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Paper 2020/1111

Extending the Signed Non-zero Bit and Sign-Aligned Columns Methods to General Bases for Use in Cryptography

Abhraneel Dutta and Aaron Hutchinson and Koray Karabina

Abstract

An efficient scalar multiplication algorithm is a crucial component of elliptic curve cryptosystems. In this paper we propose a scalar multiplication algorithm based on scalar recodings that is regular in nature and provides resistance against simple power analysis attacks. Our scalar multiplication algorithm is made from two scalar recoding algorithms called Recode and Align. Recode is the generalization of the signed non-zero bit recoding algorithm given by Hedabou, Pinel and Beneteau in 2005. It recodes the $k$-$ary$ representation of the given scalar into a signed nonzero form by means of a small lookup table. On the other hand, Align is the generalized $k$-$ary$ version of the sign-aligned columns recoding algorithm given by Faz-Hernandez, Longa and Sanchez in 2014. It recodes the $k$-$ary$ representation of a scalar in such a way that the sign of each of its digits agrees a given $\{1,-1\}$-valued sequence of signs. When analyzing the choice of $k$ in $\{2,3\}$, we find some theoretical evidence that $k=3$ may offer better performance in certain scenarios.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
Elliptic curvesscalar multiplicationside-channel analysisscalar recoding
Contact author(s)
adutta2016 @ fau edu,a5hutchinson @ uwaterloo ca,koray karabina @ nrc-cnrc gc ca
History
2020-10-28: last of 2 revisions
2020-09-15: received
See all versions
Short URL
https://ia.cr/2020/1111
License
Creative Commons Attribution
CC BY
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