¹ Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China; Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences and The Chinese University of Hong Kong, Shenzhen, China; Graduate University of Chinese Academy of Sciences, Beijing, China
² Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences and The Chinese University of Hong Kong, Shenzhen, China

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Abstract—At the elliptic curve cryptosystems (ECC) implementation stage, a major concern is securing scalar multiplications against so-called side-channel attacks (SCA). Existing solutions reach the goal by inserting dummy operations (typically increase 33% computational costs) based on commonly-used binary method, which largely increases the computational costs and prohibits the deployment of ECC in computation resource-restricted devices. In this paper, we for the first time propose a secure scalar multiplication method that does not penalise the computational cost compared to binary method. We partition the bit string of the scalar in half and extracting the common substring from the two parts based on bit-wise logical operations, so as to save the number of point additions required for the computation of the common substring. Computational results demonstrate the proposed method remains approximately the same computational cost as binary method. The side-channel experiments prove that the proposed method is secure against SSCA. Also, we use the randomization technique to secure our method against differential SCA (DSCA).

Index Terms—Elliptic curve cryptosystems (ECC); sidechannel attacks (SCA); scalar multiplication; binary method; Montgomery method

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Cite: Keke Wu, Huiyun Li and Fengqi Yu, " Retrieving Lost Efficiency of Scalar Multiplications for Resisting against Side-Channel Attacks," Journal of Computers vol. 5, no. 12, pp. 1878-1884, 2010.