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The Double-Base Number System and its Application to Elliptic Curve Cryptography

Vassil Dimitrov 1 Laurent Imbert 2, 3, 1 Pradeep Mishra 4
1 CISaC - Centre for Information Security and Cryptography
2 PIMS - Pacific Institute for the Mathematical Sciences
3 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
4 ATIPS Labs - Advanced Technologies in Information Processing Systems
Abstract : We describe an algorithm for point multiplication on generic elliptic curves, based on a representation of the scalar as a sum of mixed powers of 2 and 3. The sparseness of this so-called double-base number system, combined with some efficient point tripling formulae, lead to efficient point multiplication algorithms for curves defined over both prime and binary fields. Side-channel resistance is provided thanks to side-channel atomicity.
Keywords : side-channel atomicity double-base number system ECC point multiplication
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00341742
Contributor : Laurent Imbert <>
Submitted on : Tuesday, November 25, 2008 - 6:38:08 PM
Last modification on : Wednesday, October 9, 2019 - 9:42:02 AM

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  • HAL Id : lirmm-00341742, version 1

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CNRS | ARITH | LIRMM | MIPS | UNIV-MONTPELLIER

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Vassil Dimitrov, Laurent Imbert, Pradeep Mishra. The Double-Base Number System and its Application to Elliptic Curve Cryptography. Mathematics of Computation, American Mathematical Society, 2008, 77 (262), pp.1075-1104. ⟨lirmm-00341742⟩

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