Almost fully optimized infinite classes of Boolean functions resistant to (fast) algebraic cryptanalysis

Abstract

In this paper the possibilities of an iterative concatenation method towards construction of Boolean functions resistant to algebraic cryptanalysis are investigated. The notion of ▫$\mathcal{AAR}$▫ (Algebraic Attack Resistant) function is introduced as a unified measure of protection against classical algebraic attacks as well as fast algebraic attacks. Then, it is shown that functions that posses the highest resistance to fast algebraic attacks are necessarily of maximum ▫$\mathcal{AI}$▫ (Algebraic Immunity), the notion defined as a minimum degree of functions that annihilate either ▫$f$▫ or ▫$1+f$▫. More precisely, if for any non-annihilating function ▫$g$▫ of degree ▫$e$▫ an optimum degreerelation ▫$e+d \ge n$▫ is satisfied in the product ▫$fg=h$▫ (denoting ▫$deg(h)=d$▫), then the function ▫$f$▫ in ▫$n$▫ variables must have maximum ▫$\mathcal{AI}$▫, i.e. for nonzero function ▫$g$▫ the relation ▫$fg=0$▫ or ▫$(1+f)g=0$▫ implies. The presented theoretical framework allows us to iteratively construct functions with maximum ▫$\mathcal{AI}$▫ satisfying ▫$e+d=n-1$▫, thus almost optimized resistance to fast algebraic cryptanalysis. This infinite class for the first time, apart from almost optimal resistance to algebraic cryptanalysis, in addition generates the functions that possess high nonlinearity (superior to previous constructions) and maximum algebraic degree, thus unifying most of the relevant cryptographic criteria.

Keywords

kriptoanaliza;kriptografija;algebraične lastnosti;anihilatorji;Boolova funkcija;algebraic cryptoanalysis;fast algebraic attacks;algebraic immunity;annihilators;algebraic attack resistant;high degree product;stream ciphers;Boolean function;

Data

Language:	English
Year of publishing:	2009
Typology:	1.08 - Published Scientific Conference Contribution
Organization:	UP - University of Primorska
UDC:	512.624.95
COBISS:	15119705
Views:	2983
Downloads:	140
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary keywords:	kriptoanaliza;kriptografija;algebraične lastnosti;anihilatorji;Boolova funkcija;
Type (COBISS):	Not categorized
Pages:	Str. 399-414
ID:	1474224