void G2::restore(char *bytes)
{
int i,j,n=(1<<WINDOW_SIZE);
int bytes_per_big=(MIRACL/8)*(get_mip()->nib-1);
int len=n*2*bytes_per_big;
Big x,y,B;
if (mtable!=NULL) return;
mtable=new ECn[1<<WINDOW_SIZE];
B=getB();
B=-B;
ecurve((Big)-3,B,get_modulus(),MR_PROJECTIVE); // move to twist
for (i=j=0;i<n;i++)
{
x=from_binary(bytes_per_big,&bytes[j]);
j+=bytes_per_big;
y=from_binary(bytes_per_big,&bytes[j]);
j+=bytes_per_big;
mtable[i].set(x,y);
}
B=-B;
ecurve((Big)-3,B,get_modulus(),MR_PROJECTIVE); // move back
delete [] bytes;
}
void PFC::random(G1& w)
{
Big x0;
if (RNG==NULL) x0=rand(get_modulus());
else x0=strong_rand(RNG,get_modulus());
while (!w.g.set(x0,x0)) x0+=1;
w.g*=(*cof);
}
Big H1(char *string)
{ // Hash a zero-terminated string to a number < modulus
Big h,p;
char s[HASH_LEN];
int i,j;
sha256 sh;
shs256_init(&sh);
for (i=0;;i++)
{
if (string[i]==0) break;
shs256_process(&sh,string[i]);
}
shs256_hash(&sh,s);
p=get_modulus();
h=1; j=0; i=1;
forever
{
h*=256;
if (j==HASH_LEN) {h+=i++; j=0;}
else h+=s[j++];
if (h>=p) break;
}
h%=p;
return h;
}
Big PFC::hash_to_group(char *buffer, int len)
{
Big h,p;
char s[HASH_LEN];
int i,j;
sha256 sh;
shs256_init(&sh);
for (i=0; i < len; i++)
{
shs256_process(&sh,buffer[i]);
}
shs256_hash(&sh,s);
p=get_modulus();
h=1; j=0; i=1;
forever
{
h*=256;
if (j==HASH_LEN) {h+=i++; j=0;}
else h+=(unsigned char)s[j++];
if (h>=p) break;
}
h%=p;
return h % (*ord);
}
ostream& operator<<(ostream& s,const Poly& p)
{
BOOL first=TRUE;
ZZn a;
term *ptr=p.start;
if (ptr==NULL)
{
s << "0";
return s;
}
while (ptr!=NULL)
{
a=ptr->an;
if ((Big)a<get_modulus()/2)
{
if (!first) s << " + ";
}
else
{
a=(-a);
s << " - ";
}
if (ptr->n==0)
cout << a;
else
{
if (a!=(ZZn)1) s << a << "*x";
else s << "x";
if (ptr->n!=1) s << "^" << ptr->n;
}
first=FALSE;
ptr=ptr->next;
}
return s;
}
void PFC::random(G1& w)
{
Big x0=rand(get_modulus());
while (!w.g.set(x0,x0)) x0+=1;
w.g*=(*cof);
}
Poly factor(const Poly& f,int d)
{
Poly c,u,h,g=f;
Big r,p=get_modulus();
while (degree(g) > d)
{
// random monic polynomial
u.clear();
u.addterm((ZZn)1,2*d-1);
for (int i=2*d-2;i>=0;i--)
{
r=rand(p);
u.addterm((ZZn)r,i);
}
r=(pow(p,d)-1)/2;
c=pow(u,r,g);
c.addterm((ZZn)(-1),0);
h=gcd(c,g);
if (degree(h)==0 || degree(h)==degree(g)) continue;
if (2*degree(h)>degree(g))
g=g/h;
else g=h;
}
return g;
}
void get_modulus(zz_pX& pi_1, zz_pX& pi_2, zz_pX& a, int p, int d1, int d2)
{
get_modulus(pi_1, p, d1);
get_modulus(pi_2, p, d1*d2);
// find alpha
zz_pE::init(pi_2);
zz_pEX pi;
conv(pi, pi_1);
zz_pE zero;
FindRoot(zero, pi);
a = rep(zero);
}
int main(int argc, char **argv)
{
zz_pX pi_1, pi_2, a;
get_modulus(pi_1, pi_2, a, 5, 2, 2);
long q = to_long(zz_pE::cardinality());
cout << "q = " << q << endl;
cout << "pi_1 = " << pi_1 << endl;
cout << "pi_2 = " << pi_2 << endl;
cout << "a = " << a << endl;
}
GT PFC::final_exp(const GT& z)
{
GT y;
Big p;
ZZn2 res;
res=z.g;
p=get_modulus(); // get p
res=conj(res)/res;
res=pow(res,(p+1)/(*ord)); // raise to power of (p^2-1)/q
y.g=res;
return y;
}
void set_frobenius_constant(ZZn2 &X)
{
Big p=get_modulus();
switch (get_mip()->pmod8)
{
case 5:
X.set((Big)0,(Big)1); // = (sqrt(-2)^(p-1)/2
break;
case 3: // = (1+sqrt(-1))^(p-1)/2
X.set((Big)1,(Big)1);
break;
case 7:
X.set((Big)2,(Big)1); // = (2+sqrt(-1))^(p-1)/2
default: break;
}
X=pow(X,(p-1)/3);
}
void init_NTL_ff(int p, int d, int precompute_inverses,
int precompute_square_roots, int precompute_legendre_char,
int precompute_pth_frobenius_map)
{
zz_pX pi;
get_modulus(pi, p, d);
zz_pE::init(pi);
// make sure size of finite field fits in a long
assert(zz_pE::cardinality().WideSinglePrecision());
zz_pEExtraContext c(precompute_inverses,
precompute_square_roots,
precompute_legendre_char,
precompute_pth_frobenius_map);
c.restore();
}
ostream& operator<<(ostream& s,const Ps_ZZn& p)
{
BOOL first=TRUE;
ZZn a;
term_ps_zzn *ptr=p.start;
int pw;
if (ptr==NULL)
{
s << "0";
return s;
}
while (ptr!=NULL)
{
a=ptr->an;
if (a.iszero())
{
ptr=ptr->next;
continue;
}
if ((Big)a < get_modulus()/2)
{
a=(-a);
s << " - ";
}
else if (!first) s << " + ";
first=FALSE;
pw=ptr->n*p.pwr-p.offset;
if (pw==0)
{
s << a;
ptr=ptr->next;
continue;
}
if (a==(ZZn)1) s << "x";
else s << a << "*x";
if (pw!=1) s << "^" << pw;
ptr=ptr->next;
}
return s;
}
ostream& operator<<(ostream& s,const PolyXY& p)
{
BOOL first=TRUE;
ZZn a;
termXY *ptr=p.start;
if (ptr==NULL)
{
s << "0";
return s;
}
while (ptr!=NULL)
{
a=ptr->an;
if ((Big)a<get_modulus()/2)
{
if (!first) s << " + ";
}
else
{
a=(-a);
s << " - ";
}
if (ptr->nx==0 && ptr->ny==0)
s << a;
else
{
if (a!=(ZZn)1) s << a << "*";
if (ptr->nx!=0)
{
s << "x";
if (ptr->nx!=1) s << "^" << ptr->nx;
}
if (ptr->ny!=0)
{
if (ptr->nx!=0) s << ".";
s << "y";
if (ptr->ny!=1) s << "^" << ptr->ny;
}
}
first=FALSE;
ptr=ptr->next;
}
return s;
}
void set_frobenius_constant(ZZn &X)
{ // Note X=NR^[(p-13)/18];
Big p=get_modulus();
X=pow((ZZn)NR,(p-13)/18);
}
