/* Connert the bit string BITS of length NBITS into an octet string
with a length of (QBITS+7)/8 bytes. On success store the result at
R_FRAME. */
static gpg_err_code_t
bits2octets (unsigned char **r_frame,
const void *bits, unsigned int nbits,
gcry_mpi_t q, unsigned int qbits)
{
gpg_err_code_t rc;
gcry_mpi_t z1;
/* z1 = bits2int (b) */
rc = _gcry_mpi_scan (&z1, GCRYMPI_FMT_USG, bits, (nbits+7)/8, NULL);
if (rc)
return rc;
if (nbits > qbits)
mpi_rshift (z1, z1, nbits - qbits);
/* z2 - z1 mod q */
if (mpi_cmp (z1, q) >= 0)
mpi_sub (z1, z1, q);
/* Convert to an octet string. */
rc = int2octets (r_frame, z1, (qbits+7)/8);
mpi_free (z1);
return rc;
}
/*
* Truncate opaque hash value to qbits for DSA.
* Non-opaque input is not truncated, in hope that user
* knows what is passed. It is not possible to correctly
* trucate non-opaque inputs.
*/
gpg_err_code_t
_gcry_dsa_normalize_hash (gcry_mpi_t input,
gcry_mpi_t *out,
unsigned int qbits)
{
gpg_err_code_t rc = 0;
const void *abuf;
unsigned int abits;
gcry_mpi_t hash;
if (mpi_is_opaque (input))
{
abuf = mpi_get_opaque (input, &abits);
rc = _gcry_mpi_scan (&hash, GCRYMPI_FMT_USG, abuf, (abits+7)/8, NULL);
if (rc)
return rc;
if (abits > qbits)
mpi_rshift (hash, hash, abits - qbits);
}
else
hash = input;
*out = hash;
return rc;
}
/* < 0 means right shift, > 0 means left shift */
void
mpi_shift(const mpi *p, int bits, mpi *q)
{
if (bits < 0)
mpi_rshift(p, -bits, q);
else if (bits > 0)
mpi_lshift(p, +bits, q);
}
static void
do_rshift(void)
{
if( stackidx < 1 ) {
fputs("stack underflow\n", stderr);
return;
}
mpi_rshift( stack[stackidx-1],stack[stackidx-1], 1 );
}
/* Compute binomial coefficient N choose K. */
void
mpi_binomial(uint64_t n, uint64_t k, mpi *coeff)
{
ASSERT(coeff != NULL);
/* Trivial cases */
if (k > n) {
mpi_zero(coeff);
return;
} else if (k == 0 || k == n) {
mpi_set_u32(coeff, 1);
return;
} else if (k == 1 || k == n-1) {
mpi_set_u64(coeff, n);
return;
}
/* (N-K+1) x (N-K+2) x ... x N
N choose K = ---------------------------
1 x 2 x ... x K */
mpi_t num, den;
mpi_init_u64(num, n - k + 1);
mpi_init_u32(den, 1);
for (uint64_t i = 2; i <= k; ++i) {
mpi_mul_u64(num, n - k + i, num);
mpi_mul_u64(den, i, den);
if ((i & 31) == 0) {
unsigned digits = 0;
while ((num->digits[digits] | den->digits[digits]) == 0)
++digits;
unsigned shift = mp_digit_lsb_shift(num->digits[digits] |
den->digits[digits]);
if (digits || shift) {
mpi_rshift(num, digits * MP_DIGIT_BITS + shift, num);
mpi_rshift(den, digits * MP_DIGIT_BITS + shift, den);
}
}
}
mpi_divexact(num, den, coeff);
mpi_free(num);
mpi_free(den);
}
/*
* Generate a deterministic secret exponent K less than DSA_Q. H1 is
* the to be signed digest with a length of HLEN bytes. HALGO is the
* algorithm used to create the hash. On success the value for K is
* stored at R_K.
*/
gpg_err_code_t
_gcry_dsa_gen_rfc6979_k (gcry_mpi_t *r_k,
gcry_mpi_t dsa_q, gcry_mpi_t dsa_x,
const unsigned char *h1, unsigned int hlen,
int halgo, unsigned int extraloops)
{
gpg_err_code_t rc;
unsigned char *V = NULL;
unsigned char *K = NULL;
unsigned char *x_buf = NULL;
unsigned char *h1_buf = NULL;
gcry_md_hd_t hd = NULL;
unsigned char *t = NULL;
gcry_mpi_t k = NULL;
unsigned int tbits, qbits;
int i;
qbits = mpi_get_nbits (dsa_q);
if (!qbits || !h1 || !hlen)
return GPG_ERR_EINVAL;
if (_gcry_md_get_algo_dlen (halgo) != hlen)
return GPG_ERR_DIGEST_ALGO;
/* Step b: V = 0x01 0x01 0x01 ... 0x01 */
V = xtrymalloc (hlen);
if (!V)
{
rc = gpg_err_code_from_syserror ();
goto leave;
}
for (i=0; i < hlen; i++)
V[i] = 1;
/* Step c: K = 0x00 0x00 0x00 ... 0x00 */
K = xtrycalloc (1, hlen);
if (!K)
{
rc = gpg_err_code_from_syserror ();
goto leave;
}
rc = int2octets (&x_buf, dsa_x, (qbits+7)/8);
if (rc)
goto leave;
rc = bits2octets (&h1_buf, h1, hlen*8, dsa_q, qbits);
if (rc)
goto leave;
/* Create a handle to compute the HMACs. */
rc = _gcry_md_open (&hd, halgo, (GCRY_MD_FLAG_SECURE | GCRY_MD_FLAG_HMAC));
if (rc)
goto leave;
/* Step d: K = HMAC_K(V || 0x00 || int2octets(x) || bits2octets(h1) */
rc = _gcry_md_setkey (hd, K, hlen);
if (rc)
goto leave;
_gcry_md_write (hd, V, hlen);
_gcry_md_write (hd, "", 1);
_gcry_md_write (hd, x_buf, (qbits+7)/8);
_gcry_md_write (hd, h1_buf, (qbits+7)/8);
memcpy (K, _gcry_md_read (hd, 0), hlen);
/* Step e: V = HMAC_K(V) */
rc = _gcry_md_setkey (hd, K, hlen);
if (rc)
goto leave;
_gcry_md_write (hd, V, hlen);
memcpy (V, _gcry_md_read (hd, 0), hlen);
/* Step f: K = HMAC_K(V || 0x01 || int2octets(x) || bits2octets(h1) */
rc = _gcry_md_setkey (hd, K, hlen);
if (rc)
goto leave;
_gcry_md_write (hd, V, hlen);
_gcry_md_write (hd, "\x01", 1);
_gcry_md_write (hd, x_buf, (qbits+7)/8);
_gcry_md_write (hd, h1_buf, (qbits+7)/8);
memcpy (K, _gcry_md_read (hd, 0), hlen);
/* Step g: V = HMAC_K(V) */
rc = _gcry_md_setkey (hd, K, hlen);
if (rc)
goto leave;
_gcry_md_write (hd, V, hlen);
memcpy (V, _gcry_md_read (hd, 0), hlen);
/* Step h. */
t = xtrymalloc ((qbits+7)/8+hlen);
if (!t)
{
rc = gpg_err_code_from_syserror ();
goto leave;
}
again:
for (tbits = 0; tbits < qbits;)
{
/* V = HMAC_K(V) */
rc = _gcry_md_setkey (hd, K, hlen);
if (rc)
goto leave;
_gcry_md_write (hd, V, hlen);
memcpy (V, _gcry_md_read (hd, 0), hlen);
/* T = T || V */
memcpy (t+(tbits+7)/8, V, hlen);
tbits += 8*hlen;
}
/* k = bits2int (T) */
mpi_free (k);
k = NULL;
rc = _gcry_mpi_scan (&k, GCRYMPI_FMT_USG, t, (tbits+7)/8, NULL);
if (rc)
goto leave;
if (tbits > qbits)
mpi_rshift (k, k, tbits - qbits);
/* Check: k < q and k > 1 */
if (!(mpi_cmp (k, dsa_q) < 0 && mpi_cmp_ui (k, 0) > 0))
{
/* K = HMAC_K(V || 0x00) */
rc = _gcry_md_setkey (hd, K, hlen);
if (rc)
goto leave;
_gcry_md_write (hd, V, hlen);
_gcry_md_write (hd, "", 1);
memcpy (K, _gcry_md_read (hd, 0), hlen);
/* V = HMAC_K(V) */
rc = _gcry_md_setkey (hd, K, hlen);
if (rc)
goto leave;
_gcry_md_write (hd, V, hlen);
memcpy (V, _gcry_md_read (hd, 0), hlen);
goto again;
}
/* The caller may have requested that we introduce some extra loops.
This is for example useful if the caller wants another value for
K because the last returned one yielded an R of 0. Because this
is very unlikely we implement it in a straightforward way. */
if (extraloops)
{
extraloops--;
/* K = HMAC_K(V || 0x00) */
rc = _gcry_md_setkey (hd, K, hlen);
if (rc)
goto leave;
_gcry_md_write (hd, V, hlen);
_gcry_md_write (hd, "", 1);
memcpy (K, _gcry_md_read (hd, 0), hlen);
/* V = HMAC_K(V) */
rc = _gcry_md_setkey (hd, K, hlen);
if (rc)
goto leave;
_gcry_md_write (hd, V, hlen);
memcpy (V, _gcry_md_read (hd, 0), hlen);
goto again;
}
/* log_mpidump (" k", k); */
leave:
xfree (t);
_gcry_md_close (hd);
xfree (h1_buf);
xfree (x_buf);
xfree (K);
xfree (V);
if (rc)
mpi_free (k);
else
*r_k = k;
return rc;
}
/****************
* Calculate the multiplicative inverse X of A mod N
* That is: Find the solution x for
* 1 = (a*x) mod n
*/
int mpi_invm(MPI x, const MPI a, const MPI n)
{
/* Extended Euclid's algorithm (See TAOPC Vol II, 4.5.2, Alg X)
* modified according to Michael Penk's solution for Exercice 35
* with further enhancement */
MPI u = NULL, v = NULL;
MPI u1 = NULL, u2 = NULL, u3 = NULL;
MPI v1 = NULL, v2 = NULL, v3 = NULL;
MPI t1 = NULL, t2 = NULL, t3 = NULL;
unsigned k;
int sign;
int odd = 0;
int rc = -ENOMEM;
if (mpi_copy(&u, a) < 0)
goto cleanup;
if (mpi_copy(&v, n) < 0)
goto cleanup;
for (k = 0; !mpi_test_bit(u, 0) && !mpi_test_bit(v, 0); k++) {
if (mpi_rshift(u, u, 1) < 0)
goto cleanup;
if (mpi_rshift(v, v, 1) < 0)
goto cleanup;
}
odd = mpi_test_bit(v, 0);
u1 = mpi_alloc_set_ui(1);
if (!u1)
goto cleanup;
if (!odd) {
u2 = mpi_alloc_set_ui(0);
if (!u2)
goto cleanup;
}
if (mpi_copy(&u3, u) < 0)
goto cleanup;
if (mpi_copy(&v1, v) < 0)
goto cleanup;
if (!odd) {
v2 = mpi_alloc(mpi_get_nlimbs(u));
if (!v2)
goto cleanup;
if (mpi_sub(v2, u1, u) < 0)
goto cleanup; /* U is used as const 1 */
}
if (mpi_copy(&v3, v) < 0)
goto cleanup;
if (mpi_test_bit(u, 0)) { /* u is odd */
t1 = mpi_alloc_set_ui(0);
if (!t1)
goto cleanup;
if (!odd) {
t2 = mpi_alloc_set_ui(1);
if (!t2)
goto cleanup;
t2->sign = 1;
}
if (mpi_copy(&t3, v) < 0)
goto cleanup;
t3->sign = !t3->sign;
goto Y4;
} else {
t1 = mpi_alloc_set_ui(1);
if (!t1)
goto cleanup;
if (!odd) {
t2 = mpi_alloc_set_ui(0);
if (!t2)
goto cleanup;
}
if (mpi_copy(&t3, u) < 0)
goto cleanup;
}
do {
do {
if (!odd) {
if (mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0)) { /* one is odd */
if (mpi_add(t1, t1, v) < 0)
goto cleanup;
if (mpi_sub(t2, t2, u) < 0)
goto cleanup;
}
if (mpi_rshift(t1, t1, 1) < 0)
goto cleanup;
if (mpi_rshift(t2, t2, 1) < 0)
goto cleanup;
if (mpi_rshift(t3, t3, 1) < 0)
goto cleanup;
} else {
if (mpi_test_bit(t1, 0))
if (mpi_add(t1, t1, v) < 0)
goto cleanup;
if (mpi_rshift(t1, t1, 1) < 0)
goto cleanup;
if (mpi_rshift(t3, t3, 1) < 0)
goto cleanup;
}
Y4:
;
} while (!mpi_test_bit(t3, 0)); /* while t3 is even */
if (!t3->sign) {
if (mpi_set(u1, t1) < 0)
goto cleanup;
if (!odd)
if (mpi_set(u2, t2) < 0)
goto cleanup;
if (mpi_set(u3, t3) < 0)
goto cleanup;
} else {
if (mpi_sub(v1, v, t1) < 0)
goto cleanup;
sign = u->sign;
u->sign = !u->sign;
if (!odd)
if (mpi_sub(v2, u, t2) < 0)
goto cleanup;
u->sign = sign;
sign = t3->sign;
t3->sign = !t3->sign;
if (mpi_set(v3, t3) < 0)
goto cleanup;
t3->sign = sign;
}
if (mpi_sub(t1, u1, v1) < 0)
goto cleanup;
if (!odd)
if (mpi_sub(t2, u2, v2) < 0)
goto cleanup;
if (mpi_sub(t3, u3, v3) < 0)
goto cleanup;
if (t1->sign) {
if (mpi_add(t1, t1, v) < 0)
goto cleanup;
if (!odd)
if (mpi_sub(t2, t2, u) < 0)
goto cleanup;
}
} while (mpi_cmp_ui(t3, 0)); /* while t3 != 0 */
/* mpi_lshift( u3, k ); */
rc = mpi_set(x, u1);
cleanup:
mpi_free(u1);
mpi_free(v1);
mpi_free(t1);
if (!odd) {
mpi_free(u2);
mpi_free(v2);
mpi_free(t2);
}
mpi_free(u3);
mpi_free(v3);
mpi_free(t3);
mpi_free(u);
mpi_free(v);
return rc;
}
/****************
* Calculate the multiplicative inverse X of A mod N
* That is: Find the solution x for
* 1 = (a*x) mod n
*/
int
_gcry_mpi_invm (gcry_mpi_t x, gcry_mpi_t a, gcry_mpi_t n)
{
#if 0
gcry_mpi_t u, v, u1, u2, u3, v1, v2, v3, q, t1, t2, t3;
gcry_mpi_t ta, tb, tc;
u = mpi_copy(a);
v = mpi_copy(n);
u1 = mpi_alloc_set_ui(1);
u2 = mpi_alloc_set_ui(0);
u3 = mpi_copy(u);
v1 = mpi_alloc_set_ui(0);
v2 = mpi_alloc_set_ui(1);
v3 = mpi_copy(v);
q = mpi_alloc( mpi_get_nlimbs(u)+1 );
t1 = mpi_alloc( mpi_get_nlimbs(u)+1 );
t2 = mpi_alloc( mpi_get_nlimbs(u)+1 );
t3 = mpi_alloc( mpi_get_nlimbs(u)+1 );
while( mpi_cmp_ui( v3, 0 ) ) {
mpi_fdiv_q( q, u3, v3 );
mpi_mul(t1, v1, q); mpi_mul(t2, v2, q); mpi_mul(t3, v3, q);
mpi_sub(t1, u1, t1); mpi_sub(t2, u2, t2); mpi_sub(t3, u3, t3);
mpi_set(u1, v1); mpi_set(u2, v2); mpi_set(u3, v3);
mpi_set(v1, t1); mpi_set(v2, t2); mpi_set(v3, t3);
}
/* log_debug("result:\n");
log_mpidump("q =", q );
log_mpidump("u1=", u1);
log_mpidump("u2=", u2);
log_mpidump("u3=", u3);
log_mpidump("v1=", v1);
log_mpidump("v2=", v2); */
mpi_set(x, u1);
mpi_free(u1);
mpi_free(u2);
mpi_free(u3);
mpi_free(v1);
mpi_free(v2);
mpi_free(v3);
mpi_free(q);
mpi_free(t1);
mpi_free(t2);
mpi_free(t3);
mpi_free(u);
mpi_free(v);
#elif 0
/* Extended Euclid's algorithm (See TAOCP Vol II, 4.5.2, Alg X)
* modified according to Michael Penk's solution for Exercise 35 */
/* FIXME: we can simplify this in most cases (see Knuth) */
gcry_mpi_t u, v, u1, u2, u3, v1, v2, v3, t1, t2, t3;
unsigned k;
int sign;
u = mpi_copy(a);
v = mpi_copy(n);
for(k=0; !mpi_test_bit(u,0) && !mpi_test_bit(v,0); k++ ) {
mpi_rshift(u, u, 1);
mpi_rshift(v, v, 1);
}
u1 = mpi_alloc_set_ui(1);
u2 = mpi_alloc_set_ui(0);
u3 = mpi_copy(u);
v1 = mpi_copy(v); /* !-- used as const 1 */
v2 = mpi_alloc( mpi_get_nlimbs(u) ); mpi_sub( v2, u1, u );
v3 = mpi_copy(v);
if( mpi_test_bit(u, 0) ) { /* u is odd */
t1 = mpi_alloc_set_ui(0);
t2 = mpi_alloc_set_ui(1); t2->sign = 1;
t3 = mpi_copy(v); t3->sign = !t3->sign;
goto Y4;
}
else {
t1 = mpi_alloc_set_ui(1);
t2 = mpi_alloc_set_ui(0);
t3 = mpi_copy(u);
}
do {
do {
if( mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0) ) { /* one is odd */
mpi_add(t1, t1, v);
mpi_sub(t2, t2, u);
}
mpi_rshift(t1, t1, 1);
mpi_rshift(t2, t2, 1);
mpi_rshift(t3, t3, 1);
Y4:
;
} while( !mpi_test_bit( t3, 0 ) ); /* while t3 is even */
if( !t3->sign ) {
mpi_set(u1, t1);
mpi_set(u2, t2);
mpi_set(u3, t3);
}
else {
mpi_sub(v1, v, t1);
sign = u->sign; u->sign = !u->sign;
mpi_sub(v2, u, t2);
u->sign = sign;
sign = t3->sign; t3->sign = !t3->sign;
mpi_set(v3, t3);
t3->sign = sign;
}
mpi_sub(t1, u1, v1);
mpi_sub(t2, u2, v2);
mpi_sub(t3, u3, v3);
if( t1->sign ) {
mpi_add(t1, t1, v);
mpi_sub(t2, t2, u);
}
} while( mpi_cmp_ui( t3, 0 ) ); /* while t3 != 0 */
/* mpi_lshift( u3, k ); */
mpi_set(x, u1);
mpi_free(u1);
mpi_free(u2);
mpi_free(u3);
mpi_free(v1);
mpi_free(v2);
mpi_free(v3);
mpi_free(t1);
mpi_free(t2);
mpi_free(t3);
#else
/* Extended Euclid's algorithm (See TAOCP Vol II, 4.5.2, Alg X)
* modified according to Michael Penk's solution for Exercise 35
* with further enhancement */
gcry_mpi_t u, v, u1, u2=NULL, u3, v1, v2=NULL, v3, t1, t2=NULL, t3;
unsigned k;
int sign;
int odd ;
if (!mpi_cmp_ui (a, 0))
return 0; /* Inverse does not exists. */
if (!mpi_cmp_ui (n, 1))
return 0; /* Inverse does not exists. */
u = mpi_copy(a);
v = mpi_copy(n);
for(k=0; !mpi_test_bit(u,0) && !mpi_test_bit(v,0); k++ ) {
mpi_rshift(u, u, 1);
mpi_rshift(v, v, 1);
}
odd = mpi_test_bit(v,0);
u1 = mpi_alloc_set_ui(1);
if( !odd )
u2 = mpi_alloc_set_ui(0);
u3 = mpi_copy(u);
v1 = mpi_copy(v);
if( !odd ) {
v2 = mpi_alloc( mpi_get_nlimbs(u) );
mpi_sub( v2, u1, u ); /* U is used as const 1 */
}
v3 = mpi_copy(v);
if( mpi_test_bit(u, 0) ) { /* u is odd */
t1 = mpi_alloc_set_ui(0);
if( !odd ) {
t2 = mpi_alloc_set_ui(1); t2->sign = 1;
}
t3 = mpi_copy(v); t3->sign = !t3->sign;
goto Y4;
}
else {
t1 = mpi_alloc_set_ui(1);
if( !odd )
t2 = mpi_alloc_set_ui(0);
t3 = mpi_copy(u);
}
do {
do {
if( !odd ) {
if( mpi_test_bit(t1, 0) || mpi_test_bit(t2, 0) ) { /* one is odd */
mpi_add(t1, t1, v);
mpi_sub(t2, t2, u);
}
mpi_rshift(t1, t1, 1);
mpi_rshift(t2, t2, 1);
mpi_rshift(t3, t3, 1);
}
else {
if( mpi_test_bit(t1, 0) )
mpi_add(t1, t1, v);
mpi_rshift(t1, t1, 1);
mpi_rshift(t3, t3, 1);
}
Y4:
;
} while( !mpi_test_bit( t3, 0 ) ); /* while t3 is even */
if( !t3->sign ) {
mpi_set(u1, t1);
if( !odd )
mpi_set(u2, t2);
mpi_set(u3, t3);
}
else {
mpi_sub(v1, v, t1);
sign = u->sign; u->sign = !u->sign;
if( !odd )
mpi_sub(v2, u, t2);
u->sign = sign;
sign = t3->sign; t3->sign = !t3->sign;
mpi_set(v3, t3);
t3->sign = sign;
}
mpi_sub(t1, u1, v1);
if( !odd )
mpi_sub(t2, u2, v2);
mpi_sub(t3, u3, v3);
if( t1->sign ) {
mpi_add(t1, t1, v);
if( !odd )
mpi_sub(t2, t2, u);
}
} while( mpi_cmp_ui( t3, 0 ) ); /* while t3 != 0 */
/* mpi_lshift( u3, k ); */
mpi_set(x, u1);
mpi_free(u1);
mpi_free(v1);
mpi_free(t1);
if( !odd ) {
mpi_free(u2);
mpi_free(v2);
mpi_free(t2);
}
mpi_free(u3);
mpi_free(v3);
mpi_free(t3);
mpi_free(u);
mpi_free(v);
#endif
return 1;
}
