// find a prime p of length n and a generator alpha of Z^*_p
// Alg 4.86 Menezes et al () Handbook, p.164
void
gensafeprime(mpint *p, mpint *alpha, int n, int accuracy)
{
mpint *q, *b;
q = mpnew(n-1);
while(1){
genprime(q, n-1, accuracy);
mpleft(q, 1, p);
mpadd(p, mpone, p); // p = 2*q+1
if(probably_prime(p, accuracy))
break;
}
// now find a generator alpha of the multiplicative
// group Z*_p of order p-1=2q
b = mpnew(0);
while(1){
mprand(n, genrandom, alpha);
mpmod(alpha, p, alpha);
mpmul(alpha, alpha, b);
mpmod(b, p, b);
if(mpcmp(b, mpone) == 0)
continue;
mpexp(alpha, q, p, b);
if(mpcmp(b, mpone) != 0)
break;
}
mpfree(b);
mpfree(q);
}
struct reesa_privkey* genpriv () {
/* Allocate a new private key ready-to-use
*/
struct reesa_privkey* priv = malloc(sizeof(struct reesa_privkey));
mpz_init(priv->q);
mpz_init(priv->p);
mpz_init(priv->modulus);
mpz_init(priv->totient_modulus);
mpz_init(priv->private_exponent);
mpz_init_set_str(priv->public_exponent, "65537", 10);
gmp_randstate_t random_state;
gmp_randinit_default(random_state);
gmp_randseed_ui(random_state, ++random_seed);
void genprime(mpz_t, gmp_randstate_t);
genprime(priv->q, random_state);
genprime(priv->p, random_state);
gmp_randclear(random_state);
mpz_mul(priv->modulus, priv->p, priv->q);
mpz_t p1;
mpz_init(p1);
mpz_sub_ui(p1, priv->p, 1);
mpz_t q1;
mpz_init(q1);
mpz_sub_ui(q1, priv->q, 1);
mpz_mul(priv->totient_modulus, p1, q1);
mpz_clear(q1);
mpz_clear(p1);
int inverse(mpz_t, const mpz_t, const mpz_t);
inverse(priv->private_exponent, priv->public_exponent, priv->totient_modulus);
return priv;
}
int main(int argc, char **argv)
{
prime_t start = argc > 1 ? atol(argv[1]) : 0,
stop = argc > 2 ? atol(argv[2]) + 1 : 0,
x, last;
struct timeval begin, end;
double duration;
for (x = start; x < stop; x += start)
{
gettimeofday(&begin, NULL);
last = genprime(x);
gettimeofday(&end, NULL);
duration = (double)(end.tv_sec - begin.tv_sec) +
((double)(end.tv_usec) - (double)(begin.tv_usec)) / 1000000.0;
printf ("Found %8lu primes in %10.5f seconds (last was %10lu)\n",
x, (float)duration, last);
}
return 0;
}
RSApriv*
rsagen(int nlen, int elen, int rounds)
{
mpint *p, *q, *e, *d, *phi, *n, *t1, *t2, *kp, *kq, *c2;
RSApriv *rsa;
p = mpnew(nlen/2);
q = mpnew(nlen/2);
n = mpnew(nlen);
e = mpnew(elen);
d = mpnew(0);
phi = mpnew(nlen);
// create the prime factors and euclid's function
genprime(p, nlen/2, rounds);
genprime(q, nlen - mpsignif(p) + 1, rounds);
mpmul(p, q, n);
mpsub(p, mpone, e);
mpsub(q, mpone, d);
mpmul(e, d, phi);
// find an e relatively prime to phi
t1 = mpnew(0);
t2 = mpnew(0);
mprand(elen, genrandom, e);
if(mpcmp(e,mptwo) <= 0)
itomp(3, e);
// See Menezes et al. p.291 "8.8 Note (selecting primes)" for discussion
// of the merits of various choices of primes and exponents. e=3 is a
// common and recommended exponent, but doesn't necessarily work here
// because we chose strong rather than safe primes.
for(;;){
mpextendedgcd(e, phi, t1, d, t2);
if(mpcmp(t1, mpone) == 0)
break;
mpadd(mpone, e, e);
}
mpfree(t1);
mpfree(t2);
// compute chinese remainder coefficient
c2 = mpnew(0);
mpinvert(p, q, c2);
// for crt a**k mod p == (a**(k mod p-1)) mod p
kq = mpnew(0);
kp = mpnew(0);
mpsub(p, mpone, phi);
mpmod(d, phi, kp);
mpsub(q, mpone, phi);
mpmod(d, phi, kq);
rsa = rsaprivalloc();
rsa->pub.ek = e;
rsa->pub.n = n;
rsa->dk = d;
rsa->kp = kp;
rsa->kq = kq;
rsa->p = p;
rsa->q = q;
rsa->c2 = c2;
mpfree(phi);
return rsa;
}
int main()
{
int t,n,i,j,k,p,s,e,x,y,c,ans,f,d;
for(i=0;i<100;i++)
check[i]=0;
prime[0]=2;
c=genprime(1000000);
// printf("%d\n",prime[c-1]);
// printf("%d\n",c);
// for(i=0;i<c;i++)
// printf("%d ",prime[i]);
// printf("\n");
scanf("%d",&t);
while(t--)
{
scanf("%d %lld %d",&n,&m,&p);
for(i=1;i<=n;i++)
{
scanf("%d",&tazo[i]);
a[i].root=i;
a[i].wt=tazo[i];
a[i].count=1;
}
for(i=0;i<m;i++)
{
scanf("%d %d",&s,&e);
x=find(s);
y=find(e);
// printf("%d %d\n",x,y);
if(x!=y)
{
unionset(x,y);
}
}
ans=0;
for(i=1;i<=n;i++)
{
// printf("%d %d %d %d\n",i,a[i].root,a[i].wt,a[i].count);
if(a[i].root==i)
{
f=0;
d=(a[i].wt+p);
for(j=0;j<c;j++)
{
if(d==prime[j])
{
f=1;
break;
}
}
// printf("f : %d\n",f);
if(f==1)
{
ans++;
}
}
}
printf("%d\n",ans);
}
return 0;
}
