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https://github.com/Proxmark/proxmark3.git
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implementing hf mf hardnested:
- generated statelist with bitflip nonces - check first nonce bytes for bitflip property - select more than one "best" first bytes
This commit is contained in:
pwpiwi
parent
eeb1816533
commit
83b19f1a46
1 changed files with 171 additions and 58 deletions
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@ -25,6 +25,41 @@
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#include "util.h"
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#include "nonce2key/crapto1.h"
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static const float p_K[257] = { // the probability that a random nonce has a Sum Property == K
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0.0290, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0083, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0006, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0339, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0048, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0934, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0119, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0489, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0602, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.4180, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0602, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0489, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0119, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0934, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0048, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0339, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0006, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0083, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0290 };
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typedef struct noncelistentry {
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uint32_t nonce_enc;
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@ -36,6 +71,7 @@ typedef struct noncelist {
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uint16_t num;
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uint16_t Sum;
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uint16_t Sum8_guess;
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uint8_t BitFlip[2];
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float Sum8_prob;
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bool updated;
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noncelistentry_t *first;
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@ -50,6 +86,9 @@ static uint8_t best_first_byte;
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static uint16_t guessed_Sum8;
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static float guessed_Sum8_confidence;
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#define MAX_BEST_BYTES 20
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static uint8_t best_first_bytes[MAX_BEST_BYTES];
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typedef enum {
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EVEN_STATE = 0,
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@ -74,6 +113,7 @@ typedef struct {
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partial_indexed_statelist_t partial_statelist_odd[17];
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partial_indexed_statelist_t partial_statelist_even[17];
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partial_indexed_statelist_t statelist_bitflip;
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statelist_t *candidates = NULL;
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@ -211,49 +251,16 @@ static float sum_probability(uint16_t K, uint16_t n, uint16_t k)
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{
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const uint16_t N = 256;
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const float p[257] = {
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0.0290, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0083, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0006, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0339, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0048, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0934, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0119, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0489, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0602, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.4180, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0602, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0489, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0119, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0934, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0048, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0339, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0006, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0083, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
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0.02900 };
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if (k > K || p[K] == 0.0) return 0.0;
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if (k > K || p_K[K] == 0.0) return 0.0;
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double p_T_is_k_when_S_is_K = p_hypergeometric(N, K, n, k);
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double p_S_is_K = p[K];
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double p_S_is_K = p_K[K];
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double p_T_is_k = 0;
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for (uint16_t i = 0; i <= 256; i++) {
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if (p[i] != 0.0) {
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p_T_is_k += p[i] * p_hypergeometric(N, i, n, k);
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if (p_K[i] != 0.0) {
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p_T_is_k += p_K[i] * p_hypergeometric(N, i, n, k);
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}
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}
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return(p_T_is_k_when_S_is_K * p_S_is_K / p_T_is_k);
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@ -355,12 +362,54 @@ static void Tests()
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SumProperty(pcs), pcs->odd & 0x00ffffff, pcs->even & 0x00ffffff);
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crypto1_destroy(pcs);
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printf("\nTests: BitFlipProperties odd/even:\n");
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for (uint16_t i = 0; i < 256; i++) {
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printf("[%3d]:%c%c ", i, nonces[i].BitFlip[ODD_STATE]?'o':' ', nonces[i].BitFlip[EVEN_STATE]?'e':' ');
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if (i % 8 == 7) {
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printf("\n");
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}
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}
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printf("\nTests: number of states with BitFlipProperty: %d, (= %1.3f%% of total states)\n", statelist_bitflip.len, 100.0 * statelist_bitflip.len / (1<<20));
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printf("\nTests: Best %d first bytes:\n", MAX_BEST_BYTES);
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for (uint16_t i = 0; i < MAX_BEST_BYTES; i++) {
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uint8_t best_byte = best_first_bytes[i];
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uint16_t best_num = nonces[best_byte].num;
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uint16_t best_sum = nonces[best_byte].Sum;
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uint16_t best_sum8 = nonces[best_byte].Sum8_guess;
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float confidence = nonces[best_byte].Sum8_prob;
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printf("Byte: %02x, n = %2d, k = %2d, Sum(a8): %3d, Confidence: %2.1f%%\n", best_byte, best_num, best_sum, best_sum8, confidence*100);
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}
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}
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static void sort_best_first_bytes(void)
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{
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for (uint16_t i = 0; i < 256; i++ ) {
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uint16_t j = 0;
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float prob1 = nonces[i].Sum8_prob;
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float prob2 = nonces[best_first_bytes[0]].Sum8_prob;
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while (prob1 < prob2 && j < MAX_BEST_BYTES-1) {
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prob2 = nonces[best_first_bytes[++j]].Sum8_prob;
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}
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if (prob1 >= prob2) {
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for (uint16_t k = MAX_BEST_BYTES-1; k > j; k--) {
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best_first_bytes[k] = best_first_bytes[k-1];
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}
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best_first_bytes[j] = i;
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}
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}
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}
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static float estimate_second_byte_sum(uint8_t *best_first_byte, uint16_t *best_Sum8_guess)
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{
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float max_prob = 0.0;
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for (uint16_t i = 0; i < MAX_BEST_BYTES; i++) {
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best_first_bytes[i] = 0;
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}
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for (uint16_t first_byte = 0; first_byte < 256; first_byte++) {
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float Sum8_prob = 0.0;
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uint16_t Sum8 = 0;
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@ -382,7 +431,15 @@ static float estimate_second_byte_sum(uint8_t *best_first_byte, uint16_t *best_S
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*best_Sum8_guess = nonces[first_byte].Sum8_guess;
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}
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}
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return max_prob;
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sort_best_first_bytes();
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float total_prob = 1.0;
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for (uint16_t i = 0; i < 10; i++) {
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total_prob *= nonces[best_first_bytes[i]].Sum8_prob;
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}
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return total_prob;
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}
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@ -437,12 +494,14 @@ int static acquire_nonces(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_
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uint32_t flags = 0;
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uint8_t write_buf[9];
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uint32_t total_num_nonces = 0;
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uint32_t next_thousand = 1000;
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uint32_t next_fivehundred = 500;
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uint32_t total_added_nonces = 0;
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FILE *fnonces = NULL;
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UsbCommand resp;
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#define CONFIDENCE_THRESHOLD 0.95 // Collect nonces until we are certain enough to have guessed Sum(a8) correctly
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#define CONFIDENCE_THRESHOLD 0.8 // Collect nonces until we are certain enough that the following brute force is successfull
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printf("Acquiring nonces...\n");
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clearCommandBuffer();
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@ -505,16 +564,12 @@ int static acquire_nonces(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_
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if (first_byte_num == 256 ) {
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// printf("first_byte_num = %d, first_byte_Sum = %d\n", first_byte_num, first_byte_Sum);
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float last_confidence = guessed_Sum8_confidence;
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uint16_t last_Sum8 = guessed_Sum8;
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guessed_Sum8_confidence = estimate_second_byte_sum(&best_first_byte, &guessed_Sum8);
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if (guessed_Sum8_confidence > last_confidence || guessed_Sum8 != last_Sum8 || total_num_nonces > next_thousand) {
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next_thousand = (total_num_nonces/1000+1) * 1000;
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PrintAndLog("Acquired %5d nonces (%5d with distinct bytes 0 and 1). Guessed Sum(a8) = %3d for first nonce byte = 0x%02x, probability for correct guess = %1.2f%%",
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if (total_num_nonces > next_fivehundred) {
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next_fivehundred = (total_num_nonces/500+1) * 500;
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printf("Acquired %5d nonces (%5d with distinct bytes 0 and 1). Probability that we correctly guessed Sum(a8) for ten different bytes = %1.2f%%\n",
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total_num_nonces,
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total_added_nonces,
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guessed_Sum8,
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best_first_byte,
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guessed_Sum8_confidence*100);
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}
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if (guessed_Sum8_confidence >= CONFIDENCE_THRESHOLD) {
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@ -547,6 +602,9 @@ int static acquire_nonces(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_
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static int init_partial_statelists(void)
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{
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const uint32_t sizes_odd[17] = { 125601, 0, 17607, 0, 73421, 0, 182033, 0, 248801, 0, 181737, 0, 74241, 0, 18387, 0, 126757 };
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const uint32_t sizes_even[17] = { 62862, 0, 8934, 0, 37153, 0, 89354, 0, 124401, 0, 92532, 0, 36679, 0, 9064, 0, 63318 };
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printf("Allocating memory for partial statelists...\n");
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for (uint16_t i = 0; i <= 16; i++) {
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partial_statelist_odd[i].len = 0;
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@ -554,7 +612,7 @@ static int init_partial_statelists(void)
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partial_statelist_odd[i].states = NULL;
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} else {
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// 20 Bits are relevant for odd states. Less than a half per Sum is expected
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partial_statelist_odd[i].states = malloc(sizeof(uint32_t) << 19);
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partial_statelist_odd[i].states = malloc(sizeof(uint32_t) * sizes_odd[i]);
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if (partial_statelist_odd[i].states == NULL) {
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PrintAndLog("Cannot allocate enough memory. Aborting");
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return 4;
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@ -568,7 +626,7 @@ static int init_partial_statelists(void)
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partial_statelist_even[i].states = NULL;
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} else {
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// 19 Bits are relevant for even states. Less than a half per Sum is expected
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partial_statelist_even[i].states = malloc(sizeof(uint32_t) << 18);
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partial_statelist_even[i].states = malloc(sizeof(uint32_t) * sizes_even[i]);
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if (partial_statelist_even[i].states == NULL) {
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PrintAndLog("Cannot allocate enough memory. Aborting");
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return 4;
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@ -627,6 +685,29 @@ static int init_partial_statelists(void)
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}
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static void init_BitFlip_statelist(void)
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{
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printf("Generating bitflip statelist...\n");
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uint32_t *p = statelist_bitflip.states = malloc(sizeof(uint32_t) << 20);
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uint32_t index = -1;
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for (uint32_t state = 0; state < (1 << 20); state++) {
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if (filter(state) != filter(state^1)) {
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if ((state & 0x000ff000) != index) {
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index = state & 0x000ff000;
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}
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if (statelist_bitflip.index[index >> 12] == NULL) {
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statelist_bitflip.index[index >> 12] = p;
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}
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*p++ = state;
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}
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}
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// set len and add End Of List marker
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statelist_bitflip.len = p - statelist_bitflip.states;
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*p = 0xffffffff;
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statelist_bitflip.states = realloc(statelist_bitflip.states, sizeof(uint32_t) * (statelist_bitflip.len + 1));
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}
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static void add_state(statelist_t *sl, uint32_t state, odd_even_t odd_even)
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{
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uint32_t *p;
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@ -782,7 +863,7 @@ static void generate_candidates(uint16_t sum_a0, uint16_t sum_a8)
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for (statelist_t *sl = candidates; sl != NULL; sl = sl->next) {
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maximum_states += (uint64_t)sl->len[ODD_STATE] * sl->len[EVEN_STATE] * 2;
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}
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printf("Estimated number of possible keys with S(a0) = %d AND S(a8)=%d: %lld (2^%1.1f)\n", sum_a0, sum_a8, maximum_states, log(maximum_states)/log(2.0));
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printf("Estimated number of remaining possible keys: %lld (2^%1.1f)\n", maximum_states, log(maximum_states)/log(2.0));
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TestIfKeyExists(0xffffffffffff);
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TestIfKeyExists(0xa0a1a2a3a4a5);
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@ -790,6 +871,29 @@ static void generate_candidates(uint16_t sum_a0, uint16_t sum_a8)
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}
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static void Check_for_FilterFlipProperties(void)
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{
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printf("Checking for Filter Flip Properties...\n");
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for (uint16_t i = 0; i < 256; i++) {
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nonces[i].BitFlip[ODD_STATE] = false;
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nonces[i].BitFlip[EVEN_STATE] = false;
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}
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for (uint16_t i = 0; i < 256; i++) {
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||||
uint8_t parity1 = (nonces[i].first->par_enc) >> 3; // parity of first byte
|
||||
uint8_t parity2_odd = (nonces[i^0x80].first->par_enc) >> 3; // XOR 0x80 = last bit flipped
|
||||
uint8_t parity2_even = (nonces[i^0x40].first->par_enc) >> 3; // XOR 0x40 = second last bit flipped
|
||||
|
||||
if (parity1 == parity2_odd) { // has Bit Flip Property for odd bits
|
||||
nonces[i].BitFlip[ODD_STATE] = true;
|
||||
} else if (parity1 == parity2_even) { // has Bit Flip Property for even bits
|
||||
nonces[i].BitFlip[EVEN_STATE] = true;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
int mfnestedhard(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_t trgBlockNo, uint8_t trgKeyType, bool nonce_file_read, bool nonce_file_write, bool slow)
|
||||
{
|
||||
|
||||
|
|
@ -809,6 +913,7 @@ int mfnestedhard(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_t trgBloc
|
|||
guessed_Sum8_confidence = 0.0;
|
||||
|
||||
init_partial_statelists();
|
||||
init_BitFlip_statelist();
|
||||
|
||||
if (nonce_file_read) { // use pre-acquired data from file nonces.bin
|
||||
if (read_nonce_file() != 0) {
|
||||
|
|
@ -822,18 +927,26 @@ int mfnestedhard(uint8_t blockNo, uint8_t keyType, uint8_t *key, uint8_t trgBloc
|
|||
}
|
||||
}
|
||||
|
||||
Check_for_FilterFlipProperties();
|
||||
|
||||
Tests();
|
||||
|
||||
PrintAndLog("");
|
||||
PrintAndLog("Sum(a0) = %d", first_byte_Sum);
|
||||
PrintAndLog("Guess for Sum(a8) = %d for first nonce byte = 0x%02x, n = %d, k = %d, probability for correct guess = %1.0f%%\n",
|
||||
guessed_Sum8,
|
||||
best_first_byte,
|
||||
nonces[best_first_byte].num,
|
||||
nonces[best_first_byte].Sum,
|
||||
guessed_Sum8_confidence*100);
|
||||
PrintAndLog("Best 10 first bytes: %02x, %02x, %02x, %02x, %02x, %02x, %02x, %02x, %02x, %02x",
|
||||
best_first_bytes[0],
|
||||
best_first_bytes[1],
|
||||
best_first_bytes[2],
|
||||
best_first_bytes[3],
|
||||
best_first_bytes[4],
|
||||
best_first_bytes[5],
|
||||
best_first_bytes[6],
|
||||
best_first_bytes[7],
|
||||
best_first_bytes[8],
|
||||
best_first_bytes[9] );
|
||||
PrintAndLog("Confidence that all respective Sum(a8) properties are guessed correctly: %2.1f%%", guessed_Sum8_confidence * 100);
|
||||
|
||||
generate_candidates(first_byte_Sum, guessed_Sum8);
|
||||
generate_candidates(first_byte_Sum, nonces[best_first_bytes[0]].Sum8_guess);
|
||||
|
||||
PrintAndLog("Brute force phase not yet implemented");
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue