Generalized Scalar Multiplication Secure against SPA, DPA, and RPA

Atsuko MIYAJI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.10   pp.2833-2842
Publication Date: 2008/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.10.2833
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Cryptography and Information Security
elliptic curve scalar multiplication,  ZPA,  RPA,  DPA,  SPA,  

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In the execution on a smart card, elliptic curve cryptosystems have to be secure against side channel attacks such as the simple power analysis (SPA), the differential power analysis (DPA), and the refined power analysis (RPA), and so on. MMM-algorithm proposed by Mamiya, Miyaji, and Morimoto is a scalar multiplication algorithm secure against SPA, DPA, and RPA, which can decrease the computational complexity by increasing the size of a pre-computed table. However, it provides only 4 different cases of pre-computed tables. From the practical point of view, a wider range of time-memory tradeoffs is usually desired. This paper generalizes MMM-algorithm to improve the flexibility of tables as well as the computational complexity. Our improved algorithm is secure, efficient and flexible for the storage size.