On the algebraic immunity of direct sum constructions

Reference : On the algebraic immunity of direct sum constructions


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	Focus Areas :	Security, Reliability and Trust
	To cite this reference:	http://hdl.handle.net/10993/52558

Title :	On the algebraic immunity of direct sum constructions
Language :	English
Author, co-author :	Meaux, Pierrick [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > PI Coron]
Publication date :	2022
Journal title :	Discrete Applied Mathematics
Volume :	320
Pages :	223--234
Peer reviewed :	Yes
Audience :	International
Keywords :	[en] Boolean Functions ; Algebraic Immunity ; , Direct Sum
Abstract :	[en] In this paper, we study sufficient conditions to improve the lower bound on the algebraic immunity of a direct sum of Boolean functions. We exhibit three properties on the component functions such that satisfying one of them is sufficient to ensure that the algebraic immunity of their direct sum exceeds the maximum of their algebraic immunities. These properties can be checked while computing the algebraic immunity and they allow to determine better the security provided by functions central in different cryptographic constructions such as stream ciphers, pseudorandom generators, and weak pseudorandom functions. We provide examples for each property and determine the exact algebraic immunity of candidate constructions.
Permalink :	http://hdl.handle.net/10993/52558
DOI :	10.1016/j.dam.2022.05.021
Other URL :	https://doi.org/10.1016/j.dam.2022.05.021

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