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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 $\mathbb{F}_{2^m}$. 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.

SPA-Resistant Scalar Multiplication on Hyperelliptic Curve Cryptosystems Combining Divisor Decomposition Technique and Joint Regular Form