from sympy import isprime, nextprime

def pollards_rho(G, Q, curve_order):
    x = G
    y = G
    factor = 1
    while factor == 1:
        x = curve_add(x, G, curve_order)
        y = curve_add(y, G, curve_order)
        y = curve_add(y, G, curve_order)
        factor = gcd(abs(x[0]-y[0]), curve_order)
    return factor

def curve_add(p1, p2, curve_order):
    # Simplified elliptic curve addition
    return (p1[0] + p2[0], p1[1] + p2[1]) % curve_order

def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

# Example parameters (not for secp256k1)
G = (3, 7)  # Generator point
Q = (13, 17)  # Public key
curve_order = 19  # Elliptic curve order

d = pollards_rho(G, Q, curve_order)
print(f"Private key (d): {d}")