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package ecckrypt;
import java.math.BigInteger;

/**
 *
 * @author Student
 */
class PECC
{
    BigInteger x,y,a,b,q;
    PECC(BigInteger x, BigInteger y, BigInteger a, BigInteger b, BigInteger q)
    {
        this.a = a;
        this.b = b;
        this.x = x;
        this.y = y;
        this.q = q;
    }
}
public class ECCKRYPT {


    /**
     * @param args the command line arguments
     */
    public static BigInteger ODW(BigInteger m, BigInteger n)
    {
        BigInteger a, ap, s, sp, t, tp, r, q;
        BigInteger L1 = new BigInteger("1"), L0=new BigInteger("0");
        a = m;
        ap = n;
        s = L1;
        sp=L0;
        t=L0;
        tp = L1;

        while(ap.compareTo(L0) !=0)
        {
          q = a.divide(ap);
          r = a; a=ap; ap=r.subtract(q.multiply(ap));
          r = s; s=sp; sp=r.subtract(q.multiply(sp));
          r = t; t=tp; tp=r.subtract(q.multiply(tp));
        }
        if (t.compareTo(L0)>0) r=t;
        else  r=t.add(n);
        return r;
    }

    public static PECC DOD(PECC P1, PECC P2)
    {
        BigInteger x1, x2, x3, y1, y2, y3, lam, q, dwa, trzy;
        x1 = P1.x;
        x2 = P2.x;
        x3 = new BigInteger("0");

        y1 = P1.y;
        y2 = P2.y;
        y3 = new BigInteger("0");

        dwa = new BigInteger("2");
        trzy = new BigInteger("3");
        q = P1.q;


        if (x1.compareTo(x2)!=0)
        {
            lam = x2.subtract(x1);
            lam = ODW(lam, P1.q);
            lam = lam.multiply(y2.subtract(y1));
            lam = lam.mod(q);
            x3 = lam.multiply(lam);
            x3 = (x3.subtract(x1)).subtract(x2);
            x3 = x3.mod(q);
            y3 = (x1.subtract(x3)).multiply(lam);
            y3 = y3.subtract(y1);
            y3 = y3.mod(q);

        }

        else
        {
            if (y1.compareTo(y2)==0)
            {
             lam = ODW(dwa.multiply(y1), q);
             BigInteger r;
             r = trzy.multiply(x1.multiply(x1));

             r = r.add(P1.a);
             lam = lam.multiply(r);
             x3 = lam.multiply(lam);
             x3 = x3.subtract(dwa.multiply(x1));
             x3 = x3.mod(q);
             y3 = (x1.subtract(x3)).multiply(lam);
             y3 = y3.subtract(y1);
             y3 = y3.mod(q);

            }

        }
        return new PECC (x3, y3, P1.a, P1.b, q);

    }
    public static PECC MNOZENIE(BigInteger k, PECC P)
    {
        BigInteger i = new BigInteger("1");
        BigInteger jeden = i;
        PECC R = P;
        while(i.compareTo(k) < 0)
        {
            R = DOD(R, P);
            i.add(jeden);
        }
        return R;
    }

    public static BigInteger SLegendrea(BigInteger a, BigInteger p) {
        BigInteger jeden = new BigInteger("1");
        BigInteger dwa = new BigInteger("2");

        return (a.modPow((p.subtract(jeden)).divide(dwa),p));
    }

    public static BigInteger pierw(BigInteger r, BigInteger q){
        BigInteger L1 = new BigInteger("1");
        BigInteger L2 = new BigInteger("2");
        BigInteger r1 = r.divide(L2);
        while((r1.multiply(r1)).compareTo(r)>0)
            r1.subtract(L1);
        return r1;
    }
    void Wyswietlanie (PECC P)
    {
        System.out.print("( "+P.x+" , "+P.y+" )");
    }

    public static void main(String[] args) {


        BigInteger p, q, a, b, L1, L2, L10, x, r1, r2, y;
        int n = 177;


        p = new BigInteger("3");
        p = p.nextProbablePrime();

        L2 = new BigInteger("2");
        L1 = new BigInteger("1");
        L10 = new BigInteger("10");
        q = p.pow(n);
        a = L1;
        b = L2;
        b = b.nextProbablePrime();
        while (b.compareTo(q)>0)
        {
            b = b.divide(L2);
            b = b.nextProbablePrime();
        }

        System.out.println("Rownanie krzywej eleptycznej:\n" +
                "(y^2=x^3+x"+b+") mod "+q);

        do {
            x = q.divide(L10);
            r1 = ((x.pow(3)).add(x)).add(b);
            r1 = r1.mod(q);
            r2 = SLegendrea(r1,q);
        } while (r2.compareTo(L1)!=0);
        y = pierw(r1,q);
    }

}