Paper 2010/311

Combining leak--resistant arithmetic for elliptic curves defined over $\F_p$ and RNS representation

J. C. Bajard, S. Duquesne, and M. Ercegovac


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.

Available format(s)
Publication info
Published elsewhere. Unknown where it was published
ellicptic curvesleak resistanceRNSarithmetic
Contact author(s)
sylvain duquesne @ univ-rennes1 fr
2010-05-25: received
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Creative Commons Attribution


      author = {J. C.  Bajard and S.  Duquesne and M.  Ercegovac},
      title = {Combining leak--resistant arithmetic for elliptic curves defined over $\F_p$ and RNS representation},
      howpublished = {Cryptology ePrint Archive, Paper 2010/311},
      year = {2010},
      note = {\url{}},
      url = {}
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