void jacobian_double(struct jacobian_point *p, const struct domain_params *dp)
{
if (gcry_mpi_cmp_ui(p->z, 0)) {
if (gcry_mpi_cmp_ui(p->y, 0)) {
gcry_mpi_t t1, t2;
t1 = gcry_mpi_snew(0);
t2 = gcry_mpi_snew(0);
gcry_mpi_mulm(t1, p->x, p->x, dp->m);
gcry_mpi_addm(t2, t1, t1, dp->m);
gcry_mpi_addm(t2, t2, t1, dp->m);
gcry_mpi_mulm(t1, p->z, p->z, dp->m);
gcry_mpi_mulm(t1, t1, t1, dp->m);
gcry_mpi_mulm(t1, t1, dp->a, dp->m);
gcry_mpi_addm(t1, t1, t2, dp->m);
gcry_mpi_mulm(p->z, p->z, p->y, dp->m);
gcry_mpi_addm(p->z, p->z, p->z, dp->m);
gcry_mpi_mulm(p->y, p->y, p->y, dp->m);
gcry_mpi_addm(p->y, p->y, p->y, dp->m);
gcry_mpi_mulm(t2, p->x, p->y, dp->m);
gcry_mpi_addm(t2, t2, t2, dp->m);
gcry_mpi_mulm(p->x, t1, t1, dp->m);
gcry_mpi_subm(p->x, p->x, t2, dp->m);
gcry_mpi_subm(p->x, p->x, t2, dp->m);
gcry_mpi_subm(t2, t2, p->x, dp->m);
gcry_mpi_mulm(t1, t1, t2, dp->m);
gcry_mpi_mulm(t2, p->y, p->y, dp->m);
gcry_mpi_addm(t2, t2, t2, dp->m);
gcry_mpi_subm(p->y, t1, t2, dp->m);
gcry_mpi_release(t1);
gcry_mpi_release(t2);
}
else
gcry_mpi_set_ui(p->z, 0);
}
}
void point_add(struct affine_point *p1, const struct affine_point *p2,
const struct domain_params *dp)
{
if (! point_is_zero(p2)) {
if (! point_is_zero(p1)) {
if (! gcry_mpi_cmp(p1->x, p2->x)) {
if (! gcry_mpi_cmp(p1->y, p2->y))
point_double(p1, dp);
else
point_load_zero(p1);
}
else {
gcry_mpi_t t;
t = gcry_mpi_snew(0);
gcry_mpi_subm(t, p1->y, p2->y, dp->m);
gcry_mpi_subm(p1->y, p1->x, p2->x, dp->m);
gcry_mpi_invm(p1->y, p1->y, dp->m);
gcry_mpi_mulm(p1->y, t, p1->y, dp->m);
gcry_mpi_mulm(t, p1->y, p1->y, dp->m);
gcry_mpi_addm(p1->x, p1->x, p2->x, dp->m);
gcry_mpi_subm(p1->x, t, p1->x, dp->m);
gcry_mpi_subm(t, p2->x, p1->x, dp->m);
gcry_mpi_mulm(p1->y, p1->y, t, dp->m);
gcry_mpi_subm(p1->y, p1->y, p2->y, dp->m);
gcry_mpi_release(t);
}
}
else
point_set(p1, p2);
}
}
int point_decompress(struct affine_point *p, const gcry_mpi_t x, int yflag,
const struct domain_params *dp)
{
gcry_mpi_t h, y;
int res;
h = gcry_mpi_snew(0);
y = gcry_mpi_snew(0);
gcry_mpi_mulm(h, x, x, dp->m);
gcry_mpi_addm(h, h, dp->a, dp->m);
gcry_mpi_mulm(h, h, x, dp->m);
gcry_mpi_addm(h, h, dp->b, dp->m);
if ((res = mod_root(y, h, dp->m)))
if ((res = (gcry_mpi_cmp_ui(y, 0) || ! yflag))) {
p->x = gcry_mpi_snew(0);
p->y = gcry_mpi_snew(0);
gcry_mpi_set(p->x, x);
if (gcry_mpi_test_bit(y, 0) == yflag)
gcry_mpi_set(p->y, y);
else
gcry_mpi_sub(p->y, dp->m, y);
assert(point_on_curve(p, dp));
}
gcry_mpi_release(h);
gcry_mpi_release(y);
return res;
}
int ECDSA_verify(const char *msg, const struct affine_point *Q,
const gcry_mpi_t sig, const struct curve_params *cp)
{
gcry_mpi_t e, r, s;
struct affine_point X1, X2;
int res = 0;
r = gcry_mpi_new(0);
s = gcry_mpi_new(0);
gcry_mpi_div(s, r, sig, cp->dp.order, 0);
if (gcry_mpi_cmp_ui(s, 0) <= 0 || gcry_mpi_cmp(s, cp->dp.order) >= 0 ||
gcry_mpi_cmp_ui(r, 0) <= 0 || gcry_mpi_cmp(r, cp->dp.order) >= 0)
goto end;
gcry_mpi_scan(&e, GCRYMPI_FMT_USG, msg, 64, NULL);
gcry_mpi_mod(e, e, cp->dp.order);
gcry_mpi_invm(s, s, cp->dp.order);
gcry_mpi_mulm(e, e, s, cp->dp.order);
X1 = pointmul(&cp->dp.base, e, &cp->dp);
gcry_mpi_mulm(e, r, s, cp->dp.order);
X2 = pointmul(Q, e, &cp->dp);
point_add(&X1, &X2, &cp->dp);
gcry_mpi_release(e);
if (! point_is_zero(&X1)) {
gcry_mpi_mod(s, X1.x, cp->dp.order);
res = ! gcry_mpi_cmp(s, r);
}
point_release(&X1);
point_release(&X2);
end:
gcry_mpi_release(r);
gcry_mpi_release(s);
return res;
}
struct affine_point jacobian_to_affine(const struct jacobian_point *p,
const struct domain_params *dp)
{
struct affine_point r = point_new();
if (gcry_mpi_cmp_ui(p->z, 0)) {
gcry_mpi_t h;
h = gcry_mpi_snew(0);
gcry_mpi_invm(h, p->z, dp->m);
gcry_mpi_mulm(r.y, h, h, dp->m);
gcry_mpi_mulm(r.x, p->x, r.y, dp->m);
gcry_mpi_mulm(r.y, r.y, h, dp->m);
gcry_mpi_mulm(r.y, r.y, p->y, dp->m);
gcry_mpi_release(h);
}
return r;
}
/* compute 2^m (mod phi(p)), for a prime p */
static gcry_mpi_t twopowmodphi(uint64_t m, const gcry_mpi_t p) {
gcry_mpi_t phi, r;
int n;
phi = gcry_mpi_new(0);
gcry_mpi_sub_ui(phi, p, 1);
/* count number of used bits in m */
for (n = 0; ((uint64_t)1 << n) <= m; n++)
;
r = gcry_mpi_new(0);
gcry_mpi_set_ui(r, 1);
while (n) { /* square and multiply algorithm for fast exponentiation */
n--;
gcry_mpi_mulm(r, r, r, phi);
if (m & ((uint64_t)1 << n)) {
gcry_mpi_add(r, r, r);
if (gcry_mpi_cmp(r, phi) >= 0)
gcry_mpi_sub(r, r, phi);
}
}
gcry_mpi_release(phi);
return r;
}
static void
do_encrypt(gcry_mpi_t a, gcry_mpi_t b, gcry_mpi_t input, ELG_public_key *pkey )
{
gcry_mpi_t k;
/* Note: maybe we should change the interface, so that it
* is possible to check that input is < p and return an
* error code.
*/
k = gen_k( pkey->p, 1 );
gcry_mpi_powm( a, pkey->g, k, pkey->p );
/* b = (y^k * input) mod p
* = ((y^k mod p) * (input mod p)) mod p
* and because input is < p
* = ((y^k mod p) * input) mod p
*/
gcry_mpi_powm( b, pkey->y, k, pkey->p );
gcry_mpi_mulm( b, b, input, pkey->p );
#if 0
if( DBG_CIPHER )
{
log_mpidump("elg encrypted y= ", pkey->y);
log_mpidump("elg encrypted p= ", pkey->p);
log_mpidump("elg encrypted k= ", k);
log_mpidump("elg encrypted M= ", input);
log_mpidump("elg encrypted a= ", a);
log_mpidump("elg encrypted b= ", b);
}
#endif
mpi_free(k);
}
int point_on_curve(const struct affine_point *p, const struct domain_params *dp)
{
int res;
if (! (res = point_is_zero(p))) {
gcry_mpi_t h1, h2;
h1 = gcry_mpi_snew(0);
h2 = gcry_mpi_snew(0);
gcry_mpi_mulm(h1, p->x, p->x, dp->m);
gcry_mpi_addm(h1, h1, dp->a, dp->m);
gcry_mpi_mulm(h1, h1, p->x, dp->m);
gcry_mpi_addm(h1, h1, dp->b, dp->m);
gcry_mpi_mulm(h2, p->y, p->y, dp->m);
res = ! gcry_mpi_cmp(h1, h2);
gcry_mpi_release(h1);
gcry_mpi_release(h2);
}
return res;
}
/* Algorithms 4.29 and 4.30 in the "Guide to Elliptic Curve Cryptography" */
gcry_mpi_t ECDSA_sign(const char *msg, const gcry_mpi_t d,
const struct curve_params *cp)
{
struct affine_point p1;
gcry_mpi_t e, k, r, s;
#if ECDSA_DETERMINISTIC
struct aes256cprng *cprng;
cprng = ecdsa_cprng_init(msg, d, cp);
#endif
r = gcry_mpi_snew(0);
s = gcry_mpi_snew(0);
Step1:
#if ECDSA_DETERMINISTIC
k = ecdsa_cprng_get_exponent(cprng, cp);
#else
k = get_random_exponent(cp);
#endif
p1 = pointmul(&cp->dp.base, k, &cp->dp);
gcry_mpi_mod(r, p1.x, cp->dp.order);
point_release(&p1);
if (! gcry_mpi_cmp_ui(r, 0)) {
gcry_mpi_release(k);
goto Step1;
}
gcry_mpi_scan(&e, GCRYMPI_FMT_USG, msg, 64, NULL);
gcry_mpi_set_flag(e, GCRYMPI_FLAG_SECURE);
gcry_mpi_mod(e, e, cp->dp.order);
gcry_mpi_mulm(s, d, r, cp->dp.order);
gcry_mpi_addm(s, s, e, cp->dp.order);
gcry_mpi_invm(e, k, cp->dp.order);
gcry_mpi_mulm(s, s, e, cp->dp.order);
gcry_mpi_release(e);
gcry_mpi_release(k);
if (! gcry_mpi_cmp_ui(s, 0))
goto Step1;
gcry_mpi_mul(s, s, cp->dp.order);
gcry_mpi_add(s, s, r);
gcry_mpi_release(r);
#if ECDSA_DETERMINISTIC
ecdsa_cprng_done(cprng);
#endif
return s;
}
/**
* Unblind a blind-signed signature. The signature should have been generated
* with #GNUNET_CRYPTO_rsa_sign() using a hash that was blinded with
* #GNUNET_CRYPTO_rsa_blind().
*
* @param sig the signature made on the blinded signature purpose
* @param bkey the blinding key used to blind the signature purpose
* @param pkey the public key of the signer
* @return unblinded signature on success, NULL on error
*/
struct GNUNET_CRYPTO_rsa_Signature *
GNUNET_CRYPTO_rsa_unblind (struct GNUNET_CRYPTO_rsa_Signature *sig,
struct GNUNET_CRYPTO_rsa_BlindingKey *bkey,
struct GNUNET_CRYPTO_rsa_PublicKey *pkey)
{
gcry_mpi_t n;
gcry_mpi_t s;
gcry_mpi_t r_inv;
gcry_mpi_t ubsig;
int ret;
struct GNUNET_CRYPTO_rsa_Signature *sret;
ret = key_from_sexp (&n, pkey->sexp, "public-key", "n");
if (0 != ret)
ret = key_from_sexp (&n, pkey->sexp, "rsa", "n");
if (0 != ret)
{
GNUNET_break_op (0);
return NULL;
}
ret = key_from_sexp (&s, sig->sexp, "sig-val", "s");
if (0 != ret)
ret = key_from_sexp (&s, sig->sexp, "rsa", "s");
if (0 != ret)
{
gcry_mpi_release (n);
GNUNET_break_op (0);
return NULL;
}
r_inv = gcry_mpi_new (0);
if (1 !=
gcry_mpi_invm (r_inv,
bkey->r,
n))
{
GNUNET_break_op (0);
gcry_mpi_release (n);
gcry_mpi_release (r_inv);
gcry_mpi_release (s);
return NULL;
}
ubsig = gcry_mpi_new (0);
gcry_mpi_mulm (ubsig, s, r_inv, n);
gcry_mpi_release (n);
gcry_mpi_release (r_inv);
gcry_mpi_release (s);
sret = GNUNET_new (struct GNUNET_CRYPTO_rsa_Signature);
GNUNET_assert (0 ==
gcry_sexp_build (&sret->sexp,
NULL,
"(sig-val (rsa (s %M)))",
ubsig));
gcry_mpi_release (ubsig);
return sret;
}
/* deterministically generate from seed/idx a quadratic residue (mod n) */
static gcry_mpi_t gensquare(const gcry_mpi_t n, const void *seed, size_t seedlen, uint32_t idx, unsigned secpar) {
size_t buflen = secpar / 8;
uint8_t buf[buflen];
gcry_mpi_t x;
det_randomize(buf, buflen, seed, seedlen, idx);
buf[0] &= 0x7f; /* clear upper bit, so that we have x < n */
x = mpi_import(buf, buflen);
assert(gcry_mpi_cmp(x, n) < 0);
gcry_mpi_mulm(x, x, x, n);
return x;
}
static bigint_t
wrap_gcry_mpi_mulm (bigint_t w, const bigint_t a, const bigint_t b,
const bigint_t m)
{
if (w == NULL)
w = _gnutls_mpi_alloc_like (m);
if (w == NULL)
return NULL;
gcry_mpi_mulm (w, a, b, m);
return w;
}
/* Compose $(xp,xq) \in Z_p \times Z_q$ into $x \in Z_n$ using Chinese Remainder Theorem */
static void CRT_compose(gcry_mpi_t *x, const gcry_mpi_t xp, const gcry_mpi_t xq, const gcry_mpi_t p, const gcry_mpi_t q) {
gcry_mpi_t a, u;
a = gcry_mpi_new(0);
u = gcry_mpi_new(0);
*x = gcry_mpi_new(0);
gcry_mpi_subm(a, xq, xp, q);
gcry_mpi_invm(u, p, q);
gcry_mpi_mulm(a, a, u, q); /* a = (xq - xp) / p (mod q) */
gcry_mpi_mul(*x, p, a);
gcry_mpi_add(*x, *x, xp); /* x = p * ((xq - xp) / p mod q) + xp */
gcry_mpi_release(a);
gcry_mpi_release(u);
}
void FSPRG_Evolve(void *state) {
gcry_mpi_t n, x;
uint16_t secpar;
uint64_t epoch;
initialize_libgcrypt();
secpar = read_secpar(state + 0);
n = mpi_import(state + 2 + 0 * secpar / 8, secpar / 8);
x = mpi_import(state + 2 + 1 * secpar / 8, secpar / 8);
epoch = uint64_import(state + 2 + 2 * secpar / 8, 8);
gcry_mpi_mulm(x, x, x, n);
epoch++;
mpi_export(state + 2 + 1 * secpar / 8, secpar / 8, x);
uint64_export(state + 2 + 2 * secpar / 8, 8, epoch);
gcry_mpi_release(n);
gcry_mpi_release(x);
}
/**
* Blinds the given message with the given blinding key
*
* @param hash hash of the message to sign
* @param bkey the blinding key
* @param pkey the public key of the signer
* @param[out] buffer set to a buffer with the blinded message to be signed
* @return number of bytes stored in @a buffer
*/
size_t
GNUNET_CRYPTO_rsa_blind (const struct GNUNET_HashCode *hash,
struct GNUNET_CRYPTO_rsa_BlindingKey *bkey,
struct GNUNET_CRYPTO_rsa_PublicKey *pkey,
char **buffer)
{
gcry_mpi_t data;
gcry_mpi_t ne[2];
gcry_mpi_t r_e;
gcry_mpi_t data_r_e;
size_t rsize;
size_t n;
gcry_error_t rc;
char *b;
int ret;
ret = key_from_sexp (ne, pkey->sexp, "public-key", "ne");
if (0 != ret)
ret = key_from_sexp (ne, pkey->sexp, "rsa", "ne");
if (0 != ret)
{
GNUNET_break (0);
*buffer = NULL;
return 0;
}
if (0 != (rc = gcry_mpi_scan (&data,
GCRYMPI_FMT_USG,
(const unsigned char *) hash,
sizeof (struct GNUNET_HashCode),
&rsize)))
{
GNUNET_break (0);
gcry_mpi_release (ne[0]);
gcry_mpi_release (ne[1]);
*buffer = NULL;
return 0;
}
r_e = gcry_mpi_new (0);
gcry_mpi_powm (r_e,
bkey->r,
ne[1],
ne[0]);
data_r_e = gcry_mpi_new (0);
gcry_mpi_mulm (data_r_e,
data,
r_e,
ne[0]);
gcry_mpi_release (data);
gcry_mpi_release (ne[0]);
gcry_mpi_release (ne[1]);
gcry_mpi_release (r_e);
gcry_mpi_print (GCRYMPI_FMT_USG,
NULL,
0,
&n,
data_r_e);
b = GNUNET_malloc (n);
rc = gcry_mpi_print (GCRYMPI_FMT_USG,
(unsigned char *) b,
n,
&rsize,
data_r_e);
gcry_mpi_release (data_r_e);
*buffer = b;
return n;
}
void attack(int i, unsigned char *digest, int hash_len){
void* dsa_buf;
gcry_sexp_t new_dsa_key_pair;
gcry_sexp_t ciphertext , plaintext, ptx2, ctx2;
gcry_sexp_t r_param, r_tilda_param;
gcry_sexp_t s_param, s_tilda_param;
gcry_sexp_t g_param;
gcry_sexp_t p_param;
gcry_sexp_t q_param;
gcry_sexp_t m_param;
gcry_sexp_t y_param;
gcry_sexp_t x_param;
gcry_sexp_t misc_param;
gcry_error_t err;
gcry_mpi_t msg_digest, m;
gcry_mpi_t r , r_tilda;
gcry_mpi_t s , s_tilda;
gcry_mpi_t g;
gcry_mpi_t p;
gcry_mpi_t q;
gcry_mpi_t y;
gcry_mpi_t x;
retrieve_key_pair(files[i]);
//*************** CORRECT SIGNATURE ********************//
//20 is the mdlen of sha1 as specified in https://lists.gnupg.org/pipermail/gnupg-devel/2013-September/027916.html
//a well formatted number for the immaediate has an even number of digits
err = gcry_sexp_build(&plaintext, NULL, "(data (flags rfc6979) (hash %s %b))" , "sha1", hash_len , digest);
err = gcry_pk_sign(&ciphertext, plaintext, dsa_key_pair);
//now let's convert the s-expression representing r into an MPI in order
//to use it in the equation of the attack
//--------- CIPHERTEXT --------------
//intercepted during some sniffing...
r_param = gcry_sexp_find_token(ciphertext, "r", 0);
r = gcry_sexp_nth_mpi ( r_param , 1, GCRYMPI_FMT_USG);
s_param = gcry_sexp_find_token(ciphertext, "s", 0);
s = gcry_sexp_nth_mpi ( s_param , 1, GCRYMPI_FMT_USG);
//--------- PUB KEY --------------
g_param = gcry_sexp_find_token(dsa_key_pair, "g", 0);
g = gcry_sexp_nth_mpi ( g_param , 1, GCRYMPI_FMT_USG);
p_param = gcry_sexp_find_token(dsa_key_pair, "p", 0);
p = gcry_sexp_nth_mpi ( p_param , 1, GCRYMPI_FMT_USG);
q_param = gcry_sexp_find_token(dsa_key_pair, "q", 0);
q = gcry_sexp_nth_mpi ( q_param , 1, GCRYMPI_FMT_USG);
y_param = gcry_sexp_find_token(dsa_key_pair, "y", 0);
y = gcry_sexp_nth_mpi ( y_param , 1, GCRYMPI_FMT_USG);
x_param = gcry_sexp_find_token(dsa_key_pair, "x", 0);
x = gcry_sexp_nth_mpi ( x_param , 1, GCRYMPI_FMT_USG);
misc_param = gcry_sexp_find_token(dsa_key_pair, "misc-key-info", 0);
//*************** FAULTY SIGNATURE ********************//
err = gcry_sexp_build(&ptx2, NULL, "(data (flags rfc6979) (hash %s %b) (attack2_byte))" , "sha1", hash_len , digest);
err = gcry_pk_sign(&ctx2, ptx2, dsa_key_pair);
s_tilda_param = gcry_sexp_find_token(ctx2, "s", 0);
s_tilda = gcry_sexp_nth_mpi ( s_tilda_param , 1, GCRYMPI_FMT_USG);
r_tilda_param = gcry_sexp_find_token(ctx2, "r", 0);
r_tilda = gcry_sexp_nth_mpi ( r_tilda_param , 1, GCRYMPI_FMT_USG);
m_param = gcry_sexp_find_token(ptx2, "hash", 0);
m = gcry_sexp_nth_mpi ( m_param , 2, GCRYMPI_FMT_USG);
//NOW LET'S START THE ATTACK
unsigned long e = 0;
unsigned int qbits = mpi_get_nbits(q);
unsigned int pbits = mpi_get_nbits(p);
int hash_len_bits = hash_len*8;
gcry_mpi_t one = gcry_mpi_set_ui(NULL, 1);
gcry_mpi_t tmp = gcry_mpi_new(qbits);
gcry_mpi_t result = gcry_mpi_new(mpi_get_nbits(s));
gcry_mpi_invm(r,r,q); // r^-1
unsigned int j;
for(e = 0; e < qbits ; e++){
gcry_mpi_t empi = gcry_mpi_set_ui(NULL,e);
gcry_mpi_t twoi = gcry_mpi_new(e);
gcry_mpi_mul_2exp(empi, one, e); // twoi = 2^e
for( j=0; j< 256 ; j++){
gcry_mpi_t jmpi = gcry_mpi_set_ui(NULL,j);
gcry_mpi_mulm(twoi,jmpi,empi,q);
//retrieve k
gcry_mpi_mulm(tmp, s_tilda, twoi, q); // s_tilda*(2^e) modq q
gcry_mpi_subm(result, s_tilda, s, q); // s_tilda - s mod q
gcry_mpi_invm(result, result, q); // (s_tilda - s mod q)^-1
gcry_mpi_mulm(result,result, tmp, q); // s_tilda*(2^3) mod q)*(s_tilda - s mod q)^-1 === k
//retrieve x
gcry_mpi_mulm(result, s, result,q); // s*k mod q
gcry_mpi_subm(result, result, m, q); // s*k - m mod q
gcry_mpi_mulm(result, result,r,q); //(s*k -m)*r^-1 mod q
err = gcry_sexp_build(&new_dsa_key_pair,NULL,
"(key-data"
" (public-key"
" (dsa(p%m)(q%m)(g%m)(y%m)))"
" (private-key"
" (dsa(p%m)(q%m)(g%m)(y%m)(x%m))))",
p,q,g,y,p,q,g,y,result);
err = gcry_pk_sign(&ctx2, plaintext, new_dsa_key_pair);
err = gcry_pk_verify(ctx2, plaintext, dsa_key_pair);
if (err) {
//puts("gcrypt: verify failed");
continue;
}
else{
printf("\n[!!!]PRIVATE KEY %d %d BITS CRACKED!!\n" , pbits,qbits );
printf("[DBG] BYTE : %d * 2^%d FAULT: k-j*2^%d\n" , j , (int)e,(int)e); //DEBUG
DEBUG_MPI_PRINT(result,"X = ");
printf("\n");
return;
}
}
}
for(e = 0; e < qbits; e++){
gcry_mpi_t empi = gcry_mpi_set_ui(NULL,e);
gcry_mpi_t twoi = gcry_mpi_new(e);
gcry_mpi_mul_2exp(empi, one, e); // twoi = 2^e
for( j=0; j< 256 ; j++){
gcry_mpi_t jmpi = gcry_mpi_set_ui(NULL,j);
gcry_mpi_mulm(twoi,jmpi,empi,q);
//retrieve k
gcry_mpi_mulm(tmp, s_tilda, twoi, q); // s_tilda*(2^e) modq q
gcry_mpi_subm(result, s, s_tilda, q); // s_tilda - s mod q
gcry_mpi_invm(result, result, q); // (s_tilda - s mod q)^-1
gcry_mpi_mulm(result,result, tmp, q); // s_tilda*(2^3) mod q)*(s_tilda - s mod q)^-1 === k
//retrieve x
gcry_mpi_mulm(result, s, result,q); // s*k mod q
gcry_mpi_subm(result, result, m, q); // s*k - m mod q
gcry_mpi_mulm(result, result,r,q); //(s*k -m)*r^-1 mod q
err = gcry_sexp_build(&new_dsa_key_pair,NULL,
"(key-data"
" (public-key"
" (dsa(p%m)(q%m)(g%m)(y%m)))"
" (private-key"
" (dsa(p%m)(q%m)(g%m)(y%m)(x%m))))",
p,q,g,y,p,q,g,y,result);
err = gcry_pk_sign(&ctx2, plaintext, new_dsa_key_pair);
err = gcry_pk_verify(ctx2, plaintext, dsa_key_pair);
if (err) {
continue;
}
else{
printf("\n[!!!]PRIVATE KEY %d %d BITS CRACKED!!\n" , pbits,qbits );
printf("[DBG] BYTE : %d * 2^%d FAULT: k+j*2^%d\n" , j , (int)e,(int)e); //DEBUG
DEBUG_MPI_PRINT(result,"X = ");
printf("\n");
return;
}
}
}
}
void jacobian_affine_point_add(struct jacobian_point *p1,
const struct affine_point *p2,
const struct domain_params *dp)
{
if (! point_is_zero(p2)) {
if (gcry_mpi_cmp_ui(p1->z, 0)) {
gcry_mpi_t t1, t2, t3;
t1 = gcry_mpi_snew(0);
t2 = gcry_mpi_snew(0);
gcry_mpi_mulm(t1, p1->z, p1->z, dp->m);
gcry_mpi_mulm(t2, t1, p2->x, dp->m);
gcry_mpi_mulm(t1, t1, p1->z, dp->m);
gcry_mpi_mulm(t1, t1, p2->y, dp->m);
if (! gcry_mpi_cmp(p1->x, t2)) {
if (! gcry_mpi_cmp(p1->y, t1))
jacobian_double(p1, dp);
else
jacobian_load_zero(p1);
}
else {
t3 = gcry_mpi_snew(0);
gcry_mpi_subm(p1->x, p1->x, t2, dp->m);
gcry_mpi_subm(p1->y, p1->y, t1, dp->m);
gcry_mpi_mulm(p1->z, p1->z, p1->x, dp->m);
gcry_mpi_mulm(t3, p1->x, p1->x, dp->m);
gcry_mpi_mulm(t2, t2, t3, dp->m);
gcry_mpi_mulm(t3, t3, p1->x, dp->m);
gcry_mpi_mulm(t1, t1, t3, dp->m);
gcry_mpi_mulm(p1->x, p1->y, p1->y, dp->m);
gcry_mpi_subm(p1->x, p1->x, t3, dp->m);
gcry_mpi_subm(p1->x, p1->x, t2, dp->m);
gcry_mpi_subm(p1->x, p1->x, t2, dp->m);
gcry_mpi_subm(t2, t2, p1->x, dp->m);
gcry_mpi_mulm(p1->y, p1->y, t2, dp->m);
gcry_mpi_subm(p1->y, p1->y, t1, dp->m);
gcry_mpi_release(t3);
}
gcry_mpi_release(t1);
gcry_mpi_release(t2);
}
else
jacobian_load_affine(p1, p2);
}
}
void attack(int i, unsigned char *digest, int hash_len){
gcry_error_t err;
gcry_sexp_t ciphertext , plaintext, ptx2, new_dsa_key_pair;
gcry_sexp_t r_param, r_tilda_param, k_tilda_param, msg_digest_param;
gcry_sexp_t s_param, s_tilda_param;
gcry_sexp_t g_param;
gcry_sexp_t p_param;
gcry_sexp_t q_param;
gcry_sexp_t x_param, y_param;
gcry_mpi_t r , r_tilda, k_tilda, x, y;
gcry_mpi_t s , s_tilda;
gcry_mpi_t g;
gcry_mpi_t p;
gcry_mpi_t q;
gcry_mpi_t msg_digest;
retrieve_key_pair(files[i]);
//*************** CORRECT SIGNATURE ********************//
//20 is the mdlen of sha1 as specified in https://lists.gnupg.org/pipermail/gnupg-devel/2013-September/027916.html
//a well formatted number for the immaediate has an even number of digits
err = gcry_sexp_build(&plaintext, NULL, "(data (flags rfc6979) (hash %s %b))" , "sha1", hash_len , digest);
err = gcry_pk_sign(&ciphertext, plaintext, dsa_key_pair);
//now let's convert the s-expression representing r into an MPI in order
//to use it in the equation of the attack
//--------- CIPHERTEXT --------------
r_param = gcry_sexp_find_token(ciphertext, "r", 0);
r = gcry_sexp_nth_mpi ( r_param , 1, GCRYMPI_FMT_USG);
s_param = gcry_sexp_find_token(ciphertext, "s", 0);
s = gcry_sexp_nth_mpi ( s_param , 1, GCRYMPI_FMT_USG);
//--------- PUB KEY --------------
g_param = gcry_sexp_find_token(dsa_key_pair, "g", 0);
g = gcry_sexp_nth_mpi ( g_param , 1, GCRYMPI_FMT_USG);
p_param = gcry_sexp_find_token(dsa_key_pair, "p", 0);
p = gcry_sexp_nth_mpi ( p_param , 1, GCRYMPI_FMT_USG);
q_param = gcry_sexp_find_token(dsa_key_pair, "q", 0);
q = gcry_sexp_nth_mpi ( q_param , 1, GCRYMPI_FMT_USG);
x_param = gcry_sexp_find_token(dsa_key_pair, "x", 0);
x = gcry_sexp_nth_mpi ( x_param , 1, GCRYMPI_FMT_USG);
y_param = gcry_sexp_find_token(dsa_key_pair, "y", 0);
y = gcry_sexp_nth_mpi ( y_param , 1, GCRYMPI_FMT_USG);
unsigned int qbits = mpi_get_nbits(q);
unsigned int pbits = mpi_get_nbits(p);
msg_digest_param = gcry_sexp_find_token(plaintext, "hash", 0);
msg_digest = gcry_sexp_nth_mpi ( msg_digest_param , 2, GCRYMPI_FMT_USG);
//*************** FAULTY SIGNATURE ********************//
err = gcry_sexp_build(&ptx2, NULL, "(data (flags rfc6979) (hash %s %b) (attack))" , "sha1", hash_len , digest);
err = gcry_pk_sign(&ciphertext, ptx2, dsa_key_pair);
s_tilda_param = gcry_sexp_find_token(ciphertext, "s", 0);
s_tilda = gcry_sexp_nth_mpi ( s_tilda_param , 1, GCRYMPI_FMT_USG);
r_tilda_param = gcry_sexp_find_token(ciphertext, "r", 0);
r_tilda = gcry_sexp_nth_mpi ( r_tilda_param , 1, GCRYMPI_FMT_USG);
k_tilda_param = gcry_sexp_find_token(ciphertext, "k", 0);
k_tilda = gcry_sexp_nth_mpi ( k_tilda_param , 1, GCRYMPI_FMT_USG);
//POC
// 1 - choose a message
// 2 - do the correct sign and obtain s and r
// 3 - do the faulty sign and obtain s_tilda and r_tilda
gcry_mpi_t tmp = gcry_mpi_new(mpi_get_nbits(p));
gcry_mpi_t result = gcry_mpi_new(mpi_get_nbits(p));
gcry_mpi_subm(tmp, s_tilda, s,q); //s-tilda -s mod q
gcry_mpi_mulm(msg_digest, msg_digest, tmp, q); //m* (s-tilda -s mod q) mod q
gcry_mpi_mulm(tmp, r_tilda, s, q); //r_tilda - s mod q
gcry_mpi_mulm(result, s_tilda, r, q); //s_tilda - r mod q
gcry_mpi_subm(result, tmp, result, q); //(r_tilda - s mod q) - (s_tilda - r mod q) mod q
gcry_mpi_invm(result,result,q); //((r_tilda - s mod q) - (s_tilda - r mod q) mod q)^-1 mod q
gcry_mpi_mulm(result, msg_digest, result, q); //( (m* (s-tilda -s mod q) mod q) * ((r_tilda - s mod q) - (s_tilda - r mod q) mod q)^-1 mod q ) mod q == x (private key)
err = gcry_sexp_build(&new_dsa_key_pair,NULL,
"(key-data"
" (public-key"
" (dsa(p%m)(q%m)(g%m)(y%m)))"
" (private-key"
" (dsa(p%m)(q%m)(g%m)(y%m)(x%m))))",
p,q,g,y,p,q,g,y,result);
err = gcry_pk_sign(&ciphertext, plaintext, new_dsa_key_pair);
err = gcry_pk_verify(ciphertext, plaintext, dsa_key_pair);
if (err) {
printf("\nSomething went wrong...\n");
exit(0);
}
if(!printed){
DEBUG_MPI_PRINT(result,"\nX = ");
printed = 1;
}
}
