SPA-resistant scalar multiplication on hyperelliptic curve cryptosystems combining divisor decomposition technique and joint regular form

Abstract

Hyperelliptic Curve Cryptosystems (HECC) are competitive to elliptic curve cryptosystems in performance and security. Recently efficient scalar multiplication techniques using a theta divisor have been proposed. Their application, however, is limited to the case when a theta divisor is used for the base point. In this paper we propose efficient and secure scalar multiplication of a general divisor for genus 2 HECC over IF2m. The proposed method is based on two novel techniques. One is divisor decomposition technique in which a general divisor is decomposed into two theta divisors. The other is joint regular form for a pair of integers that enables efficient and secure simultaneous scalar multiplication of two theta divisors. The marriage of the above two techniques achieves both about 19% improvement of efficiency compared to the standard method and resistance against simple power analysis without any dummy operation. © International Association for Cryptologic Research 2006.