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

Povzetek

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.

Ključne besede

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;

Podatki

Jezik:	Angleški jezik
Leto izida:	2009
Tipologija:	1.08 - Objavljeni znanstveni prispevek na konferenci
Organizacija:	UP - Univerza na Primorskem
UDK:	512.624.95
COBISS:	15119705
Št. ogledov:	2983
Št. prenosov:	140
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Sekundarne ključne besede:	kriptoanaliza;kriptografija;algebraične lastnosti;anihilatorji;Boolova funkcija;
Vrsta dela (COBISS):	Delo ni kategorizirano
Strani:	Str. 399-414
ID:	1474224