


static void Tests2(void) 
{
	if (known_target_key != -1) {
		for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
			uint32_t *bitset = nonces[best_first_byte_smallest_bitarray].states_bitarray[odd_even];
			if (!test_bit24(bitset, test_state[odd_even])) {
				printf("\nBUG: known target key's %s state is not member of first nonce byte's (0x%02x) states_bitarray!\n",
					odd_even==EVEN_STATE?"even":"odd ", 
					best_first_byte_smallest_bitarray);
			}
		}
	}	

	if (known_target_key != -1) {
		for (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
			uint32_t *bitset = all_bitflips_bitarray[odd_even];
			if (!test_bit24(bitset, test_state[odd_even])) {
				printf("\nBUG: known target key's %s state is not member of all_bitflips_bitarray!\n", 
					odd_even==EVEN_STATE?"even":"odd ");
			}
		}
	}	
	
}


static uint16_t real_sum_a8 = 0;

static void set_test_state(uint8_t byte) 
{
	struct Crypto1State *pcs;
	pcs = crypto1_create(known_target_key);
	crypto1_byte(pcs, (cuid >> 24) ^ byte, true);
	test_state[ODD_STATE] = pcs->odd & 0x00ffffff;
	test_state[EVEN_STATE] = pcs->even & 0x00ffffff;
	real_sum_a8 = SumProperty(pcs);
	crypto1_destroy(pcs);
}


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) 
{
	char progress_text[80];

	srand((unsigned) time(NULL));
	brute_force_per_second = brute_force_benchmark();
	write_stats = false;

	if (tests) {
		// set the correct locale for the stats printing
		write_stats = true;
		setlocale(LC_NUMERIC, "");
		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++) {
			start_time = msclock();
			print_progress_header();
			sprintf(progress_text, "Brute force benchmark: %1.0f million (2^%1.1f) keys/s", brute_force_per_second/1000000, log(brute_force_per_second)/log(2.0));
			hardnested_print_progress(0, progress_text, (float)(1LL<<47), 0);
			sprintf(progress_text, "Starting Test #%" PRIu32 " ...", i+1);
			hardnested_print_progress(0, progress_text, (float)(1LL<<47), 0);
			if (trgkey != NULL) {
				known_target_key = bytes_to_num(trgkey, 6);
			} else {
				known_target_key = -1;
			}

			init_bitflip_bitarrays();
			init_part_sum_bitarrays();
			init_sum_bitarrays();
			init_allbitflips_array();
			init_nonce_memory();
			update_reduction_rate(0.0, true);
			
			simulate_acquire_nonces();

			set_test_state(best_first_bytes[0]);

			Tests();
			free_bitflip_bitarrays();

			fprintf(fstats, "%" PRIu16 ";%1.1f;", sums[first_byte_Sum], log(p_K0[first_byte_Sum])/log(2.0));
			fprintf(fstats, "%" PRIu16 ";%1.1f;", sums[nonces[best_first_bytes[0]].sum_a8_guess[0].sum_a8_idx], log(p_K[nonces[best_first_bytes[0]].sum_a8_guess[0].sum_a8_idx])/log(2.0));
			fprintf(fstats, "%" PRIu16 ";", real_sum_a8);
	
#ifdef DEBUG_KEY_ELIMINATION
			failstr[0] = '\0';
#endif
			bool key_found = false;
			num_keys_tested = 0;
			uint32_t num_odd = nonces[best_first_byte_smallest_bitarray].num_states_bitarray[ODD_STATE];
			uint32_t num_even = nonces[best_first_byte_smallest_bitarray].num_states_bitarray[EVEN_STATE];
			float expected_brute_force1 = (float)num_odd * num_even / 2.0;
			float expected_brute_force2 = nonces[best_first_bytes[0]].expected_num_brute_force;
			fprintf(fstats, "%1.1f;%1.1f;", log(expected_brute_force1)/log(2.0), log(expected_brute_force2)/log(2.0));
			if (expected_brute_force1 < expected_brute_force2) {
				hardnested_print_progress(num_acquired_nonces, "(Ignoring Sum(a8) properties)", expected_brute_force1, 0);
				set_test_state(best_first_byte_smallest_bitarray);
				add_bitflip_candidates(best_first_byte_smallest_bitarray);
				Tests2();
				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));
				// fprintf("fstats, "%" PRIu64 ";", maximum_states);
				best_first_bytes[0] = best_first_byte_smallest_bitarray;
				pre_XOR_nonces();
				prepare_bf_test_nonces(nonces, best_first_bytes[0]);
				key_found = brute_force();
				free(candidates->states[ODD_STATE]);
				free(candidates->states[EVEN_STATE]);
				free_candidates_memory(candidates);
				candidates = NULL;
			} else {
				pre_XOR_nonces();
				prepare_bf_test_nonces(nonces, best_first_bytes[0]);
				for (uint8_t j = 0; j < NUM_SUMS && !key_found; j++) {
					float expected_brute_force = nonces[best_first_bytes[0]].expected_num_brute_force;
					sprintf(progress_text, "(%d. guess: Sum(a8) = %" PRIu16 ")", j+1, sums[nonces[best_first_bytes[0]].sum_a8_guess[j].sum_a8_idx]);
					hardnested_print_progress(num_acquired_nonces, progress_text, expected_brute_force, 0); 
					if (sums[nonces[best_first_bytes[0]].sum_a8_guess[j].sum_a8_idx] != real_sum_a8) {
						sprintf(progress_text, "(Estimated Sum(a8) is WRONG! Correct Sum(a8) = %" PRIu16 ")", real_sum_a8);
						hardnested_print_progress(num_acquired_nonces, progress_text, expected_brute_force, 0);
					}
					// printf("Estimated remaining states: %" PRIu64 " (2^%1.1f)\n", nonces[best_first_bytes[0]].sum_a8_guess[j].num_states, log(nonces[best_first_bytes[0]].sum_a8_guess[j].num_states)/log(2.0));
					generate_candidates(first_byte_Sum, nonces[best_first_bytes[0]].sum_a8_guess[j].sum_a8_idx);
					// printf("Time for generating key candidates list: %1.0f sec (%1.1f sec CPU)\n", difftime(time(NULL), start_time), (float)(msclock() - start_clock)/1000.0);
					key_found = brute_force();
					free_statelist_cache();
					free_candidates_memory(candidates);
					candidates = NULL;
					if (!key_found) {
						// update the statistics
						nonces[best_first_bytes[0]].sum_a8_guess[j].prob = 0;
						nonces[best_first_bytes[0]].sum_a8_guess[j].num_states = 0;
						// and calculate new expected number of brute forces
						update_expected_brute_force(best_first_bytes[0]);
					}
				}
			}
			#ifdef DEBUG_KEY_ELIMINATION
			fprintf(fstats, "%1.1f;%1.0f;%d;%s\n", log(num_keys_tested)/log(2.0), (float)num_keys_tested/brute_force_per_second, key_found, failstr);
			#else
			fprintf(fstats, "%1.0f;%d\n", log(num_keys_tested)/log(2.0), (float)num_keys_tested/brute_force_per_second, key_found);
			#endif
			
			free_nonces_memory();
			free_bitarray(all_bitflips_bitarray[ODD_STATE]);
			free_bitarray(all_bitflips_bitarray[EVEN_STATE]);
			free_sum_bitarrays();
			free_part_sum_bitarrays();
		}
		fclose(fstats);
	} else {
		start_time = msclock();
		print_progress_header();
		sprintf(progress_text, "Brute force benchmark: %1.0f million (2^%1.1f) keys/s", brute_force_per_second/1000000, log(brute_force_per_second)/log(2.0));
		hardnested_print_progress(0, progress_text, (float)(1LL<<47), 0);
		init_bitflip_bitarrays();
		init_part_sum_bitarrays();
		init_sum_bitarrays();
		init_allbitflips_array();
		init_nonce_memory();
		update_reduction_rate(0.0, true);

		if (nonce_file_read) {  	// use pre-acquired data from file nonces.bin
			if (read_nonce_file() != 0) {
				return 3;
			}
			hardnested_stage = CHECK_1ST_BYTES | CHECK_2ND_BYTES;
			update_nonce_data(false);
			float brute_force;
			shrink_key_space(&brute_force);
		} 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;
			}
		}

		if (trgkey != NULL) {
			known_target_key = bytes_to_num(trgkey, 6);
			set_test_state(best_first_bytes[0]);
		} else {
			known_target_key = -1;
		}
		
		Tests();

		free_bitflip_bitarrays();
		bool key_found = false;
		num_keys_tested = 0;
		uint32_t num_odd = nonces[best_first_byte_smallest_bitarray].num_states_bitarray[ODD_STATE];
		uint32_t num_even = nonces[best_first_byte_smallest_bitarray].num_states_bitarray[EVEN_STATE];
		float expected_brute_force1 = (float)num_odd * num_even / 2.0;
		float expected_brute_force2 = nonces[best_first_bytes[0]].expected_num_brute_force;
		if (expected_brute_force1 < expected_brute_force2) {
			hardnested_print_progress(num_acquired_nonces, "(Ignoring Sum(a8) properties)", expected_brute_force1, 0);
			set_test_state(best_first_byte_smallest_bitarray);
			add_bitflip_candidates(best_first_byte_smallest_bitarray);
			Tests2();
			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));
			best_first_bytes[0] = best_first_byte_smallest_bitarray;
			pre_XOR_nonces();
			prepare_bf_test_nonces(nonces, best_first_bytes[0]);
			key_found = brute_force();
			free(candidates->states[ODD_STATE]);
			free(candidates->states[EVEN_STATE]);
			free_candidates_memory(candidates);
			candidates = NULL;
		} else {
			pre_XOR_nonces();
			prepare_bf_test_nonces(nonces, best_first_bytes[0]);
			for (uint8_t j = 0; j < NUM_SUMS && !key_found; j++) {
				float expected_brute_force = nonces[best_first_bytes[0]].expected_num_brute_force;
				sprintf(progress_text, "(%d. guess: Sum(a8) = %" PRIu16 ")", j+1, sums[nonces[best_first_bytes[0]].sum_a8_guess[j].sum_a8_idx]);
				hardnested_print_progress(num_acquired_nonces, progress_text, expected_brute_force, 0); 
				if (trgkey != NULL && sums[nonces[best_first_bytes[0]].sum_a8_guess[j].sum_a8_idx] != real_sum_a8) {
					sprintf(progress_text, "(Estimated Sum(a8) is WRONG! Correct Sum(a8) = %" PRIu16 ")", real_sum_a8);
					hardnested_print_progress(num_acquired_nonces, progress_text, expected_brute_force, 0);
				}
				// printf("Estimated remaining states: %" PRIu64 " (2^%1.1f)\n", nonces[best_first_bytes[0]].sum_a8_guess[j].num_states, log(nonces[best_first_bytes[0]].sum_a8_guess[j].num_states)/log(2.0));
				generate_candidates(first_byte_Sum, nonces[best_first_bytes[0]].sum_a8_guess[j].sum_a8_idx);
				// printf("Time for generating key candidates list: %1.0f sec (%1.1f sec CPU)\n", difftime(time(NULL), start_time), (float)(msclock() - start_clock)/1000.0);
				key_found = brute_force();
				free_statelist_cache();
				free_candidates_memory(candidates);
				candidates = NULL;
				if (!key_found) {
					// update the statistics
					nonces[best_first_bytes[0]].sum_a8_guess[j].prob = 0;
					nonces[best_first_bytes[0]].sum_a8_guess[j].num_states = 0;
					// and calculate new expected number of brute forces
					update_expected_brute_force(best_first_bytes[0]);
				}

			}
		}
		
		free_nonces_memory();
		free_bitarray(all_bitflips_bitarray[ODD_STATE]);
		free_bitarray(all_bitflips_bitarray[EVEN_STATE]);
		free_sum_bitarrays();
		free_part_sum_bitarrays();
	}

	return 0;
}