Multiple Scalar-Multiplication Algorithm over Elliptic Curve

Kunio KOBAYASHI  Hikaru MORITA  Mitsuari HAKUTA  

IEICE TRANSACTIONS on Information and Systems   Vol.E84-D    No.2    pp.271-276
Publication Date: 2001/02/01
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Applications of Information Security Techniques
multiple scalar multiplication,  elliptic curve,  

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This paper proposes an extended variant of the method by Brickel et al. for multiple scalar multiplication over an elliptic curve. In smartcard environments, the proposed method is superior to conventional methods. In particular, when the typical number of bases t=2, the proposed method is four times faster than the simultaneous multiple exponentiation method, a well known fast method for multiple scalar multiplication. Furthermore, the proposed method can change the amount of time and memory to fit various platform environment (e.g., personal computers as rich ones or mobile devices such as smartcards as poor ones) by adjusting the division bit width (division unit).