Topic: Pollard's kangaroo ECDLP solver - page 23. (Read 58537 times)

>>> Point1 = Point(0xf9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9, 0x388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672)
>>> Point2 = Point(0xc6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5, 0x1ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52a)
>>> Point3 = sub(Point1,Point2)
>>> hex(Point3.x),hex(Point3.y)
('0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798', '0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8')

import gmpy2

modulo = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
order  = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
Gx = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798
Gy = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8

class Point:
    def __init__(self, x=0, y=0):
        self.x = x
        self.y = y

PG = Point(Gx,Gy)
Z = Point(0,0) # zero-point

# returns (g, x, y) a*x + b*y = gcd(x, y)
def egcd(a, b):
    if a == 0:
        return (b, 0, 1)
    else:
        g, x, y = egcd(b % a, a)
        return (g, y - (b // a) * x, x)

def modinv(m, n = modulo):
    while m < 0:
        m += n
    g, x, _ = egcd(m, n)
    if g == 1:
        return x % n

    else: print (' no inverse exist')

def mul2(Pmul2, p = modulo):
    R = Point(0,0)
    #c = 3*Pmul2.x*Pmul2.x*modinv(2*Pmul2.y, p) % p
    c = 3*Pmul2.x*Pmul2.x*gmpy2.invert(2*Pmul2.y, p) % p
    R.x = (c*c-2*Pmul2.x) % p
    R.y = (c*(Pmul2.x - R.x)-Pmul2.y) % p
    return R

def add(Padd, Q, p = modulo):
    if Padd.x == Padd.y == 0: return Q
    if Q.x == Q.y == 0: return Padd
    if Padd == Q: return mul2(Q)
    R = Point()
    dx = (Q.x - Padd.x) % p
    dy = (Q.y - Padd.y) % p
    c = dy * gmpy2.invert(dx, p) % p
    #c = dy * modinv(dx, p) % p
    R.x = (c*c - Padd.x - Q.x) % p
    R.y = (c*(Padd.x - R.x) - Padd.y) % p
    return R

def mulk(k, Pmulk, p = modulo):
    if k == 0: return Z
    if k == 1: return Pmulk
    if (k % 2 == 0): return mulk(k//2, mul2(Pmulk, p), p)
    return add(Pmulk, mulk((k-1)//2, mul2(Pmulk, p), p), p)

def sub(P1, P2, p = modulo): #scalar subtraction P1-P2
    if P1 == P2: return Z
    if P2.x == P2.y == 0: return P1
    return add (P1, Point(P2.x, modulo - P2.y))

class Point:
    b = 7
    def __init__(self, x=float('inf'), y=float('inf')):
        self.x = x
        self.y = y
 
    def copy(self):
        return Point(self.x, self.y)
 
    def is_zero(self):
        return self.x > 1e20 or self.x < -1e20
 
    def neg(self):
        return Point(self.x, -self.y)
 
    def dbl(self):
        if self.is_zero():
            return self.copy()
        try:
            L = (3 * self.x * self.x) / (2 * self.y)
        except ZeroDivisionError:
            return Point()
        x = L * L - 2 * self.x
        return Point(x, L * (self.x - x) - self.y)
 
    def add(self, q):
        if self.x == q.x and self.y == q.y:
            return self.dbl()
        if self.is_zero():
            return q.copy()
        if q.is_zero():
            return self.copy()
        try:
            L = (q.y - self.y) / (q.x - self.x)
        except ZeroDivisionError:
            return Point()
        x = L * L - self.x - q.x
        return Point(x, L * (self.x - x) - self.y)
 
    def mul(self, n):
        p = self.copy()
        r = Point()
        i = 1
        while i <= n:
            if i&n:
                r = r.add(p)
            p = p.dbl()
            i <<= 1
        return r
 
    def __str__(self):
        return "({:.3f}, {:.3f})".format(self.x, self.y)
 
def show(s, p):
    print(s, "Zero" if p.is_zero() else p)
 
def from_y(y):
    n = y * y - Point.b
    x = n**(1./3) if n>=0 else -((-n)**(1./3))
    return Point(x, y)
 
# demonstrate
a = from_y(1)
b = from_y(2)
show("a =", a)
show("b =", b)
c = a.add(b)
show("c = a + b =", c)
d = c.neg()
show("d = -c =", d)
show("c + d =", c.add(d))
show("a + b + d =", a.add(b.add(d)))
show("a * 12345 =", a.mul(12345))

a = (-1.817, 1.000)
b = (-1.442, 2.000)
c = a + b = (10.375, -33.525)
d = -c = (10.375, 33.525)
c + d = Zero
a + b + d = Zero
a * 12345 = (10.759, 35.387)