ZZn& ZZn::operator/=(int i)
{
if (i==1) return *this;
if (i==2)
{ // make a special effort... modulus is odd
nres_div2(fn,fn);
return *this;
}
ZZn x=i;
nres_moddiv(fn,x.fn,fn);
return *this;
}
ZZn& ZZn::operator/=(int i)
{
if (i==1) return *this;
if (i==2)
{ // make a special effort... modulus is odd
copy(fn,get_mip()->w1);
if (remain(get_mip()->w1,2)!=0)
add(get_mip()->w1,get_mip()->modulus,get_mip()->w1);
subdiv(get_mip()->w1,2,get_mip()->w1);
copy(get_mip()->w1,fn);
return *this;
}
ZZn x=i;
nres_moddiv(fn,x.fn,fn);
return *this;
}
ZZn operator/(int i, const ZZn& b2)
{ZZn z=i; nres_moddiv(z.fn,b2.fn,z.fn); return z;}
int main()
{ /* factoring program using Lenstras Elliptic Curve method */
int phase,m,k,nc,iv,pos,btch,u,v;
long i,p,pa,interval;
big q,x,z,a,x1,z1,x2,z2,xt,zt,n,fvw;
static big fu[1+MULT/2];
static BOOL cp[1+MULT/2];
mip=mirsys(30,0);
q=mirvar(0);
x=mirvar(0);
z=mirvar(0);
a=mirvar(0);
x1=mirvar(0);
z1=mirvar(0);
x2=mirvar(0);
z2=mirvar(0);
n=mirvar(0);
t=mirvar(0);
s1=mirvar(0);
d1=mirvar(0);
s2=mirvar(0);
d2=mirvar(0);
ak=mirvar(0);
xt=mirvar(0);
zt=mirvar(0);
fvw=mirvar(0);
w=mirvar(0);
gprime(LIMIT1);
for (m=1;m<=MULT/2;m+=2)
if (igcd(MULT,m)==1)
{
fu[m]=mirvar(0);
cp[m]=TRUE;
}
else cp[m]=FALSE;
printf("input number to be factored\n");
cinnum(n,stdin);
if (isprime(n))
{
printf("this number is prime!\n");
return 0;
}
prepare_monty(n);
for (nc=1,k=6;k<100;k++)
{ /* try a new curve */
/* generating an elliptic curve */
u=k*k-5;
v=4*k;
convert(u,x); nres(x,x);
convert(v,z); nres(z,z);
nres_modsub(z,x,a); /* a=v-u */
copy(x,t);
nres_modmult(x,x,x);
nres_modmult(x,t,x); /* x=u^3 */
copy(z,t);
nres_modmult(z,z,z);
nres_modmult(z,t,z); /* z=v^3 */
copy(a,t);
nres_modmult(t,t,t);
nres_modmult(t,a,t); /* t=(v-u)^3 */
convert(3*u,a); nres(a,a);
convert(v,ak); nres(ak,ak);
nres_modadd(a,ak,a);
nres_modmult(t,a,t); /* t=(v-u)^3.(3u+v) */
convert(u,a); nres(a,a);
copy(a,ak);
nres_modmult(a,a,a);
nres_modmult(a,ak,a); /* a=u^3 */
convert(v,ak); nres(ak,ak);
nres_modmult(a,ak,a); /* a=u^3.v */
nres_premult(a,16,a);
nres_moddiv(t,a,ak); /* ak=(v-u)^3.(3u+v)/16u^3v */
nc++;
phase=1;
p=0;
i=0;
btch=50;
printf("phase 1 - trying all primes less than %d\n",LIMIT1);
printf("prime= %8ld",p);
forever
{ /* main loop */
if (phase==1)
{
p=mip->PRIMES[i];
if (mip->PRIMES[i+1]==0)
{ /* now change gear */
phase=2;
printf("\nphase 2 - trying last prime less than %ld\n",
LIMIT2);
printf("prime= %8ld",p);
copy(x,xt);
copy(z,zt);
nres_modadd(x,z,s2);
nres_modsub(x,z,d2); /* P = (s2,d2) */
duplication(s2,d2,x,z);
nres_modadd(x,z,s1);
nres_modsub(x,z,d1); /* 2.P = (s1,d1) */
nres_moddiv(x1,z1,fu[1]); /* fu[1] = x1/z1 */
addition(x1,z1,s1,d1,s2,d2,x2,z2); /* 3.P = (x2,z2) */
for (m=5;m<=MULT/2;m+=2)
{ /* calculate m.P = (x,z) and store fu[m] = x/z */
nres_modadd(x2,z2,s2);
nres_modsub(x2,z2,d2);
addition(x1,z1,s2,d2,s1,d1,x,z);
copy(x2,x1);
copy(z2,z1);
copy(x,x2);
copy(z,z2);
if (!cp[m]) continue;
copy(z2,fu[m]);
nres_moddiv(x2,fu[m],fu[m]);
}
ellipse(xt,zt,MULT,x,z,x2,z2);
nres_modadd(x,z,xt);
nres_modsub(x,z,zt); /* MULT.P = (xt,zt) */
iv=(int)(p/MULT);
if (p%MULT>MULT/2) iv++;
interval=(long)iv*MULT;
p=interval+1;
ellipse(x,z,iv,x1,z1,x2,z2); /* (x1,z1) = iv.MULT.P */
nres_moddiv(x1,z1,fvw); /* fvw = x1/z1 */
nres_modsub(fvw,fu[p%MULT],q);
marks(interval);
btch*=100;
i++;
continue;
}
pa=p;
while ((LIMIT1/p) > pa) pa*=p;
ellipse(x,z,(int)pa,x1,z1,x2,z2);
copy(x1,x);
copy(z1,z);
copy(z,q);
}
else
{ /* phase 2 - looking for last large prime factor of (p+1+d) */
p+=2;
pos=(int)(p%MULT);
if (pos>MULT/2)
{ /* increment giant step */
iv++;
interval=(long)iv*MULT;
p=interval+1;
marks(interval);
pos=1;
nres_moddiv(x2,z2,fvw);
nres_modadd(x2,z2,s2);
nres_modsub(x2,z2,d2);
addition(x1,z1,s2,d2,xt,zt,x,z);
copy(x2,x1);
copy(z2,z1);
copy(x,x2);
copy(z,z2);
}
if (!cp[pos]) continue;
/* if neither interval +/- pos is prime, don't bother */
if (!plus[pos] && !minus[pos]) continue;
nres_modsub(fvw,fu[pos],t);
nres_modmult(q,t,q);
}
if (i++%btch==0)
{ /* try for a solution */
printf("\b\b\b\b\b\b\b\b%8ld",p);
fflush(stdout);
egcd(q,n,t);
if (size(t)==1)
{
if (p>LIMIT2) break;
else continue;
}
if (compare(t,n)==0)
{
printf("\ndegenerate case");
break;
}
printf("\nfactors are\n");
if (isprime(t)) printf("prime factor ");
else printf("composite factor ");
cotnum(t,stdout);
divide(n,t,n);
if (isprime(n)) printf("prime factor ");
else printf("composite factor ");
cotnum(n,stdout);
return 0;
}
}
if (nc>NCURVES) break;
printf("\ntrying a different curve %d\n",nc);
}
printf("\nfailed to factor\n");
return 0;
}
