Selection of secure hyperelliptic curves of g =2 based on a subfield
Selection of Secure Hyperelliptic Curves of g = 2 Based on a Subfield

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 v2 uv=f and v2 v=f(u) defined on GF(2r). The curves defined on GF(4) and GF(8) are expanded to the curves defined on GF(4)k and GF(8)t respectively, where 38