ECPoint.java

//package ecc.elliptic;

import java.math.BigInteger;
import java.util.Arrays;
import java.io.*;

public class ECPoint 
{

	public final static BigInteger TWO = new BigInteger("2");
	public final static BigInteger THREE = new BigInteger("3");

	private EllipticCurve mother;

	private BigInteger x, y;
	private boolean iszero;

	private ECPoint[] fastcache = null;			//fastcache is an array of ECPoints
	private ECPoint[] cache = null;				//Even cache is an ECPoint array

	public void fastCache() 
	{
		try 
		{
			if(fastcache == null) 
			{
				fastcache = new ECPoint[256];				//fastcache initialised to 256 EC Points.
				fastcache[0] = new ECPoint(mother);			//First point is null.
				for(int i = 1; i < fastcache.length; i++) 		//From 1 to 256
				{
					fastcache[i] = fastcache[i-1].add(this);	//add the point repeatedly (Cumulative sum). P,2P,...
				}
			}
		} 
		catch (NoCommonMotherException e) 
		{
			System.out.println("ECPoint.fastcache: THIS CANNOT HAPPEN!!!");
		}
	}

	/** Constructs a point on an elliptic curve.
	 *@param mother The elliptic curve on wich the point is surposed to lie
	 *@param x the x coordinate of the point
	 *@param y the y coordinate of the point
	 *@exception Throws a NotOnMotherException if (x,y) is not on the mother curve.*/
	public ECPoint(EllipticCurve mother, BigInteger x, BigInteger y) throws NotOnMotherException
	{
		this.mother = mother;
		this.x = x;
		this.y = y;
		if (!mother.onCurve(this)) throw new NotOnMotherException(this);
		iszero = false;
	}

	/** Decompresses a compressed point stored in a byte-array into a new ECPoint.
	 *@param bytes the array of bytes to be decompressed
	 *@param mother the EllipticCurve the decompressed point is supposed to lie on.*/
	public ECPoint(byte[] bytes, EllipticCurve mother) 
	{
		this.mother = mother;
		if (bytes[0] == 2)
		{
			iszero = true;
			return;
		}
		boolean ymt = false;
		if(bytes[0] != 0) 
			ymt = true;
		bytes[0] = 0;
		x = new BigInteger(bytes);
		if(mother.getPPODBF() == null) System.out.println("Fuck dig!!!");
		y = x.multiply(x).add(mother.geta()).multiply(x).add(mother.getb()).modPow(mother.getPPODBF(),mother.getp());
		if(ymt != y.testBit(0)) 
		{
			y = mother.getp().subtract(y);
		}
		iszero = false;
	}

	/** IMPORTANT this renders the values of x and y to be null! Use this constructor
	 *only to create instances of a Zero class!*/
	public ECPoint(EllipticCurve e){
		x = y = BigInteger.ZERO;
		mother = e;
		iszero = true;
	}

	public byte[] compress() 
	{
		byte[] cmp = new byte[mother.getPCS()];
		if (iszero)
		{
			cmp[0] = 2;
		}
		byte[] xb = x.toByteArray();
		System.arraycopy(xb, 0, cmp, mother.getPCS()-xb.length, xb.length);
		if(y.testBit(0)) cmp[0] = 1;
		return cmp;
	}

	/** Adds another elliptic curve point to this point.
	 *@param q The point to be added
	 *@return the sum of this point on the argument
	 *@exception Throws a NoCommonMotherException if the two points don't lie on the same elliptic curve.*/
	public ECPoint add(ECPoint q) throws NoCommonMotherException
	{

		if (!hasCommonMother(q)) throw new NoCommonMotherException();

		if (this.iszero) return q;
		else if (q.isZero()) return this;

		BigInteger y1 = y;
		BigInteger y2 = q.gety();
		BigInteger x1 = x;
		BigInteger x2 = q.getx();

		BigInteger alpha;

		if (x2.compareTo(x1) == 0) 
		{

			if (!(y2.compareTo(y1) == 0)) return new ECPoint(mother);
			else 
			{
				alpha = ((x1.modPow(TWO,mother.getp())).multiply(THREE)).add(mother.geta());
				alpha = (alpha.multiply((TWO.multiply(y1)).modInverse(mother.getp()))).mod(mother.getp());
			}

		} 
		else 
		{
			alpha = ((y2.subtract(y1)).multiply((x2.subtract(x1)).modInverse(mother.getp()))).mod(mother.getp());
		} 

		BigInteger x3,y3;
		x3 = (((alpha.modPow(TWO,mother.getp())).subtract(x2)).subtract(x1)).mod(mother.getp());
		y3 = ((alpha.multiply(x1.subtract(x3))).subtract(y1)).mod(mother.getp());

		try
		{ 
			return new ECPoint(mother,x3,y3); 
		}
		catch (NotOnMotherException e)
		{
			System.out.println("Error in add!!! Result not on mother!");
			return null;
		}

	}

	public ECPoint multiply(BigInteger coef) 
	{
		/*try{
		  ECPoint result = new ECPoint(mother);		//result is initialised to null
		  byte[] coefb = coef.toByteArray();		//coefb is the number to be multiplied. i.e. q in p*q. called as p.mul(q)
		  if(fastcache != null)				//fastcache of this, i.e. p
		  {
		  for(int i = 0; i < coefb.length; i++) 
		  {
		  result = result.times256().add(fastcache[coefb[i]&255]); // result=result*256+fastcache(coefb[i]&255)
		  }
		  return result;
		  }
		  if(cache == null) 				//If cache is empty, populate it upto 16
		  {
		  cache = new ECPoint[16];
		  cache[0] = new ECPoint(mother);
		  for(int i = 1; i < cache.length; i++) 
		  {
		  cache[i] = cache[i-1].add(this);
		  }
		  }
		  for(int i = 0; i < coefb.length; i++) 
		  {
		  result = result.times16().add(cache[(coefb[i]>>4)&15]).times16().add(cache[coefb[i]&15]);
		  }
		  return result;
		  } 
		  catch (NoCommonMotherException e) 
		  {
		  System.out.println("Error in pow!!!");
		  return null;
		  }*/
		//

		//BigInteger R0=this.getx();
		//BigInteger R1=R0.add(R0);

		//Convert multiplier into binary.
		String BitNum=coef.toString(2);
	//	System.out.println(coef+"in bin form is"+BitNum);
	//	System.out.println("length of bitnum string is"+BitNum.length());	
		int nk=coef.bitCount();				//nk in paper.
	//	System.out.println(coef+" .bitcount is "+ nk);
		ECPoint result=this;
		for(int i=nk-1;i>0;i--)
		{
			try
			{
				result=result.add(result);
				if(coef.testBit(i))
					result=result.add(this);
			}
			catch(Exception e)
			{
				System.out.println("Error in multiplying");
			}
		}


		/*if(!coef.testBit(i))
		  {
		  R1=R0.add(R1);
		  R0=R0.add(R0);
		  }
		  else
		  {
		  R0=R0.add(R1);
		  R1=R1.add(R1);
		  }*/

		//ECPoint result=new ECPoint(this.mother);
		//result.x=R0;
		//BigInteger y0=R0.multiply(R0).add(this.mother.geta()).multiply(R0).add(this.mother.getb()).modPow(this.mother.getPPODBF(),this.mother.getp());
		//result.y=y0;
		return result;

	}

	private ECPoint times16() 
	{
		try 
		{
			ECPoint result = this;
			for(int i = 0; i < 4; i++) 
			{
				result = result.add(result);
			}
			return result;
		} 
		catch (Exception e) 
		{
			System.out.println("ECPoint.times16: THIS CANNOT HAPPEN!!!");
			return null;
		}
	}

	private ECPoint times256() 
	{
		try 
		{
			ECPoint result = this;
			for(int i = 0; i < 8; i++) 
			{
				result = result.add(result);
			}
			return result;
		} 
		catch (Exception e) 
		{
			System.out.println("ECPoint.times256: THIS CANNOT HAPPEN!!!");
			return null;
		}
	}

	public BigInteger getx()
	{
		return x;
	}

	public BigInteger gety()
	{
		return y;
	}

	public EllipticCurve getMother()
	{
		return mother;
	}

	public String toString()
	{
		return "(" + x.toString() + ", " + y.toString() + ")";
	}

	public boolean hasCommonMother(ECPoint p)
	{
		if (this.mother.equals(p.getMother())) return true;
		else return false;
	}

	public boolean isZero()
	{
		return iszero;
	}
}