Abstract
In this paper, we will present improvements in the secure genus 2 HEC (hyperelliptic curve) cryptosystem construction by using the CM theory. More precisely, we describe algorithmic improvements to reduce the number of significant digits necessary for the construction of class polynomials. In particular, the effectiveness of the "denominator guessing" method is estimated heuristically and verified by experiments. In addition, a secure HEC cryptosystem parameter is described. As it arises from class polynomials of degree 40 (of a CM field whose class number is 20), the practicality of the CM-method is improved.
