Fast and scalable parallel processing of scalar multiplication in elliptic curve cryptosystems
Keke Wu, Huiyun Li, Dingju Zhu · Security and Communication Networks · 2011
ABSTRACT To secure parallel systems in communication networks, in this paper, we propose a fast and scalable parallel scalar multiplication method over generic elliptic curves for elliptic curve cryptosystems, by means of our proposed scalar folding and unfolding techniques. In contrast to previous parallel scalar multiplication methods, our method can be implemented into scalable parallel computers. The optimal time complexity is k point doublings (D) plus log k point additions (A), denoted as kD + (log k)A, where k is the bit length of the scalar. If our method is applied to Koblitz curves, the optimal time complexity can be reduced to (log k)A. Furthermore, previous simple side‐channel‐protected scalar multiplication methods can be integrated into our method for resisting against simple side‐channel attacks. Copyright © 2011 John Wiley & Sons, Ltd.