static void
do_inc(void)
{
if( stackidx < 1 ) {
fputs("stack underflow\n", stderr);
return;
}
mpi_add_ui( stack[stackidx-1], stack[stackidx-1], 1 );
}
/****************
* Generate a random secret exponent k from prime p, so that k is
* relatively prime to p-1. With SMALL_K set, k will be selected for
* better encryption performance - this must never be used signing!
*/
static gcry_mpi_t
gen_k( gcry_mpi_t p, int small_k )
{
gcry_mpi_t k = mpi_alloc_secure( 0 );
gcry_mpi_t temp = mpi_alloc( mpi_get_nlimbs(p) );
gcry_mpi_t p_1 = mpi_copy(p);
unsigned int orig_nbits = mpi_get_nbits(p);
unsigned int nbits, nbytes;
char *rndbuf = NULL;
if (small_k)
{
/* Using a k much lesser than p is sufficient for encryption and
* it greatly improves the encryption performance. We use
* Wiener's table and add a large safety margin. */
nbits = wiener_map( orig_nbits ) * 3 / 2;
if( nbits >= orig_nbits )
BUG();
}
else
nbits = orig_nbits;
nbytes = (nbits+7)/8;
if( DBG_CIPHER )
log_debug("choosing a random k ");
mpi_sub_ui( p_1, p, 1);
for(;;)
{
if( !rndbuf || nbits < 32 )
{
gcry_free(rndbuf);
rndbuf = gcry_random_bytes_secure( nbytes, GCRY_STRONG_RANDOM );
}
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 this the here maybe it is
easier to do this directly in random.c Anyway, it is
highly inlikely that we will ever reach this code. */
char *pp = gcry_random_bytes_secure( 4, GCRY_STRONG_RANDOM );
memcpy( rndbuf, pp, 4 );
gcry_free(pp);
}
_gcry_mpi_set_buffer( k, rndbuf, nbytes, 0 );
for(;;)
{
if( !(mpi_cmp( k, p_1 ) < 0) ) /* check: k < (p-1) */
{
if( DBG_CIPHER )
progress('+');
break; /* no */
}
if( !(mpi_cmp_ui( k, 0 ) > 0) ) /* check: k > 0 */
{
if( DBG_CIPHER )
progress('-');
break; /* no */
}
if (gcry_mpi_gcd( temp, k, p_1 ))
goto found; /* okay, k is relative prime to (p-1) */
mpi_add_ui( k, k, 1 );
if( DBG_CIPHER )
progress('.');
}
}
found:
gcry_free(rndbuf);
if( DBG_CIPHER )
progress('\n');
mpi_free(p_1);
mpi_free(temp);
return k;
}
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 */
}
}
/****************
* We do not need to use the strongest RNG because we gain no extra
* security from it - The prime number is public and we could also
* offer the factors for those who are willing to check that it is
* indeed a strong prime. With ALL_FACTORS set to true all afcors of
* prime-1 are returned in FACTORS.
*
* mode 0: Standard
* 1: Make sure that at least one factor is of size qbits.
*/
static gcry_err_code_t
prime_generate_internal (int mode,
gcry_mpi_t *prime_generated, unsigned int pbits,
unsigned int qbits, gcry_mpi_t g,
gcry_mpi_t **ret_factors,
gcry_random_level_t randomlevel, unsigned int flags,
int all_factors,
gcry_prime_check_func_t cb_func, void *cb_arg)
{
gcry_err_code_t err = 0;
gcry_mpi_t *factors_new = NULL; /* Factors to return to the
caller. */
gcry_mpi_t *factors = NULL; /* Current factors. */
gcry_mpi_t *pool = NULL; /* Pool of primes. */
unsigned char *perms = NULL; /* Permutations of POOL. */
gcry_mpi_t q_factor = NULL; /* Used if QBITS is non-zero. */
unsigned int fbits = 0; /* Length of prime factors. */
unsigned int n = 0; /* Number of factors. */
unsigned int m = 0; /* Number of primes in pool. */
gcry_mpi_t q = NULL; /* First prime factor. */
gcry_mpi_t prime = NULL; /* Prime candidate. */
unsigned int nprime = 0; /* Bits of PRIME. */
unsigned int req_qbits; /* The original QBITS value. */
gcry_mpi_t val_2; /* For check_prime(). */
unsigned int is_secret = (flags & GCRY_PRIME_FLAG_SECRET);
unsigned int count1 = 0, count2 = 0;
unsigned int i = 0, j = 0;
if (pbits < 48)
return GPG_ERR_INV_ARG;
/* If QBITS is not given, assume a reasonable value. */
if (!qbits)
qbits = pbits / 3;
req_qbits = qbits;
/* Find number of needed prime factors. */
for (n = 1; (pbits - qbits - 1) / n >= qbits; n++)
;
n--;
val_2 = mpi_alloc_set_ui (2);
if ((! n) || ((mode == 1) && (n < 2)))
{
err = GPG_ERR_INV_ARG;
goto leave;
}
if (mode == 1)
{
n--;
fbits = (pbits - 2 * req_qbits -1) / n;
qbits = pbits - req_qbits - n * fbits;
}
else
{
fbits = (pbits - req_qbits -1) / n;
qbits = pbits - n * fbits;
}
if (DBG_CIPHER)
log_debug ("gen prime: pbits=%u qbits=%u fbits=%u/%u n=%d\n",
pbits, req_qbits, qbits, fbits, n);
prime = gcry_mpi_new (pbits);
/* Generate first prime factor. */
q = gen_prime (qbits, is_secret, randomlevel, NULL, NULL);
if (mode == 1)
q_factor = gen_prime (req_qbits, is_secret, randomlevel, NULL, NULL);
/* Allocate an array to hold the factors + 2 for later usage. */
factors = gcry_calloc (n + 2, sizeof (*factors));
if (!factors)
{
err = gpg_err_code_from_errno (errno);
goto leave;
}
/* Make a pool of 3n+5 primes (this is an arbitrary value). */
m = n * 3 + 5;
if (mode == 1) /* Need some more (for e.g. DSA). */
m += 5;
if (m < 25)
m = 25;
pool = gcry_calloc (m , sizeof (*pool));
if (! pool)
{
err = gpg_err_code_from_errno (errno);
goto leave;
}
/* Permutate over the pool of primes. */
do
{
next_try:
if (! perms)
{
/* Allocate new primes. */
for(i = 0; i < m; i++)
{
mpi_free (pool[i]);
pool[i] = NULL;
}
/* Init m_out_of_n(). */
perms = gcry_calloc (1, m);
if (! perms)
{
err = gpg_err_code_from_errno (errno);
goto leave;
}
for(i = 0; i < n; i++)
{
perms[i] = 1;
pool[i] = gen_prime (fbits, is_secret,
randomlevel, NULL, NULL);
factors[i] = pool[i];
}
}
else
{
m_out_of_n ((char*)perms, n, m);
for (i = j = 0; (i < m) && (j < n); i++)
if (perms[i])
{
if(! pool[i])
pool[i] = gen_prime (fbits, 0, 1, NULL, NULL);
factors[j++] = pool[i];
}
if (i == n)
{
gcry_free (perms);
perms = NULL;
progress ('!');
goto next_try; /* Allocate new primes. */
}
}
/* Generate next prime candidate:
p = 2 * q [ * q_factor] * factor_0 * factor_1 * ... * factor_n + 1.
*/
mpi_set (prime, q);
mpi_mul_ui (prime, prime, 2);
if (mode == 1)
mpi_mul (prime, prime, q_factor);
for(i = 0; i < n; i++)
mpi_mul (prime, prime, factors[i]);
mpi_add_ui (prime, prime, 1);
nprime = mpi_get_nbits (prime);
if (nprime < pbits)
{
if (++count1 > 20)
{
count1 = 0;
qbits++;
progress('>');
mpi_free (q);
q = gen_prime (qbits, 0, 0, NULL, NULL);
goto next_try;
}
}
else
count1 = 0;
if (nprime > pbits)
{
if (++count2 > 20)
{
count2 = 0;
qbits--;
progress('<');
mpi_free (q);
q = gen_prime (qbits, 0, 0, NULL, NULL);
goto next_try;
}
}
else
count2 = 0;
}
while (! ((nprime == pbits) && check_prime (prime, val_2, cb_func, cb_arg)));
if (DBG_CIPHER)
{
progress ('\n');
log_mpidump ("prime : ", prime);
log_mpidump ("factor q: ", q);
if (mode == 1)
log_mpidump ("factor q0: ", q_factor);
for (i = 0; i < n; i++)
log_mpidump ("factor pi: ", factors[i]);
log_debug ("bit sizes: prime=%u, q=%u",
mpi_get_nbits (prime), mpi_get_nbits (q));
if (mode == 1)
log_debug (", q0=%u", mpi_get_nbits (q_factor));
for (i = 0; i < n; i++)
log_debug (", p%d=%u", i, mpi_get_nbits (factors[i]));
progress('\n');
}
if (ret_factors)
{
/* Caller wants the factors. */
factors_new = gcry_calloc (n + 4, sizeof (*factors_new));
if (! factors_new)
{
err = gpg_err_code_from_errno (errno);
goto leave;
}
if (all_factors)
{
i = 0;
factors_new[i++] = gcry_mpi_set_ui (NULL, 2);
factors_new[i++] = mpi_copy (q);
if (mode == 1)
factors_new[i++] = mpi_copy (q_factor);
for(j=0; j < n; j++)
factors_new[i++] = mpi_copy (factors[j]);
}
else
{
i = 0;
if (mode == 1)
{
factors_new[i++] = mpi_copy (q_factor);
for (; i <= n; i++)
factors_new[i] = mpi_copy (factors[i]);
}
else
for (; i < n; i++ )
factors_new[i] = mpi_copy (factors[i]);
}
}
if (g)
{
/* Create a generator (start with 3). */
gcry_mpi_t tmp = mpi_alloc (mpi_get_nlimbs (prime));
gcry_mpi_t b = mpi_alloc (mpi_get_nlimbs (prime));
gcry_mpi_t pmin1 = mpi_alloc (mpi_get_nlimbs (prime));
if (mode == 1)
err = GPG_ERR_NOT_IMPLEMENTED;
else
{
factors[n] = q;
factors[n + 1] = mpi_alloc_set_ui (2);
mpi_sub_ui (pmin1, prime, 1);
mpi_set_ui (g, 2);
do
{
mpi_add_ui (g, g, 1);
if (DBG_CIPHER)
{
log_debug ("checking g:");
gcry_mpi_dump (g);
log_printf ("\n");
}
else
progress('^');
for (i = 0; i < n + 2; i++)
{
mpi_fdiv_q (tmp, pmin1, factors[i]);
/* No mpi_pow(), but it is okay to use this with mod
prime. */
gcry_mpi_powm (b, g, tmp, prime);
if (! mpi_cmp_ui (b, 1))
break;
}
if (DBG_CIPHER)
progress('\n');
}
while (i < n + 2);
mpi_free (factors[n+1]);
mpi_free (tmp);
mpi_free (b);
mpi_free (pmin1);
}
}
if (! DBG_CIPHER)
progress ('\n');
leave:
if (pool)
{
for(i = 0; i < m; i++)
mpi_free (pool[i]);
gcry_free (pool);
}
if (factors)
gcry_free (factors); /* Factors are shallow copies. */
if (perms)
gcry_free (perms);
mpi_free (val_2);
mpi_free (q);
mpi_free (q_factor);
if (! err)
{
*prime_generated = prime;
if (ret_factors)
*ret_factors = factors_new;
}
else
{
if (factors_new)
{
for (i = 0; factors_new[i]; i++)
mpi_free (factors_new[i]);
gcry_free (factors_new);
}
mpi_free (prime);
}
return err;
}
/****************
* We do not need to use the strongest RNG because we gain no extra
* security from it - The prime number is public and we could also
* offer the factors for those who are willing to check that it is
* indeed a strong prime.
*
* mode 0: Standard
* 1: Make sure that at least one factor is of size qbits.
*/
MPI
generate_elg_prime( int mode, unsigned pbits, unsigned qbits,
MPI g, MPI **ret_factors )
{
int n; /* number of factors */
int m; /* number of primes in pool */
unsigned fbits; /* length of prime factors */
MPI *factors; /* current factors */
MPI *pool; /* pool of primes */
MPI q; /* first prime factor (variable)*/
MPI prime; /* prime test value */
MPI q_factor; /* used for mode 1 */
byte *perms = NULL;
int i, j;
int count1, count2;
unsigned nprime;
unsigned req_qbits = qbits; /* the requested q bits size */
MPI val_2 = mpi_alloc_set_ui( 2 );
/* find number of needed prime factors */
for(n=1; (pbits - qbits - 1) / n >= qbits; n++ )
;
n--;
if( !n || (mode==1 && n < 2) )
log_fatal("can't gen prime with pbits=%u qbits=%u\n", pbits, qbits );
if( mode == 1 ) {
n--;
fbits = (pbits - 2*req_qbits -1) / n;
qbits = pbits - req_qbits - n*fbits;
}
else {
fbits = (pbits - req_qbits -1) / n;
qbits = pbits - n*fbits;
}
if( DBG_CIPHER )
log_debug("gen prime: pbits=%u qbits=%u fbits=%u/%u n=%d\n",
pbits, req_qbits, qbits, fbits, n );
prime = mpi_alloc( (pbits + BITS_PER_MPI_LIMB - 1) / BITS_PER_MPI_LIMB );
q = gen_prime( qbits, 0, 0 );
q_factor = mode==1? gen_prime( req_qbits, 0, 0 ) : NULL;
/* allocate an array to hold the factors + 2 for later usage */
factors = m_alloc_clear( (n+2) * sizeof *factors );
/* make a pool of 3n+5 primes (this is an arbitrary value) */
m = n*3+5;
if( mode == 1 )
m += 5; /* need some more for DSA */
if( m < 25 )
m = 25;
pool = m_alloc_clear( m * sizeof *pool );
/* permutate over the pool of primes */
count1=count2=0;
do {
next_try:
if( !perms ) {
/* allocate new primes */
for(i=0; i < m; i++ ) {
mpi_free(pool[i]);
pool[i] = NULL;
}
/* init m_out_of_n() */
perms = m_alloc_clear( m );
for(i=0; i < n; i++ ) {
perms[i] = 1;
pool[i] = gen_prime( fbits, 0, 0 );
factors[i] = pool[i];
}
}
else {
m_out_of_n( perms, n, m );
for(i=j=0; i < m && j < n ; i++ )
if( perms[i] ) {
if( !pool[i] )
pool[i] = gen_prime( fbits, 0, 0 );
factors[j++] = pool[i];
}
if( i == n ) {
m_free(perms); perms = NULL;
progress('!');
goto next_try; /* allocate new primes */
}
}
mpi_set( prime, q );
mpi_mul_ui( prime, prime, 2 );
if( mode == 1 )
mpi_mul( prime, prime, q_factor );
for(i=0; i < n; i++ )
mpi_mul( prime, prime, factors[i] );
mpi_add_ui( prime, prime, 1 );
nprime = mpi_get_nbits(prime);
if( nprime < pbits ) {
if( ++count1 > 20 ) {
count1 = 0;
qbits++;
progress('>');
mpi_free (q);
q = gen_prime( qbits, 0, 0 );
goto next_try;
}
}
else
count1 = 0;
if( nprime > pbits ) {
if( ++count2 > 20 ) {
count2 = 0;
qbits--;
progress('<');
mpi_free (q);
q = gen_prime( qbits, 0, 0 );
goto next_try;
}
}
else
count2 = 0;
} while( !(nprime == pbits && check_prime( prime, val_2 )) );
if( DBG_CIPHER ) {
progress('\n');
log_mpidump( "prime : ", prime );
log_mpidump( "factor q: ", q );
if( mode == 1 )
log_mpidump( "factor q0: ", q_factor );
for(i=0; i < n; i++ )
log_mpidump( "factor pi: ", factors[i] );
log_debug("bit sizes: prime=%u, q=%u", mpi_get_nbits(prime), mpi_get_nbits(q) );
if( mode == 1 )
fprintf(stderr, ", q0=%u", mpi_get_nbits(q_factor) );
for(i=0; i < n; i++ )
fprintf(stderr, ", p%d=%u", i, mpi_get_nbits(factors[i]) );
progress('\n');
}
if( ret_factors ) { /* caller wants the factors */
*ret_factors = m_alloc_clear( (n+2) * sizeof **ret_factors);
i = 0;
if( mode == 1 ) {
(*ret_factors)[i++] = mpi_copy( q_factor );
for(; i <= n; i++ )
(*ret_factors)[i] = mpi_copy( factors[i] );
}
else {
for(; i < n; i++ )
(*ret_factors)[i] = mpi_copy( factors[i] );
}
}
if( g ) { /* create a generator (start with 3)*/
MPI tmp = mpi_alloc( mpi_get_nlimbs(prime) );
MPI b = mpi_alloc( mpi_get_nlimbs(prime) );
MPI pmin1 = mpi_alloc( mpi_get_nlimbs(prime) );
if( mode == 1 )
BUG(); /* not yet implemented */
factors[n] = q;
factors[n+1] = mpi_alloc_set_ui(2);
mpi_sub_ui( pmin1, prime, 1 );
mpi_set_ui(g,2);
do {
mpi_add_ui(g, g, 1);
if( DBG_CIPHER ) {
log_debug("checking g: ");
mpi_print( stderr, g, 1 );
}
else
progress('^');
for(i=0; i < n+2; i++ ) {
/*fputc('~', stderr);*/
mpi_fdiv_q(tmp, pmin1, factors[i] );
/* (no mpi_pow(), but it is okay to use this with mod prime) */
mpi_powm(b, g, tmp, prime );
if( !mpi_cmp_ui(b, 1) )
break;
}
if( DBG_CIPHER )
progress('\n');
} while( i < n+2 );
mpi_free(factors[n+1]);
mpi_free(tmp);
mpi_free(b);
mpi_free(pmin1);
}
if( !DBG_CIPHER )
progress('\n');
m_free( factors ); /* (factors are shallow copies) */
for(i=0; i < m; i++ )
mpi_free( pool[i] );
m_free( pool );
m_free(perms);
mpi_free(val_2);
mpi_free(q);
return prime;
}
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;
}
