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cmdhfmfhard.c
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cmdhfmfhard.c
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//-----------------------------------------------------------------------------
// 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 <nfc/nfc.h>
//#include "proxmark3.h"
//#include "comms.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_bf_core.h"
#include "hardnested/hardnested_bitarray_core.h"
#include <zlib.h>
#include "hardnested/tables.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.z"
#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
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) {
switch (GetSIMDInstrAuto()) {
case SIMD_AVX512:
strcpy(instruction_set, "AVX512F");
break;
case SIMD_AVX2:
strcpy(instruction_set, "AVX2");
break;
case SIMD_AVX:
strcpy(instruction_set, "AVX");
break;
case SIMD_SSE2:
strcpy(instruction_set, "SSE2");
break;
case SIMD_MMX:
strcpy(instruction_set, "MMX");
break;
default:
strcpy(instruction_set, "no");
break;
}
}
static void print_progress_header(void) {
char progress_text[80];
char instr_set[12] = {0};
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 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
}
#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 voidpf inflate_malloc(voidpf opaque, uInt items, uInt size)
//{
// return malloc(items*size);
//}
//
//
//static void inflate_free(voidpf opaque, voidpf address)
//{
// free(address);
//}
#define OUTPUT_BUFFER_LEN 80
#define INPUT_BUFFER_LEN 80
//----------------------------------------------------------------------------
// Initialize decompression of the respective (HF or LF) FPGA stream
//----------------------------------------------------------------------------
//static void init_inflate(z_streamp compressed_stream, uint8_t *input_buffer, uint32_t insize, uint8_t *output_buffer, uint32_t outsize)
//{
//
// // initialize z_stream structure for inflate:
// compressed_stream->next_in = input_buffer;
// compressed_stream->avail_in = insize;
// compressed_stream->next_out = output_buffer;
// compressed_stream->avail_out = outsize;
// compressed_stream->zalloc = &inflate_malloc;
// compressed_stream->zfree = &inflate_free;
//
// inflateInit2(compressed_stream, 0);
//
//}
const char *get_my_executable_directory() {
char cwd[1024];
static char dir_path[sizeof (cwd) + 1];
if (getcwd(cwd, sizeof (cwd)) == NULL) {
perror("getcwd() error");
exit(EXIT_FAILURE);
}
snprintf(dir_path, sizeof dir_path, "%s%s", cwd, "/");
return dir_path;
}
static void init_bitflip_bitarrays(void) {
#if defined (DEBUG_REDUCTION)
uint8_t line = 0;
#endif
// z_stream compressed_stream;
lzma_stream strm = LZMA_STREAM_INIT;
// 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];
// bitflip_info ttt = get_bitflip(2);
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");
bitflip_info p = get_bitflip(odd_even, bitflip);
if (p.input_buffer != NULL) {
// continue;
// } else {
// fseek(statesfile, 0, SEEK_END);
// uint32_t filesize = (uint32_t)ftell(statesfile);
// rewind(statesfile);
// uint8_t input_buffer[filesize];
// size_t bytesread = fread(input_buffer, 1, filesize, statesfile);
// if (bytesread != filesize) {
// printf("File read error with %s. Aborting...\n", state_file_name);
// fclose(statesfile);
// exit(5);
// }
// fclose(statesfile);
uint32_t count = 0;
// init_inflate(&compressed_stream, input_buffer, filesize, (uint8_t *)&count, sizeof(count));
lzma_init_inflate(&strm, p.input_buffer, p.len, (uint8_t *) & count, sizeof (count));
// inflate(&compressed_stream, Z_SYNC_FLUSH);
if ((float) count / (1 << 24) < IGNORE_BITFLIP_THRESHOLD) {
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");
// inflateEnd(&compressed_stream);
lzma_end(&strm);
exit(4);
}
// compressed_stream.next_out = (uint8_t *)bitset;
// compressed_stream.avail_out = sizeof(uint32_t) * (1<<19);
// inflate(&compressed_stream, Z_SYNC_FLUSH);
lzma_init_inflate(&strm, p.input_buffer, p.len, (uint8_t *) bitset, sizeof (uint32_t) * (1 << 19));
// bitset++; //ignore first 4 bytes
effective_bitflip[odd_even][num_effective_bitflips[odd_even]++] = bitflip;
bitflip_bitarrays[odd_even][bitflip] = bitset;
bitflip_bitarrays[odd_even][bitflip]++;
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
}
// inflateEnd(&compressed_stream);
}
}
effective_bitflip[odd_even][num_effective_bitflips[odd_even]] = 0x400; // EndOfList marker
}
lzma_end(&strm);
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 (odd_even_t odd_even = EVEN_STATE; odd_even <= ODD_STATE; odd_even++) {
for (uint16_t bitflip = 0x001; bitflip < 0x400; bitflip++) {
if (bitflip_bitarrays[odd_even][bitflip] != NULL) {
bitflip_bitarrays[odd_even][bitflip]--;
free_bitarray(bitflip_bitarrays[odd_even][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);
}