抄録
In this paper, we consider the security of Montgomery-form elliptic curve cryptosystems in two ways. First, we estimate the number of Montgomery-form elliptic curves for a fixed key-size. As a result, the number of Montgomery-form curves is nearly equal to that of Weierstrass-form curves. Second, we consider transformability of a Weierstrass-form elliptic curve to a Montgomery-form one. Then we discuss adaptability of attacks for Montgomery-form elliptic curve cryptosystems to those for Weierstrass-form ones. In addition, we compare the number of Montgomery-form curve to other special types of elliptic curves, including Koblitz curves, anomalous curves, and supersingular curves.
