anomalous.py

# http://www.monnerat.info/publications/anomalous.pdf

def anon_prime(m):
    while True:
        p = (19*m*(m + 1)) + 5
        if is_prime(p):
            return p
        m += 1


def anom_curve():
    m = 2**64 # Set approx size of p
    p = anon_prime(m)
    E = EllipticCurve(GF(p), j=j_D)
        
    if E.order() == p:
        return E
    E1 = E.quadratic_twist()
    assert E1.order() == p
    return E1
  
D = 19
j_D = -2^15*3^3
E = anom_curve()