Enhanced Digital Signature using RNS Digit Exponent Representation

Thomas Plantard 1 Jean-Marc Robert 2
2 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) involves modular expo-nentiation, 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. However, due to the cost of the memory , to its small size and to the latency of access, previous research sought for minimization of the storage. In this paper, taking into account the modern processor features and the growing size of the cache memory, we improve the storage/efficiency trade-off, by using a RNS Digit exponent representation. We then propose algorithms for modular exponentiation. The storage is lower for equivalent complexities for modular exponenti-ation computation. The implementation performances show significant memory saving, up to 3 times for the largest NIST standardized key sizes compared to state of the art approaches.
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Communication dans un congrès
International Workshop on the Arithmetic of Finite Fields, WAIFI 2016, Jul 2016, Gand, Belgium. Springer, lncs (à paraître). 〈http://cage.ugent.be/waifi/〉
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Thomas Plantard, Jean-Marc Robert. Enhanced Digital Signature using RNS Digit Exponent Representation. International Workshop on the Arithmetic of Finite Fields, WAIFI 2016, Jul 2016, Gand, Belgium. Springer, lncs (à paraître). 〈http://cage.ugent.be/waifi/〉. 〈hal-01337561〉

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