Pollard's Rho

RSA Factorization

POC

def rsa_attack_with_rho(n):
    """Break RSA by factoring n"""
    factor = pollard_rho(n)
    if factor and factor != n:
        p, q = factor, n // factor
        return compute_rsa_private_key(p, q, e)
    return None

Elliptic Curve Discrete Log (ECDLP)

POC

def pollard_rho_ecdlp(curve, point_p, point_q):
    """
    Solve: point_q = k * point_p (find k)
    Used to break weak elliptic curve implementations
    """
    # Pollard's Rho for elliptic curves
    # Different function f(x) = x + point_p or 2*x based on x
    
    x = random_point_on_curve(curve)
    y = x
    
    while True:
        x = rho_function_ec(x, point_p, curve)
        y = rho_function_ec(rho_function_ec(y, point_p, curve), point_p, curve)
        
        if x == y:  # Collision detected
            # Extract discrete log using collision
            return extract_discrete_log(x, y, point_p, point_q)

General Discrete Logarithm

POC

def pollard_rho_discrete_log(g, h, p):
    """
    Solve: h = g^x mod p (find x)
    Breaks weak discrete log implementations
    """
    # Similar structure but different function
    return pollard_rho_dlog_implementation(g, h, p)