Efficient elliptic curve scalar multiplication algorithms resistant to power analysis

Authors:
Ning Zhang;Zhixiong Chen;Guozhen Xiao
Affiliations:
National Key Laboratory of ISN, Xidian University, Xi'an, Shaanxi 710071, PR China;National Key Laboratory of ISN, Xidian University, Xi'an, Shaanxi 710071, PR China and Putian University, Putian, Fujian 351100, PR China;National Key Laboratory of ISN, Xidian University, Xi'an, Shaanxi 710071, PR China
Venue:
Information Sciences: an International Journal
Year:
2007

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Abstract

This paper presents four algorithms for securing elliptic curve scalar multiplication against power analysis. The highest-weight binary form (HBF) of scalars and randomization are applied to resist power analysis. By using a special method to recode the scalars, the proposed algorithms do not suffer from simple power analysis (SPA). With the randomization of the secret scalar or base point, three of the four algorithms are secure against differential power analysis (DPA), refined power analysis (RPA) and zero-value point attacks (ZPA). The countermeasures are also immune to the doubling attack. Fast Shamir's method is used in order to improve the efficiency of parallel scalar multiplication. Compared with previous countermeasures, the new countermeasures achieve higher security and do not impact overall performance.