Efficient and Secure Elliptic Curve Scalar Multiplication Based on Quadruple-and-Add

Shuang-Gen Liu ； Si-Jia An ； Yi-Wei Du

《International Journal of Network Security》 23卷5期 (2021/09) Pp. 750-757

https://doi.org/10.6633/IJNS.202109_23(5).02

摘要

Elliptic curve cryptosystem is one of the main directions of public-key cryptography. Because the short key and efficient arithmetic has attracted increasing attention, particularly in resource-limited hardware environments such as smart cards and phone cards. Scalar multiplication is the most core operation in the elliptic curve cryptosystems, and its operating speed affects the efficiency of the entire cryptosystem. Previous studies have researched how to improve the efficiency of scalar multiplication. In this paper, we propose a new efficient and secure elliptic curve scalar multiplication algorithm. Based on the generalized Fibonacci sequence, a new addition chain is proposed. The new algorithm iterates the ＂4P +Q＂ operation every time and has the powerful ability to resist SPA (Simple Power Attack) naturally. Compared with the existing chains, the new addition chain proposed in this study has a shorter chain length, and combine with the new affine coordinates, can further improve the efficiency. The experimental results indicate that the new algorithm is 27.9% faster than Fibonacci-and-add and 13.1% faster than GRAC (Golden Ratio Addition Chain).

關鍵字

Addition Chain ； Elliptic Curve ； Fibonacci Sequence ； Scalar Multiplication ； Simple Power Analysis