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Title:
Combining leak–resistant arithmetic for elliptic curves defined over \F_p and RNS representation
Authors: J. C. Bajard, S. Duquesne, M. Ercegovac
Abstract:In this paper we combine the residue number system (RNS) representation and the leak-resistant arithmetic on elliptic curves. These two techniques are relevant for implementation of elliptic curve cryptography on embedded devices.\ % since they have leak-resistance properties. It is well known that the RNS multiplication is very efficient whereas the reduction step is costly. Hence, we optimize formulae for basic operations arising in leak-resistant arithmetic on elliptic curves (unified addition, Montgomery ladder) in order to minimize the number of modular reductions. We also improve the complexity of the RNS modular reduction step. As a result, we show how to obtain a competitive secured implementation.\ Finally, %we recall the main advantages of the RNS representation, %especially in hardware and for embedded devices, and we show that, contrary to other approaches, ours takes optimally the advantage of a dedicated parallel architecture.
ePrint: https://eprint.iacr.org/2010/311
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