static int build_index(const MPI *exparray, int k, int i, int t)
{
int j, bitno;
int index = 0;
bitno = t - i;
for (j = k - 1; j >= 0; j--) {
index <<= 1;
if (mpi_test_bit(exparray[j], bitno))
index |= 1;
}
return index;
}
static int
build_index( MPI *exparray, int k, int i, int t )
{
int j, bitno;
int index = 0;
bitno = t-i;
for(j=k-1; j >= 0; j-- ) {
index <<= 1;
if( mpi_test_bit( exparray[j], bitno ) )
index |= 1;
}
/*log_debug("t=%d i=%d index=%d\n", t, i, index );*/
return index;
}
/* Encode (X,Y) using the EdDSA scheme. MINLEN is the required length
in bytes for the result. If WITH_PREFIX is set the returned buffer
is prefixed with a 0x40 byte. On success 0 is returned and a
malloced buffer with the encoded point is stored at R_BUFFER; the
length of this buffer is stored at R_BUFLEN. */
static gpg_err_code_t
eddsa_encode_x_y (gcry_mpi_t x, gcry_mpi_t y, unsigned int minlen,
int with_prefix,
unsigned char **r_buffer, unsigned int *r_buflen)
{
unsigned char *rawmpi;
unsigned int rawmpilen;
int off = with_prefix? 1:0;
rawmpi = _gcry_mpi_get_buffer_extra (y, minlen, off?-1:0, &rawmpilen, NULL);
if (!rawmpi)
return gpg_err_code_from_syserror ();
if (mpi_test_bit (x, 0) && rawmpilen)
rawmpi[off + rawmpilen - 1] |= 0x80; /* Set sign bit. */
if (off)
rawmpi[0] = 0x40;
*r_buffer = rawmpi;
*r_buflen = rawmpilen + off;
return 0;
}
/* Scalar point multiplication - the main function for ECC. If takes
an integer SCALAR and a POINT as well as the usual context CTX.
RESULT will be set to the resulting point. */
void
_gcry_mpi_ec_mul_point (mpi_point_t result,
gcry_mpi_t scalar, mpi_point_t point,
mpi_ec_t ctx)
{
#if 0
/* Simple left to right binary method. GECC Algorithm 3.27 */
unsigned int nbits;
int i;
nbits = mpi_get_nbits (scalar);
mpi_set_ui (result->x, 1);
mpi_set_ui (result->y, 1);
mpi_set_ui (result->z, 0);
for (i=nbits-1; i >= 0; i--)
{
_gcry_mpi_ec_dup_point (result, result, ctx);
if (mpi_test_bit (scalar, i) == 1)
_gcry_mpi_ec_add_points (result, result, point, ctx);
}
#else
gcry_mpi_t x1, y1, z1, k, h, yy;
unsigned int i, loops;
mpi_point_struct p1, p2, p1inv;
x1 = mpi_alloc_like (ctx->p);
y1 = mpi_alloc_like (ctx->p);
h = mpi_alloc_like (ctx->p);
k = mpi_copy (scalar);
yy = mpi_copy (point->y);
if ( mpi_is_neg (k) )
{
k->sign = 0;
ec_invm (yy, yy, ctx);
}
if (!mpi_cmp_ui (point->z, 1))
{
mpi_set (x1, point->x);
mpi_set (y1, yy);
}
else
{
gcry_mpi_t z2, z3;
z2 = mpi_alloc_like (ctx->p);
z3 = mpi_alloc_like (ctx->p);
ec_mulm (z2, point->z, point->z, ctx);
ec_mulm (z3, point->z, z2, ctx);
ec_invm (z2, z2, ctx);
ec_mulm (x1, point->x, z2, ctx);
ec_invm (z3, z3, ctx);
ec_mulm (y1, yy, z3, ctx);
mpi_free (z2);
mpi_free (z3);
}
z1 = mpi_copy (mpi_const (MPI_C_ONE));
mpi_mul (h, k, mpi_const (MPI_C_THREE)); /* h = 3k */
loops = mpi_get_nbits (h);
if (loops < 2)
{
/* If SCALAR is zero, the above mpi_mul sets H to zero and thus
LOOPs will be zero. To avoid an underflow of I in the main
loop we set LOOP to 2 and the result to (0,0,0). */
loops = 2;
mpi_clear (result->x);
mpi_clear (result->y);
mpi_clear (result->z);
}
else
{
mpi_set (result->x, point->x);
mpi_set (result->y, yy);
mpi_set (result->z, point->z);
}
mpi_free (yy); yy = NULL;
p1.x = x1; x1 = NULL;
p1.y = y1; y1 = NULL;
p1.z = z1; z1 = NULL;
point_init (&p2);
point_init (&p1inv);
for (i=loops-2; i > 0; i--)
{
_gcry_mpi_ec_dup_point (result, result, ctx);
if (mpi_test_bit (h, i) == 1 && mpi_test_bit (k, i) == 0)
{
point_set (&p2, result);
_gcry_mpi_ec_add_points (result, &p2, &p1, ctx);
}
if (mpi_test_bit (h, i) == 0 && mpi_test_bit (k, i) == 1)
{
point_set (&p2, result);
/* Invert point: y = p - y mod p */
point_set (&p1inv, &p1);
ec_subm (p1inv.y, ctx->p, p1inv.y, ctx);
_gcry_mpi_ec_add_points (result, &p2, &p1inv, ctx);
}
}
point_free (&p1);
point_free (&p2);
point_free (&p1inv);
mpi_free (h);
mpi_free (k);
#endif
}
/*
* Return true if n is probably a prime
*/
static int
is_prime (gcry_mpi_t n, int steps, unsigned int *count)
{
gcry_mpi_t x = mpi_alloc( mpi_get_nlimbs( n ) );
gcry_mpi_t y = mpi_alloc( mpi_get_nlimbs( n ) );
gcry_mpi_t z = mpi_alloc( mpi_get_nlimbs( n ) );
gcry_mpi_t nminus1 = mpi_alloc( mpi_get_nlimbs( n ) );
gcry_mpi_t a2 = mpi_alloc_set_ui( 2 );
gcry_mpi_t q;
unsigned i, j, k;
int rc = 0;
unsigned nbits = mpi_get_nbits( n );
mpi_sub_ui( nminus1, n, 1 );
/* Find q and k, so that n = 1 + 2^k * q . */
q = mpi_copy ( nminus1 );
k = mpi_trailing_zeros ( q );
mpi_tdiv_q_2exp (q, q, k);
for (i=0 ; i < steps; i++ )
{
++*count;
if( !i )
{
mpi_set_ui( x, 2 );
}
else
{
gcry_mpi_randomize( x, nbits, GCRY_WEAK_RANDOM );
/* Make sure that the number is smaller than the prime and
keep the randomness of the high bit. */
if ( mpi_test_bit ( x, nbits-2) )
{
mpi_set_highbit ( x, nbits-2); /* Clear all higher bits. */
}
else
{
mpi_set_highbit( x, nbits-2 );
mpi_clear_bit( x, nbits-2 );
}
assert ( mpi_cmp( x, nminus1 ) < 0 && mpi_cmp_ui( x, 1 ) > 0 );
}
gcry_mpi_powm ( y, x, q, n);
if ( mpi_cmp_ui(y, 1) && mpi_cmp( y, nminus1 ) )
{
for ( j=1; j < k && mpi_cmp( y, nminus1 ); j++ )
{
gcry_mpi_powm(y, y, a2, n);
if( !mpi_cmp_ui( y, 1 ) )
goto leave; /* Not a prime. */
}
if (mpi_cmp( y, nminus1 ) )
goto leave; /* Not a prime. */
}
progress('+');
}
rc = 1; /* May be a prime. */
leave:
mpi_free( x );
mpi_free( y );
mpi_free( z );
mpi_free( nminus1 );
mpi_free( q );
mpi_free( a2 );
return rc;
}
static gcry_mpi_t
gen_prime (unsigned int nbits, int secret, int randomlevel,
int (*extra_check)(void *, gcry_mpi_t), void *extra_check_arg)
{
gcry_mpi_t prime, ptest, pminus1, val_2, val_3, result;
int i;
unsigned int x, step;
unsigned int count1, count2;
int *mods;
/* if ( DBG_CIPHER ) */
/* log_debug ("generate a prime of %u bits ", nbits ); */
if (nbits < 16)
log_fatal ("can't generate a prime with less than %d bits\n", 16);
mods = gcry_xmalloc( no_of_small_prime_numbers * sizeof *mods );
/* Make nbits fit into gcry_mpi_t implementation. */
val_2 = mpi_alloc_set_ui( 2 );
val_3 = mpi_alloc_set_ui( 3);
prime = secret? gcry_mpi_snew ( nbits ): gcry_mpi_new ( nbits );
result = mpi_alloc_like( prime );
pminus1= mpi_alloc_like( prime );
ptest = mpi_alloc_like( prime );
count1 = count2 = 0;
for (;;)
{ /* try forvever */
int dotcount=0;
/* generate a random number */
gcry_mpi_randomize( prime, nbits, randomlevel );
/* Set high order bit to 1, set low order bit to 1. If we are
generating a secret prime we are most probably doing that
for RSA, to make sure that the modulus does have the
requested key size we set the 2 high order bits. */
mpi_set_highbit (prime, nbits-1);
if (secret)
mpi_set_bit (prime, nbits-2);
mpi_set_bit(prime, 0);
/* Calculate all remainders. */
for (i=0; (x = small_prime_numbers[i]); i++ )
mods[i] = mpi_fdiv_r_ui(NULL, prime, x);
/* Now try some primes starting with prime. */
for(step=0; step < 20000; step += 2 )
{
/* Check against all the small primes we have in mods. */
count1++;
for (i=0; (x = small_prime_numbers[i]); i++ )
{
while ( mods[i] + step >= x )
mods[i] -= x;
if ( !(mods[i] + step) )
break;
}
if ( x )
continue; /* Found a multiple of an already known prime. */
mpi_add_ui( ptest, prime, step );
/* Do a fast Fermat test now. */
count2++;
mpi_sub_ui( pminus1, ptest, 1);
gcry_mpi_powm( result, val_2, pminus1, ptest );
if ( !mpi_cmp_ui( result, 1 ) )
{
/* Not composite, perform stronger tests */
if (is_prime(ptest, 5, &count2 ))
{
if (!mpi_test_bit( ptest, nbits-1-secret ))
{
progress('\n');
log_debug ("overflow in prime generation\n");
break; /* Stop loop, continue with a new prime. */
}
if (extra_check && extra_check (extra_check_arg, ptest))
{
/* The extra check told us that this prime is
not of the caller's taste. */
progress ('/');
}
else
{
/* Got it. */
mpi_free(val_2);
mpi_free(val_3);
mpi_free(result);
mpi_free(pminus1);
mpi_free(prime);
gcry_free(mods);
return ptest;
}
}
}
if (++dotcount == 10 )
{
progress('.');
dotcount = 0;
}
}
progress(':'); /* restart with a new random value */
}
}
/*
* Generate a random secret exponent K less than Q.
* Note that ECDSA uses this code also to generate D.
*/
gcry_mpi_t
_gcry_dsa_gen_k (gcry_mpi_t q, int security_level)
{
gcry_mpi_t k = mpi_alloc_secure (mpi_get_nlimbs (q));
unsigned int nbits = mpi_get_nbits (q);
unsigned int nbytes = (nbits+7)/8;
char *rndbuf = NULL;
/* To learn why we don't use mpi_mod to get the requested bit size,
read the paper: "The Insecurity of the Digital Signature
Algorithm with Partially Known Nonces" by Nguyen and Shparlinski.
Journal of Cryptology, New York. Vol 15, nr 3 (2003) */
if (DBG_CIPHER)
log_debug ("choosing a random k of %u bits at seclevel %d\n",
nbits, security_level);
for (;;)
{
if ( !rndbuf || nbits < 32 )
{
xfree (rndbuf);
rndbuf = _gcry_random_bytes_secure (nbytes, security_level);
}
else
{ /* Change only some of the higher bits. We could improve
this by directly requesting more memory at the first call
to get_random_bytes() and use these extra bytes here.
However the required management code is more complex and
thus we better use this simple method. */
char *pp = _gcry_random_bytes_secure (4, security_level);
memcpy (rndbuf, pp, 4);
xfree (pp);
}
_gcry_mpi_set_buffer (k, rndbuf, nbytes, 0);
/* Make sure we have the requested number of bits. This code
looks a bit funny but it is easy to understand if you
consider that mpi_set_highbit clears all higher bits. We
don't have a clear_highbit, thus we first set the high bit
and then clear it again. */
if (mpi_test_bit (k, nbits-1))
mpi_set_highbit (k, nbits-1);
else
{
mpi_set_highbit (k, nbits-1);
mpi_clear_bit (k, nbits-1);
}
if (!(mpi_cmp (k, q) < 0)) /* check: k < q */
{
if (DBG_CIPHER)
log_debug ("\tk too large - again\n");
continue; /* no */
}
if (!(mpi_cmp_ui (k, 0) > 0)) /* check: k > 0 */
{
if (DBG_CIPHER)
log_debug ("\tk is zero - again\n");
continue; /* no */
}
break; /* okay */
}
xfree (rndbuf);
return k;
}
/****************
* 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;
}
/****************
* Return true if n is probably a prime
*/
static int
is_prime( MPI n, int steps, int *count )
{
MPI x = mpi_alloc( mpi_get_nlimbs( n ) );
MPI y = mpi_alloc( mpi_get_nlimbs( n ) );
MPI z = mpi_alloc( mpi_get_nlimbs( n ) );
MPI nminus1 = mpi_alloc( mpi_get_nlimbs( n ) );
MPI a2 = mpi_alloc_set_ui( 2 );
MPI q;
unsigned i, j, k;
int rc = 0;
unsigned nbits = mpi_get_nbits( n );
mpi_sub_ui( nminus1, n, 1 );
/* find q and k, so that n = 1 + 2^k * q */
q = mpi_copy( nminus1 );
k = mpi_trailing_zeros( q );
mpi_tdiv_q_2exp(q, q, k);
for(i=0 ; i < steps; i++ ) {
++*count;
if( !i ) {
mpi_set_ui( x, 2 );
}
else {
/*mpi_set_bytes( x, nbits-1, get_random_byte, 0 );*/
{ char *p = get_random_bits( nbits, 0, 0 );
mpi_set_buffer( x, p, (nbits+7)/8, 0 );
m_free(p);
}
/* make sure that the number is smaller than the prime
* and keep the randomness of the high bit */
if( mpi_test_bit( x, nbits-2 ) ) {
mpi_set_highbit( x, nbits-2 ); /* clear all higher bits */
}
else {
mpi_set_highbit( x, nbits-2 );
mpi_clear_bit( x, nbits-2 );
}
assert( mpi_cmp( x, nminus1 ) < 0 && mpi_cmp_ui( x, 1 ) > 0 );
}
mpi_powm( y, x, q, n);
if( mpi_cmp_ui(y, 1) && mpi_cmp( y, nminus1 ) ) {
for( j=1; j < k && mpi_cmp( y, nminus1 ); j++ ) {
mpi_powm(y, y, a2, n);
if( !mpi_cmp_ui( y, 1 ) )
goto leave; /* not a prime */
}
if( mpi_cmp( y, nminus1 ) )
goto leave; /* not a prime */
}
progress('+');
}
rc = 1; /* may be a prime */
leave:
mpi_free( x );
mpi_free( y );
mpi_free( z );
mpi_free( nminus1 );
mpi_free( q );
return rc;
}
static MPI
gen_prime( unsigned nbits, int secret, int randomlevel )
{
unsigned nlimbs;
MPI prime, ptest, pminus1, val_2, val_3, result;
int i;
unsigned x, step;
unsigned count1, count2;
int *mods;
if( 0 && DBG_CIPHER )
log_debug("generate a prime of %u bits ", nbits );
if( !no_of_small_prime_numbers ) {
for(i=0; small_prime_numbers[i]; i++ )
no_of_small_prime_numbers++;
}
mods = m_alloc( no_of_small_prime_numbers * sizeof *mods );
/* make nbits fit into MPI implementation */
nlimbs = (nbits + BITS_PER_MPI_LIMB - 1) / BITS_PER_MPI_LIMB;
val_2 = mpi_alloc_set_ui( 2 );
val_3 = mpi_alloc_set_ui( 3);
prime = secret? mpi_alloc_secure( nlimbs ): mpi_alloc( nlimbs );
result = mpi_alloc_like( prime );
pminus1= mpi_alloc_like( prime );
ptest = mpi_alloc_like( prime );
count1 = count2 = 0;
for(;;) { /* try forvever */
int dotcount=0;
/* generate a random number */
{ char *p = get_random_bits( nbits, randomlevel, secret );
mpi_set_buffer( prime, p, (nbits+7)/8, 0 );
m_free(p);
}
/* set high order bit to 1, set low order bit to 1 */
mpi_set_highbit( prime, nbits-1 );
mpi_set_bit( prime, 0 );
/* calculate all remainders */
for(i=0; (x = small_prime_numbers[i]); i++ )
mods[i] = mpi_fdiv_r_ui(NULL, prime, x);
/* now try some primes starting with prime */
for(step=0; step < 20000; step += 2 ) {
/* check against all the small primes we have in mods */
count1++;
for(i=0; (x = small_prime_numbers[i]); i++ ) {
while( mods[i] + step >= x )
mods[i] -= x;
if( !(mods[i] + step) )
break;
}
if( x )
continue; /* found a multiple of an already known prime */
mpi_add_ui( ptest, prime, step );
/* do a faster Fermat test */
count2++;
mpi_sub_ui( pminus1, ptest, 1);
mpi_powm( result, val_2, pminus1, ptest );
if( !mpi_cmp_ui( result, 1 ) ) { /* not composite */
/* perform stronger tests */
if( is_prime(ptest, 5, &count2 ) ) {
if( !mpi_test_bit( ptest, nbits-1 ) ) {
progress('\n');
log_debug("overflow in prime generation\n");
break; /* step loop, continue with a new prime */
}
mpi_free(val_2);
mpi_free(val_3);
mpi_free(result);
mpi_free(pminus1);
mpi_free(prime);
m_free(mods);
return ptest;
}
}
if( ++dotcount == 10 ) {
progress('.');
dotcount = 0;
}
}
progress(':'); /* restart with a new random value */
}
}
/* Recover X from Y and SIGN (which actually is a parity bit). */
gpg_err_code_t
_gcry_ecc_eddsa_recover_x (gcry_mpi_t x, gcry_mpi_t y, int sign, mpi_ec_t ec)
{
gpg_err_code_t rc = 0;
gcry_mpi_t u, v, v3, t;
static gcry_mpi_t p58, seven;
if (ec->dialect != ECC_DIALECT_ED25519)
return GPG_ERR_NOT_IMPLEMENTED;
if (!p58)
p58 = scanval ("0FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD");
if (!seven)
seven = mpi_set_ui (NULL, 7);
u = mpi_new (0);
v = mpi_new (0);
v3 = mpi_new (0);
t = mpi_new (0);
/* Compute u and v */
/* u = y^2 */
mpi_mulm (u, y, y, ec->p);
/* v = b*y^2 */
mpi_mulm (v, ec->b, u, ec->p);
/* u = y^2-1 */
mpi_sub_ui (u, u, 1);
/* v = b*y^2+1 */
mpi_add_ui (v, v, 1);
/* Compute sqrt(u/v) */
/* v3 = v^3 */
mpi_powm (v3, v, mpi_const (MPI_C_THREE), ec->p);
/* t = v3 * v3 * u * v = u * v^7 */
mpi_powm (t, v, seven, ec->p);
mpi_mulm (t, t, u, ec->p);
/* t = t^((p-5)/8) = (u * v^7)^((p-5)/8) */
mpi_powm (t, t, p58, ec->p);
/* x = t * u * v^3 = (u * v^3) * (u * v^7)^((p-5)/8) */
mpi_mulm (t, t, u, ec->p);
mpi_mulm (x, t, v3, ec->p);
/* Adjust if needed. */
/* t = v * x^2 */
mpi_mulm (t, x, x, ec->p);
mpi_mulm (t, t, v, ec->p);
/* -t == u ? x = x * sqrt(-1) */
mpi_neg (t, t);
if (!mpi_cmp (t, u))
{
static gcry_mpi_t m1; /* Fixme: this is not thread-safe. */
if (!m1)
m1 = scanval ("2B8324804FC1DF0B2B4D00993DFBD7A7"
"2F431806AD2FE478C4EE1B274A0EA0B0");
mpi_mulm (x, x, m1, ec->p);
/* t = v * x^2 */
mpi_mulm (t, x, x, ec->p);
mpi_mulm (t, t, v, ec->p);
/* -t == u ? x = x * sqrt(-1) */
mpi_neg (t, t);
if (!mpi_cmp (t, u))
rc = GPG_ERR_INV_OBJ;
}
/* Choose the desired square root according to parity */
if (mpi_test_bit (x, 0) != !!sign)
mpi_sub (x, ec->p, x);
mpi_free (t);
mpi_free (v3);
mpi_free (v);
mpi_free (u);
return rc;
}
