Efficient Fixed Base Exponentiation and Scalar Multiplication based on a Multiplicative Splitting Exponent Recoding

Jean-Marc Robert 1 Christophe Negre 1 Thomas Plantard 2
1 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : Digital Signature Algorithm (DSA) (resp. ECDSA) involves modular exponentiation (resp. scalar multiplication) of a public and known base by a random one-time exponent. In order to speed-up this operation, well-known methods take advantage of the memorization of base powers (resp. base multiples). Best approaches are the Fixed-base Radix-R method and the Fixed-base Comb method. In this paper we present a new approach for storage/online computation trade-off, by using a multiplicative splitting of the digits of the exponent radix-R representation. We adapt classical algorithms for modular exponentiation and scalar multiplication in order to take advantage of the proposed exponent recoding. An analysis of the complexity for practical size shows that our proposed approach involves a lower storage for a given level of online computation. This is confirmed by implementation results showing significant memory saving, up to 3 times for the largest NIST standardized key sizes, compared to the state of the art approaches.
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Jean-Marc Robert, Christophe Negre, Thomas Plantard. Efficient Fixed Base Exponentiation and Scalar Multiplication based on a Multiplicative Splitting Exponent Recoding. Journal of Cryptographic Engineering, Springer, 2019, 9 (2), pp.115-136. ⟨10.1007/s13389-018-0196-7⟩. ⟨lirmm-01926767⟩

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