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1.
Almost fully optimized infinite classes of Boolean functions resistant to (fast) algebraic cryptanalysis
Enes Pašalić, 2009, published scientific conference contribution

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.
Found in: ključnih besedah
Summary of found: ...iterative concatenation method towards construction of Boolean functions resistant to algebraic cryptanalysis are investigated. The...
Keywords: algebraic cryptoanalysis, fast algebraic attacks, algebraic immunity, annihilators, algebraic attack resistant, high degree product, stream ciphers, Boolean function
Published: 15.10.2013; Views: 1536; Downloads: 70
URL Full text (0,00 KB)

2.
Finite structures in cryptology
Enes Pašalić, 2013, invited lecture at foreign university

Found in: ključnih besedah
Summary of found: ...multiple Boolean function, bent function, cryptology, ...
Keywords: multiple Boolean function, bent function, cryptology
Published: 15.10.2013; Views: 1084; Downloads: 12
URL Full text (0,00 KB)

3.
Linear separation of connected dominating sets in graphs
Nina Chiarelli, Martin Milanič, 2019, original scientific article

Found in: ključnih besedah
Summary of found: ...minimal separator, 1-Sperner hypergraph, threshold hypergraph, threshold Boolean function...
Keywords: connected dominating set, connected domination, connected-domishold graph, forbidden induced subgraph characterization, split graph, chordal graph, minimal cutset, minimal separator, 1-Sperner hypergraph, threshold hypergraph, threshold Boolean function
Published: 04.04.2019; Views: 364; Downloads: 106
URL Full text (0,00 KB)

4.
On certain properties of APN and AB functions
Amar Bapić, 2019, master's thesis

Found in: ključnih besedah
Summary of found: ... Boolean function, APN function, AB function...
Keywords: Boolean function, APN function, AB function
Published: 25.07.2019; Views: 268; Downloads: 12
URL Full text (0,00 KB)

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