Selection of Secure Hyperelliptic Curves of g = 2 Based on a Subfield

摘要

In the implementation of hyperelliptic curve cryptosystems, a siginificant step is the selection of secure hyperelliptic curves on which the Jacobian is constructed. In this paper, we discuss the hyperelliptic curves of g = 2 such as v~2 + uv = f and v~2 + v = f(u) defined on GF(2~r). The curves denned on GF(4) and GF(8) are expanded to the curves defined on GF(4)~k and GF(8)~t respectively, where 38 < k < 70, 25 < t < 50. We also find out all the secure curves of g = 2 that are suitable for establishing cryptosystems.