Complementary dual codes for counter-measures to side-channel attacks

Claude  Carlet; Sylvain  Guilley

doi:10.3934/amc.2016.10.131

Article Contents

2016, Volume 10, Issue 1: 131-150. Doi: 10.3934/amc.2016.10.131

This issue Previous Article On applications of orbit codes to storage Next Article Further results on fibre products of Kummer covers and curves with many points over finite fields

Complementary dual codes for counter-measures to side-channel attacks

Claude Carlet^1, and
Sylvain Guilley^2,

1.
LAGA, UMR 7539, CNRS, University of Paris VIII and University of Paris XIII, Department of Mathematics, 2 rue de la liberte, 93 526 Saint-Denis Cedex
2.
TELECOM-ParisTech, Crypto Group | Paris-Saclay University | CNRS LTCI, 37/39 rue Dareau, 75 634 Paris Cedex 13

Received: November 30, 2014

Revised: August 31, 2015

Published: January 2016

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Abstract

We recall why linear codes with complementary duals (LCD codes) play a role in counter-measures to passive and active side-channel analyses on embedded cryptosystems. The rate and the minimum distance of such LCD codes must be as large as possible. We recall the known primary construction of such codes with cyclic codes, and investigate other constructions, with expanded Reed-Solomon codes and generalized residue codes, for which we study the idempotents. These constructions do not allow to reach all the desired parameters. We study then those secondary constructions which preserve the LCD property, and we characterize conditions under which codes obtained by direct sum, direct product, puncturing, shortening, extending codes, or obtained by the Plotkin sum, can be LCD.

Keywords:

Side-channel analysis,
fault injection analysis,
hardware trojan horses,
linear codes with complementary duals (LCD),
cyclic codes,
Bose,
Ray-Chaudhuri and Hocquenghem (BCH) codes,
generalized residue codes.

Mathematics Subject Classification: Primary: 94B15, 94B65; Secondary: 14G50.

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