The elliptic curve cryptosystem is a popular cryptosystem. Its safety depends on the difficulty of the elliptic curve discrete logarithm problem (ECDLP). From the viewpoint of ECDLP, it is very interesting to determine the order of elliptic curves. We tabulate the order of elliptic curves on the finite field of characteristic two using the Schoof algorithm, which is an efficient algorithm to decide orders. The Schoof algorithm is carried out by O(log(8)q). Because the calculation of y(q2) occupies most of the time used to execute the Schoof algorithm, it is necessary to reduce the amount of y(q2) calculations.
finite field of characteristic two