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cpaAttack.c
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cpaAttack.c
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#include <stdio.h>
#include <stdbool.h>
#include <assert.h>
#include <time.h>
#include <stdlib.h>
#include <errno.h>
#include <string.h>
#include <pthread.h>
#include "NewHope/api.h"
#include "NewHope/poly.h"
#include "NewHope/cpapke.h"
#include "printParamas.h"
#define AT_SUCCESS 0
#define AT_FILE_OPEN_ERROR -1
#define AT_DATA_ERROR -3
#define AT_CRYPTO_FAILURE -4
#define printf //
static void encode_c(unsigned char *r, const poly *b, const poly *v);
// Multithreading stuff
pthread_mutex_t lock;
void * testRun(void * arg);
/***************************** Attack related *******************************/
#define SS_BITS (NEWHOPE_N/4)
#define MAX_TRIES 20
#define QUADRUPLET_SIZE 4
#define TEST_RANGE 8
#define S 1536 /** q = 8s + 1 **/
typedef struct {
int16_t l[QUADRUPLET_SIZE];
} quadruplet_t __attribute__ ((aligned (32)));
typedef struct {
bool b[TEST_RANGE];
}oracle_bitmap_t;
typedef struct {
unsigned char key[CRYPTO_BYTES];
} keyHypothesis_t;
void full_attack();
int key_recovery(poly *sk_guess, unsigned char * sk, uint16_t * n_not_recovered);
void sampleRandom(quadruplet_t * q, int16_t lower_bound, int16_t upper_bound);
void init(oracle_bitmap_t * b);
void create_attack_ct(const poly *Uhat, quadruplet_t *l, unsigned char * attack_ct);
bool checkAtBorders(quadruplet_t * l, int quadruplet_index, int16_t target_index, const poly * Uhat,
keyHypothesis_t * k, unsigned char *sk);
uint8_t testAndFindTau(int8_t *tau, uint8_t *sign_changes, quadruplet_t *l, const int quadruplet_index,
const int16_t target_index, const poly *Uhat, keyHypothesis_t *k,
oracle_bitmap_t *oracle_results, unsigned char * sk);
bool mismatchOracle(const unsigned char * ciphertext, keyHypothesis_t * hypothesis, unsigned char *sk);
int16_t find_s(const int8_t * tau);
void zero(poly * p);
void genfakeU(poly * U, int k);
void printPoly(poly * p);
/*****************************************************************************/
int main(){
if (pthread_mutex_init(&lock, NULL) != 0)
{
printf("\n mutex init failed\n");
return 1;
}
pthread_t t1, t2,t3, t4;
pthread_create(&t1, NULL, testRun, NULL);
pthread_create(&t2, NULL, testRun, NULL);
pthread_create(&t3, NULL, testRun, NULL);
pthread_create(&t4, NULL, testRun, NULL);
pthread_join(t1, NULL);
pthread_join(t2, NULL);
pthread_join(t3, NULL);
pthread_join(t4, NULL);
}
void * testRun(void * arg){
FILE * log = fopen("attack.log", "a+");
if(log == NULL){
printf("File could not open: %s", strerror(errno));
return NULL;
}
for (int i = 0; i < 20; ++i) {
full_attack(log);
}
fclose(log);
return NULL;
}
void full_attack(FILE * log) {
int ret_val;
uint16_t n_not_recovered = 0;
// unsigned char ct[CRYPTO_CIPHERTEXTBYTES], ss[CRYPTO_BYTES], ss1[CRYPTO_BYTES];
unsigned char pk[CRYPTO_PUBLICKEYBYTES], sk[CRYPTO_SECRETKEYBYTES];
poly sk_guess;
zero(&sk_guess);
srand(time(0));
// get some keys
if ( (ret_val = crypto_kem_keypair(pk, sk)) != 0) {
printf("crypto_kem_keypair returned <%d>\n", ret_val);
return;
}
// // Attack starting here
int queries = key_recovery(&sk_guess, sk, &n_not_recovered);
poly s;
poly_frombytes(&s, sk);
poly_invntt(&s);
printf("guess :[");
for(int i = 0; i < NEWHOPE_N; i++){
printf("%d, ", sk_guess.coeffs[i]);
}
printf("]\nreal s:[");
for (int j = 0; j < NEWHOPE_N; j++) {
printf("%d, ",s.coeffs[j] % NEWHOPE_Q);
}
printf("]\n");
int not_findable = 0;
int correct = 0;
for (int j = 0; j < NEWHOPE_N; j++) {
uint16_t real_coefficient = s.coeffs[j] % NEWHOPE_Q;
if(real_coefficient > 4 && real_coefficient < 12283) {
not_findable++;
} else {
if(sk_guess.coeffs[j] != real_coefficient){
printf("wrong at %d real: %d vs. %d\n", j, real_coefficient, sk_guess.coeffs[j]);
} else {
correct++;
}
}
}
printf("%d correct - %d wrong not possible: %d\n", correct, NEWHOPE_N - correct, not_findable);
pthread_mutex_lock(&lock);
fprintf(log,"%d;%d;%d;%d;%d\n",correct,NEWHOPE_N - correct, n_not_recovered, not_findable, queries);
pthread_mutex_unlock(&lock);
}
int key_recovery(poly *sk_guess, unsigned char * sk, uint16_t * n_not_recovered){
int queries = 0;
unsigned char attack_ct[CRYPTO_CIPHERTEXTBYTES];
// creating the guessed key for the hacker \nu_E = (1,0,0,...,0)
keyHypothesis_t attacker_key_hypotesis;
for(int i = 0; i < CRYPTO_BYTES; i++){
attacker_key_hypotesis.key[i] = 0;
}
attacker_key_hypotesis.key[0] = 1;
for(int k = 0; k < SS_BITS; k++){
poly Uhat;
zero(&Uhat);
genfakeU(&Uhat, k);
// printf("U: ");printPoly(&Uhat); ///DEBUG
//target the coefficients in a quadruplet after each other
for( int j = 0; j < 4; ++j){
bool not_found_yet = true;
printf("Target index:%d quadruplet index: %d \n", k, j);
//search for each index until we find it.
while (not_found_yet == true) {
int tries = 0;
uint8_t sign_change = 0;
int8_t tau[2] = {-10, -10};
while (tries < MAX_TRIES && sign_change < 2) {
quadruplet_t l;
sign_change = 0;
oracle_bitmap_t oracleErrors;
init(&oracleErrors);
sampleRandom(&l, -4, 3); //l := drawl()
//Border check ???
if(checkAtBorders(&l, j,k, &Uhat,&attacker_key_hypotesis, sk)){
printf("l:[%d, %d, %d, %d] ", l.l[0], l.l[1], l.l[2],l.l[3]);
printf("[+,");
//if the borders are ok then we have positive oracle result on the borders
oracleErrors.b[0] = oracleErrors.b[TEST_RANGE - 1] = true;
//this tries l_j \in [-3,2] and already fingers \tau_1 and \tau_2 out
queries += testAndFindTau(tau, &sign_change, &l, j, k, &Uhat, &attacker_key_hypotesis,
&oracleErrors, sk);
tries++;
printf("+] ");
}
//check borders uses 2 queries
queries +=2;
}
//check if we didn't manage to find something proper
if(tries == MAX_TRIES && tau[1] == -10){
printf("\nClould not find coefficient %d :(\n", k+(j * SS_BITS));
(*n_not_recovered)++;
not_found_yet = false;
} else {
// FindS
int16_t guess_for_s = find_s(tau);
//more complex checks here in magma but they are not executed...
// may be interesting for debug
// test_hypothesis(guess_for_s, k, j);
//saving the recovered coefficient
sk_guess->coeffs[k + (j * SS_BITS)] = ((guess_for_s + NEWHOPE_Q) % NEWHOPE_Q );
printf("s[%d] = %d", k + (j * SS_BITS), guess_for_s);
not_found_yet = false;
printf("\n");
}
}
}
}
printf("Finished hole attack took %d queries and could not find: %d coefficients\n", queries, *n_not_recovered);
return queries;
}
/**
* Queries optimizations
* Checks if we have postive result on the borders of l \in [-4,3] as this is needed for a favorable case
* Uses two oracle queries
* @param l the quadruplet values to test
* @param quadruplet_index the target index of the the quadruplet
* @param target_index the global target index in S
* @param U Attacker (Bob) public key
* @param k the guessed key
* @return
*/
bool checkAtBorders(quadruplet_t * l, const int quadruplet_index, const int16_t target_index, const poly * Uhat,
keyHypothesis_t * k, unsigned char * sk){
uint16_t backup;
bool errorLowerBound;
bool errorUpperBound;
unsigned char attack_ct[CRYPTO_CIPHERTEXTBYTES];
backup = l->l[quadruplet_index];
l->l[quadruplet_index] = -4;
create_attack_ct(Uhat, l, attack_ct);
errorLowerBound = mismatchOracle(attack_ct, k, sk);
l->l[quadruplet_index] = 3;
create_attack_ct(Uhat, l, attack_ct);
errorUpperBound = mismatchOracle(attack_ct, k, sk);
//restoring the quadruplet
l->l[quadruplet_index] = backup;
return (errorLowerBound == true) && (errorUpperBound == true);
}
/**
* Checks on the "quadruplet_index" of l in the range of [-3,2] and figures out the sign changes tau_1 and tau_2
* This function assumes the borders of the quadruplet are already checked and oracle_results contains the correct
* values
* @param tau OUTPUT tau_1 and tau_2
* @param sign_changes how often a sign change was found
* @param l current targeted quadruplet
* @param quadruplet_index the index in the quadruplet that is targeted
* @param target_index the global target index in S needed to create the ciphertext
* @param U the public key from the attacker(Bob) needed to create the ciphertext
* @param k the guessed shared secret key before hashing
* @param oracle_results the bitmap with the orecle results for this targeted quadruplet
* @return number of queries used
*/
uint8_t testAndFindTau(int8_t *tau, uint8_t *sign_changes, quadruplet_t *l, const int quadruplet_index,
const int16_t target_index, const poly *Uhat, keyHypothesis_t *k,
oracle_bitmap_t *oracle_results, unsigned char * sk) {
uint8_t queries = 0;
int16_t l_test_value = -3; //start with -3 as this
unsigned char attack_ct[CRYPTO_CIPHERTEXTBYTES];
for (int i = 1; i < TEST_RANGE - 1; ++i) {
l->l[quadruplet_index] = l_test_value;
create_attack_ct(Uhat, l, attack_ct);
oracle_results->b[i] = mismatchOracle(attack_ct, k, sk);
// printf("\n");
oracle_results->b[i] == true ? printf("+,") : printf("-,");
queries++;
//check and set tau_2 from false(0) -> true(1)
if (oracle_results->b[i-1] == false && oracle_results->b[i] == true) {
(*sign_changes)++; //should always be 2 here but this is taken from the magma code
tau[1] = l_test_value - 1; //using the test value as this closer to the paper instead of magma version
//not fully necessary but again follow the magma code
for (int r = i +1; r < TEST_RANGE - 1; ++r) {
oracle_results->b[r] = true;
}
}
//check and set tau_1 from true(1) -> false(0)
if(oracle_results->b[i-1] == true && oracle_results->b[i] == false){
(*sign_changes)++; //should be 1 here ...
tau[0] = l_test_value; //using the test value as this closer to the paper instead of magma version
}
//check if only have on time false(0) then this is the case at at i=6 under the assumtion that we stop after finding
// tau_2 otherwise
if(i == 6 && oracle_results->b[i] == false){
(*sign_changes)++;
tau[1] = l_test_value; //original is i but we are using indices starting form 0 instead of 1
}
// after 2 sign changes we have all information and can stop
// if((*sign_changes) > 1) {
// for (int j = i+1; j < TEST_RANGE - 1; ++j) {
// oracle_results->b[i] = true;
// printf("+,");
// }
// break;
// }
//update test value for next run
l_test_value++;
}
return queries;
}
/**
* Fill the given quadruplet with random numbers in the given range
* @param q
* @param lower_bound
* @param upper_bound
*/
void sampleRandom(quadruplet_t * q, int16_t lower_bound, int16_t upper_bound){
assert(lower_bound < upper_bound);
int16_t dist = upper_bound - lower_bound + 1;
for (int i = 0; i < QUADRUPLET_SIZE; ++i) {
q->l[i] = (rand() % dist) + lower_bound;
}
// ///DEBUG
// q->l[0] = 2;
// q->l[1] = 2;
// q->l[2] = 1;
// q->l[3] = -2;
}
void init(oracle_bitmap_t * b){
for (int i = 0; i < TEST_RANGE; ++i) {
b->b[i] = false;
}
}
/**
* Gernerates the fake public key from the attacker(Bob) with
* U = s/2 x^(-k)
* and converts to ntt domain
* @param output U
* @param input k
*/
void genfakeU(poly * U, int k){
zero(U);
if(k == 0){
U->coeffs[0] = S/2;
} else{
U->coeffs[NEWHOPE_N - k] = NEWHOPE_Q - (S/2);
}
poly_ntt(U);
poly_invntt(U);
poly_ntt(U);
}
/**
* Creates an ciphertext that can be used for the attack and stores it in the global attack_ct
* @param Uhat in NTT domain
* @param l
*/
void create_attack_ct(const poly * uhat, quadruplet_t *l, unsigned char * attack_ct) {
poly c;
zero(&c);
for (int i = 0; i < QUADRUPLET_SIZE; ++i) {
//the paper only says (l->l[i] + 4 % 8) but as this gets compressed, we need to "decompress first"
c.coeffs[i*SS_BITS] = ((l->l[i] + 4 % 8) * NEWHOPE_Q) / 8;
// c.coeffs[i*SS_BITS] = (l->l[i] + 4 % 8);
}
// printf("C[768]:%d\n", c.coeffs[768]);
encode_c(attack_ct, uhat, &c);
}
/**
* This takes a chiphertext and checks if this this ciphertext creates the same key than the given hypothesis
* @param ciphertext
* @param hypothesis
* @return false(0) if the keys are the same otherwise true(1)
*/
bool mismatchOracle(const unsigned char * ciphertext, keyHypothesis_t * hypothesis, unsigned char * sk){
unsigned char ss[CRYPTO_BYTES];
//first get the shared key from Alice
cpapke_dec(ss, ciphertext, sk);
// printf("compare ss: ");
// printPrams(ss, CRYPTO_BYTES);
//
// printf("\ncompare hp: ");
// printPrams(hypothesis->key, CRYPTO_BYTES);
// printf("\n");
//now compare the hypothesis with the key from alice
uint16_t errors = 0;
for (int i = 0; i < CRYPTO_BYTES; ++i) {
if (hypothesis->key[i] != ss[i]) {
if(i != 0) printf("Something strange, error outside of index 0 - %d\n", i);
errors++;
}
}
// exit(1);
return errors == 0 ? false : true;
}
/**
* Takes tau_1 and tau_2 and creates a guess for the coefficient of s according to these tau's
* This only the second half of the FindS algo from the paper
* @param tau
* @return
*/
int16_t find_s(const int8_t * tau_1_2){
int16_t tau;
int16_t guess_for_s;
if(tau_1_2[0] == -10) {
//we only got tau_2
tau = tau_1_2[1];
} else {
//the normal case
tau = tau_1_2[0] + tau_1_2[1];
}
if((tau % 2) == 0){
guess_for_s = tau;
} else {
guess_for_s = (2*(tau>>1)) + 1;
}
return guess_for_s;
}
/**
* fills the polynom with zero coefficients
* @param p
*/
void zero(poly * p){
for (int i = 0; i < NEWHOPE_N; ++i) {
p->coeffs[i] = 0;
}
}
/**
* prints all coefficients of the polynom p
* @param p
*/
void printPoly(poly * p){
printf("[");
for (int i= 0; i < NEWHOPE_N; ++i) {
printf("%d:%d ,", i,p->coeffs[i]);
}
printf("]\n");
}
/*************************************************
* Name: encode_c
*
* Description: Serialize the ciphertext as concatenation of the
* serialization of the polynomial b and serialization
* of the compressed polynomial v
*
* Arguments: - unsigned char *r: pointer to the output serialized ciphertext
* - const poly *b: pointer to the input polynomial b
* - const poly *v: pointer to the input polynomial v
**************************************************/
static void encode_c(unsigned char *r, const poly *b, const poly *v)
{
poly_tobytes(r,b);
poly_compress(r+NEWHOPE_POLYBYTES,v);
}