#include <iostream.h>

void myInvMod(long *k3,const long k2,const long x)
{
     	long u,v,t,t1,t2,q,r;
     
		u=k2;v=x;
         if(u<0)
		 {
			 cout<<"#######################This is break by inversion of a negative number.\n";
		 }

         t1=1;t2=0;

         while(u!=1)
		 {
             if(u==0)cout<<"u is equal to 0;"<<endl;
			 q=(v-v%u)/u;r=v-q*u;t=t2-q*t1;
             v=u;u=r;t2=t1;t1=t;
		 }
		 
		 if(t1<0)
			 *k3=x-(-t1)%x;
		 else
			 *k3=t1%x;
}


void tuoadd(const long x1,const long y1, long *x2,long *y2,const long x,const long a,long n)
{
	//(X1,Y1)N次數乘,結果為(*X2,*Y2)
	int i;
	long k,k1,k2,k3,x3,y3;
	*x2=x1;*y2=y1;

	for(i=2;i<=n;i++)                                           //x1=3;y1=10;x2=9;y2=7;x=23;a=1;//
	{
		if((*x2==x1)&&(*y2==y1))
		{
			k1=3*x1*x1+a;
			k2=2*y1;
		}
		else
		{
			k1=*y2-y1;
			k2=*x2-x1;
		}
		
		if(k2<0)
			k2=x-(-k2)%x;
		else
			k2=k2%x;

		if(k2==0)
		{
			//k2=23;
			cout<<"i="<<i<<endl;
			cout<<"k2 is equal to zero here!"<<endl;
			cout<<"x1="<<x1<<"y1="<<y1<<endl;
			cout<<"x2="<<*x2<<"y2="<<*y2<<endl;
		}

	    myInvMod(&k3,k2,x);
		
		if((k1*k3)<0)
			k=x-(-(k1*k3))%x;
		else
			k=(k1*k3)%x;
		
		x3=k*k-x1-(*x2);
		
		if(x3<0)
			*x2=x-(-x3)%x;
		else
			*x2=x3%x;
	
		y3=k*(x1-x3)-y1;
		
		if(y3<0)
			*y2=x-(-y3)%x;
		else
			*y2=y3%x;

		cout<<"i="<<i<<"   ("<<*x2<<","<<*y2<<")"<<endl;
	}
}

void tuoadd2(const long x1,const long y1, long *x2,long *y2,const long x,const long a)
{
	//(x1,y1)+(*x2,*y2)=(*x2,*y2)
	long k,k1,k2,k3,x3,y3;
	
	if(((*x2)==(x1))&&((*y2)==(y1)))
	{
		k1=3*(x1)*(x1)+a;
		k2=2*(y1);
	}
	else
	{
		k1=(*y2)-(y1);
		k2=(*x2)-(x1);
	}
	
	if(k2<0)
		k2=x-(-k2)%x;
	else
		k2=k2%x;

	if(k2==0)
	{
		cout<<"k2 is equal to zero here!"<<endl;
		cout<<"x1="<<x1<<"y1="<<y1<<endl;
		cout<<"x2="<<*x2<<"y2="<<*y2<<endl;
	}

	myInvMod(&k3,k2,x);
		
	if((k1*k3)<0)
		k=x-(-(k1*k3))%x;
	else
		k=(k1*k3)%x;
		
	x3=k*k-(x1)-(*x2);
		
	if(x3<0)
		(*x2)=x-(-x3)%x;
	else
		(*x2)=x3%x;
	
	y3=k*((x1)-x3)-(y1);
	
	if(y3<0)
		*y2=x-(-y3)%x;
	else
		*y2=y3%x;
}

void Signature(long xb,long yb,long Hm,long n,long a,long q,long d,long *r,long *s)
{
	long k,Inv_k,x2,y2,t;
	k=3;
	tuoadd(xb,yb,&x2,&y2,q,a,k);
	cout<<"This is in Signature!"<<endl;
	cout<<"x2="<<x2<<"  y2="<<y2<<endl;

	if(x2<0)
		*r=n-(-x2)%n;
	else
		*r=x2%n;

	myInvMod(&Inv_k,k,n);

	t=(Inv_k*(Hm+d*(*r)));
	if(t<0)
		*s=n-(-t)%n;
	else
		*s=t%n;

	cout<<"*r="<<*r<<"  *s="<<*s<<endl;

}

void Verification(long xb,long yb,long xu,long yu,long Hm,long r,long q,long a,long s,long n)
{
	long Inv_s, x1,y1,x2,y2,w,u1,u2;

	cout<<"This is in Verification!"<<endl;
	cout<<"r="<<r<<endl;
	myInvMod(&Inv_s,s,n);

	if(Inv_s<0)
		w=n-(-Inv_s)%n;
	else
		w=Inv_s%n;

	if((Hm*w)<0)
		u1=n-(-(Hm*w))%n;
	else
		u1=(Hm*w)%n;

	if((r*w)<0)
		u2=n-(-(r*w))%n;
	else
		u2=(r*w)%n;


	cout<<"w="<<w<<"  u1="<<u1<<"  u2="<<u2<<endl;
	tuoadd(xb,yb,&x1,&y1,q,a,u1);
	tuoadd(xu,yu,&x2,&y2,q,a,u2);
	tuoadd2(x1,y1,&x2,&y2,q,a);
	cout<<"x2="<<x2<<" y2="<<y2<<endl;

	if(x2==r)
		cout<<"Accept the signature!"<<endl;
	else
		cout<<"Reject the signature!"<<endl;

}



void main()
{
   	
	cout<<"===================================================="<<endl;
    cout<<"             橢圓曲線數字簽名驗證函數               "<<endl;
    cout<<"===================================================="<<endl;
	cout<<"this is in main program."<<endl;
    /*
     Domain parameters for an elliptic curve scheme describes an elliptic curve E defined over a finite field
     Fq, a base point P belongs to E(Fq), and its order n. The parameters should be chosen so that the ECDLP
     is resistant to all known attacks. The parameters (q,FR,S,a,b,P,n,h) has the following form:

     q=23; a=1; b=1; P=(x1,y1); n=28; h=1;

     where n is the order of the base point P; h is the cofactor #E(Fq)/n
	    a and b are coefficients of equation of the elliptic curve E over Fq.
		the representation of the elliptic curve is :y2=x3+ax+b

     */

    long q,a,b,xb,yb,n,h,d,r,s,xu,yu,Hm;
    
	q=11;   // the modulus of the finite field;
	a=1; b=6; // y2=x3+ax+b;
	xb=2;yb=7; // P=(2,7) base point of elliptic curve;
	n=13; h=1; 
	d=7;  // d is private key;
	Hm=4; // Hm is hash funcation of message;
    tuoadd(xb,yb,&xu,&yu,q,a,d); // Q=(xu,yu) is the public key;

	cout<<"xu="<<xu<<"yu="<<yu<<endl;

	Signature(xb,yb,Hm,n,a,q,d,&r,&s);
	Verification(xb,yb,xu,yu,Hm,r,q,a,s,n);

	/*
	x1=2;y1=7; // P=(2,7);   
   tuoadd(x1,y1,&x2,&y2,q,a,n);
   tuoadd2(x1,y1,&x2,&y2,x,a);
   cout<<"  ("<<x2<<","<<y2<<")"<<endl;
   */

}