The 2-Adic CM Method for Genus 2 Curves with Application to Cryptography

Abstract. The complex multiplication (CM) method for genus 2 is currently the most efficient way of generating genus 2 hyperelliptic curves defined over large prime fields and suitable for cryptography. Since low class number might be seen as a potential threat, it is of interest to push the method as far as possible. We have thus designed a new algorithm for the construction of CM invariants of genus 2 curves, using 2-adic lifting of an input curve over a small finite field. This provides a numerically stable alternative to the complex analytic method in the first phase of the CM method for genus 2. As an example we compute an irreducible factor of the Igusa class polynomial system for the quartic CM field Q(i

• Type: Conference
• Year: 2006
• Where: ASIACRYPT
• Authors: Pierrick Gaudry, T. Houtmann, D. Kohel, Christophe Ritzenthaler, A. Weng
• Keywords: ASIACRYPT 2006, Class Number, Cryptology, Large Prime Field, Quartic Cm Field