Attack Cryptosystems Based on HCDLP

We present an algorithm for solving the discrete logarithm problem on hyperelliptic curves defined over finite field when the cyclic group can be represented by special form. On the general case, we design a method to attack on hyperelliptic curve cryptosystems. As an example, we illustrate an attack on the Twin Diffie-Hellman key agreement scheme[5]. As a byproduct, we enumerate the isomorphism classes of genus 2 hyperelliptic curves which satisfy some special conditions over a finite field