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

In the implementation of hyperelliptic curve cryptosystems, asiginificant step is the selection of secure hyperelliptic curves onwhich the Jacobian is constructed. In this paper, we discuss thehyperelliptic curves of g=2 such as v^2+uv=f and v^2+v=f(u) defined on GF(2^r). 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