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Combining Montgomery Ladder for Elliptic Curves Defined over $\F_p$ and RNS Representation

Abstract : In this paper, we combine the RNS representation and the Montgomery ladder on elliptic curves in Weierstrass form. These two techniques are relevant for implementation of elliptic curve cryptogra- phy on embedded devices since they have leak-resistance properties. We optimize formulae for addition and doubling of the Montgomery lad- der in terms of modular reductions to obtain a competitive and secure implementation. Afterwards, we explain the advantages of the RNS rep- resentation, especially in hardware and for embedded devices, and show that, contrary to other approaches, ours takes optimal advantage of a dedicated parallel architecture.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00102859
Contributor : Christine Carvalho de Matos <>
Submitted on : Monday, October 2, 2006 - 5:06:07 PM
Last modification on : Friday, January 10, 2020 - 3:36:04 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 1:20:21 AM

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  • HAL Id : lirmm-00102859, version 1

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Jean-Claude Bajard, Sylvain Duquesne, Nicolas Méloni. Combining Montgomery Ladder for Elliptic Curves Defined over $\F_p$ and RNS Representation. [Research Report] 06041, LIR. 2006. ⟨lirmm-00102859⟩

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