int main()
{ /* program to find a trap-door prime */
BOOL found;
int i,spins;
long seed;
big pp[NPRIMES],q,p,t;
FILE *fp;
mirsys(50,0);
for (i=0;i<NPRIMES;i++) pp[i]=mirvar(0);
q=mirvar(0);
t=mirvar(0);
p=mirvar(0);
printf("Enter 9 digit seed= ");
scanf("%ld",&seed);
getchar();
irand(seed);
printf("Enter 4 digit seed= ");
scanf("%d",&spins);
getchar();
for (i=0;i<spins;i++) brand();
convert(2,pp[0]);
do
{ /* find prime p = 2.pp[1].pp[2]....+1 */
convert(2,p);
for (i=1;i<NPRIMES-1;i++)
{ /* generate all but last prime */
bigdig(i+6,10,q);
nxprime(q,pp[i]);
multiply(p,pp[i],p);
}
do
{ /* find last prime component such that p is prime */
nxprime(q,q);
copy(q,pp[NPRIMES-1]);
multiply(p,pp[NPRIMES-1],t);
incr(t,1,t);
} while(!isprime(t));
copy(t,p);
found=TRUE;
for (i=0;i<NPRIMES;i++)
{ /* check that PROOT is a primitive root */
decr(p,1,q);
divide(q,pp[i],q);
powltr(PROOT,q,p,t);
if (size(t)==1)
{
found=FALSE;
break;
}
}
} while (!found);
fp=fopen("prime.dat","wt");
fprintf(fp,"%d\n",NPRIMES);
for (i=0;i<NPRIMES;i++) cotnum(pp[i],fp);
fclose(fp);
printf("prime= \n");
cotnum(p,stdout);
return 0;
}
void primemod(int bits,big p)
{
do {
printf("%d bit prime.....\n",bits);
bigbits(bits,p);
nxprime(p,p);
} while (logb2(p)!=bits);
}
int main()
{
FILE *fp;
big p,q,h,g,n,s,t;
long seed;
miracl *mip=mirsys(100,0);
p=mirvar(0);
q=mirvar(0);
h=mirvar(0);
g=mirvar(0);
n=mirvar(0);
s=mirvar(0);
t=mirvar(0);
/* randomise */
printf("Enter 9 digit random number seed = ");
scanf("%ld",&seed);
getchar();
irand(seed);
/* generate q */
forever
{
bigbits(QBITS,q);
nxprime(q,q);
if (logb2(q)>QBITS) continue;
break;
}
printf("q= ");
cotnum(q,stdout);
/* generate p */
expb2(PBITS,t);
decr(t,1,t);
premult(q,2,n);
divide(t,n,t);
expb2(PBITS-1,s);
decr(s,1,s);
divide(s,n,s);
forever
{
bigrand(t,p);
if (mr_compare(p,s)<=0) continue;
premult(p,2,p);
multiply(p,q,p);
incr(p,1,p);
copy(p,n);
if (isprime(p)) break;
}
printf("p= ");
cotnum(p,stdout);
/* generate g */
do {
decr(p,1,t);
bigrand(t,h);
divide(t,q,t);
powmod(h,t,p,g);
} while (size(g)==1);
printf("g= ");
cotnum(g,stdout);
fp=fopen("common.dss","wt");
fprintf(fp,"%d\n",PBITS);
mip->IOBASE=16;
cotnum(p,fp);
cotnum(q,fp);
cotnum(g,fp);
fclose(fp);
return 0;
}
int main()
{
FILE *fp;
big q,p,p1,h,t,g,low,high;
big pool[POOL_SIZE];
BOOL fail;
int i,j,p1bits,np;
long seed,m,permutation;
miracl *mip=mirsys(100,0);
q=mirvar(0);
p=mirvar(0);
h=mirvar(0);
t=mirvar(0);
g=mirvar(0);
p1=mirvar(0);
low=mirvar(0);
high=mirvar(0);
gprime(10000);
/* randomise */
printf("Enter 9 digit random number seed = ");
scanf("%ld",&seed);
getchar();
irand(seed);
p1bits=PBITS-QBITS-1;
/* find number of primes pa, pb, pc etc., that will be needed */
np=1;
while (p1bits/np >= OBITS) np++;
np--;
/* find the high/low limits for these primes, so that
the generated prime p will be exactly PBITS in length */
expb2(p1bits-1,t);
nroot(t,np,low); /* np-th integer root */
incr(low,1,low);
premult(t,2,t);
decr(t,1,t);
nroot(t,np,high);
subtract(high,low,t); /* raise low limit up to half-way... */
subdiv(t,2,t);
subtract(high,t,low);
/* generate q */
forever
{ /* make sure leading two bits of q 11... */
expb2(QBITS,q);
bigbits(QBITS-2,t);
subtract(q,t,q);
nxprime(q,q);
if (logb2(q)>QBITS) continue;
break;
}
printf("q= (%d bits)\n",logb2(q));
cotnum(q,stdout);
/* generate prime pool from which permutations of np
primes will be picked until a Lim-Lee prime is found */
for (i=0;i<POOL_SIZE;i++)
{ /* generate the primes pa, pb, pc etc.. */
pool[i]=mirvar(0);
forever
{
bigrand(high,p1);
if (mr_compare(p1,low)<0) continue;
nxprime(p1,p1);
if (mr_compare(p1,high)>0) continue;
copy(p1,pool[i]);
break;
}
}
/* The '1' bits in the permutation indicate which primes are
picked from the pool. If np=5, start at 11111, then 101111 etc */
permutation=1L;
for (i=0;i<np;i++) permutation<<=1;
permutation-=1; /* permuation = 2^np-1 */
/* generate p */
fail=FALSE;
forever
{
convert(1,p1);
for (i=j=0,m=1L;j<np;i++,m<<=1)
{
if (i>=POOL_SIZE)
{ /* ran out of primes... */
fail=TRUE;
break;
}
if (m&permutation)
{
multiply(p1,pool[i],p1);
j++;
}
}
if (fail) break;
printf(".");
premult(q,2,p);
multiply(p,p1,p);
incr(p,1,p);
permutation=increment(permutation);
if (logb2(p)!=PBITS) continue;
if (isprime(p)) break;
}
if (fail)
{
printf("\nFailed - very unlikely! - try increasing POOL_SIZE\n");
return 0;
}
printf("\np= (%d bits)\n",logb2(p));
cotnum(p,stdout);
/* finally find g */
do {
decr(p,1,t);
bigrand(t,h);
divide(t,q,t);
powmod(h,t,p,g);
} while(size(g)==1);
printf("g= (%d bits)\n",logb2(g));
cotnum(g,stdout);
fp=fopen("common.dss","wt");
fprintf(fp,"%d\n",PBITS);
mip->IOBASE=16;
cotnum(p,fp);
cotnum(q,fp);
cotnum(g,fp);
fclose(fp);
return 0;
}