Elliptic Curve Prime factorisation

[mukesh tiwari]

Hello all , I have implemented Elliptic curve prime factorisation
using wikipedia [ http://en.wikipedia.org/wiki/Lenstra_elliptic_curve_factorization].
I think that this code is not optimised and posting for further
improvement. Feel free to comment and if you have any link regarding
Elliptic curve prime factorisation , kindly post it.
Thank you

import math
import random

#y^2=x^3+ax+b mod n

def extended_gcd(a,b):   # taken from wikipedia
	x,y,lastx,lasty=0,1,1,0
	while b!=0:
		q=a/b
		a,b=b,a%b
		x,lastx=(lastx-q*x,x)
		y,lasty=(lasty-q*y,y)
	if a<0:
		return (-a,-lastx,-lasty)
	else:
		return (a,lastx,lasty)
def gcd(a,b):
        if a < 0:  a = -a
        if b < 0:  b = -b
        if a == 0: return b
        if b == 0: return a
        while b != 0:
                (a, b) = (b, a%b)
        return a

def randomCurve(N):
	A,u,v=random.randrange(N),random.randrange(N),random.randrange(N)
        B=(v*v-u*u*u-A*u)%N
        return [(A,B,N),(u,v)]

def addPoint(E,p_1,p_2):
	if p_1=="Identity": return [p_2,1]
	if p_2=="Identity": return [p_1,1]
	a,b,n=E
	(x_1,y_1)=p_1
	(x_2,y_2)=p_2
	x_1%=n
	y_1%=n
	x_2%=n
	y_2%=n
	if x_1 != x_2 :
		d,u,v=extended_gcd(x_1-x_2,n)
		s=((y_1-y_2)*u)%n
		x_3=(s*s-x_1-x_2)%n
		y_3=(-y_1-s*(x_3-x_1))%n
	else:
		if (y_1+y_2)%n==0:return ["Identity",1]
		else:
			d,u,v=extended_gcd(2*y_1,n)
			s=((3*x_1*x_1+a)*u)%n
			x_3=(s*s-2*x_1)%n
			y_3=(-y_1-s*(x_3-x_1))%n

	return [(x_3,y_3),d]

def mulPoint(E,P,m):
	Ret="Identity"
	d=1
	while m!=0:
		if m%2!=0: Ret,d=addPoint(E,Ret,P)
		if d!=1 : return [Ret,d]  # as soon as i got anything otherthan 1
return
		P,d=addPoint(E,P,P)
		if d!=1 : return [Ret,d]
		m>>=1
	return [Ret,d]




def ellipticFactor(N,m,times=5):
	for i in xrange(times):
		E,P=randomCurve(N);
		Q,d=mulPoint(E,P,m)
		if d!=1 : return d
	return N

if __name__=="__main__":
	n=input()
	m=int(math.factorial(1000))
	while n!=1:
		k=ellipticFactor(n,m)
		n/=k
		print k