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2. Coding theory and applications, solved exercises and problems of cyclic codesEnes Pašalić, 2013, other educational material Found in: osebi Keywords: finite field, counting cyclic codes, codeword, Hamming code, Ternary Golay code, BCH code, BCH decoding, Fire code, Erasure corrections, MDS code, convolutional code Published: 15.10.2013; Views: 1482; Downloads: 32 Full text (0,00 KB) This document has more files! More...

3. Almost fully optimized infinite classes of Boolean functions resistant to (fast) algebraic cryptanalysisEnes 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 nonannihilating 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 ▫$e+d=n1$▫, 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: osebi Keywords: algebraic cryptoanalysis, fast algebraic attacks, algebraic immunity, annihilators, algebraic attack resistant, high degree product, stream ciphers, Boolean function Published: 15.10.2013; Views: 1602; Downloads: 72 Full text (0,00 KB) 
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5. Further results on the relation between nonlinearity and resiliency for Boolean functionsEnes Pašalić, Thomas Johansson, 1999, published scientific conference contribution (invited lecture) Abstract: A good design of a Boolean function used in a stream cipher requires that the function satisfies certain criteria in order to resist different attacks. In this paper we study the tradeoff between two such criteria, the nonlinearity and the resiliency. The results are twofold. Firstly, we establish the maximum nonlinearity for a fixed resiliency in certain cases. Secondly, we present a simple search algorithm for finding Boolean functions with good nonlinearity and some fixed resiliency. Found in: osebi Keywords: Boolean functions, cryptography, optimisation, search problems, stream cipher, attacks, maximum nonlinearity, search algorithm, fixed resiliency Published: 15.10.2013; Views: 1437; Downloads: 71 Full text (0,00 KB) 
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7. Collisions for variants of the BLAKE hash functionJanoš Vidali, Peter Nose, Enes Pašalić, 2010, original scientific article Found in: osebi Keywords: BLAKE, BLOKE, BRAKE, collision, cryptography, fixed point, hash functions Published: 15.10.2013; Views: 1613; Downloads: 32 Full text (0,00 KB) 
8. On cryptographically significant mappings over GF(2 [sup] n)Enes Pašalić, 2008, published scientific conference contribution Abstract: In this paper we investigate the algebraic properties of important cryptographic primitives called substitution boxes (Sboxes). An Sbox is a mapping that takes ▫$n$▫ binary inputs whose image is a binary ▫$m$▫tuple; therefore it is represented as ▫$F:\text{GF}(2)^n \rightarrow \text{GF}(2)^m$▫. One of the most important cryptographic applications is the case ▫$n = m$▫, thus the Sbox may be viewed as a function over ▫$\text{GF}(2^n)$▫. We show that certain classes of functions over ▫$\text{GF}(2^n)$▫ do not possess a cryptographic property known as APN (AlmostPerfect Nonlinear) permutations. On the other hand, when ▫$n$▫ is odd, an infinite class of APN permutations may be derived in a recursive manner, that is starting with a specific APN permutation on ▫$\text{GF}(2^k), k$▫ odd, APN permutations are derived over ▫$\text{GF}(2^{k+2i})$▫ for any ▫$i \geq 1$▫. Some theoretical results related to permutation polynomials and algebraic properties of the functions in the ring ▫$\text{GF}(q)[x,y]$▫ are also presented. For sparse polynomials over the field ▫$\text{GF}(2^n)$▫, an efficient algorithm for finding low degree I/O equations is proposed. Found in: osebi Keywords: cryptoanalysis, cryptography, permutation polynomials, power mappings, APN functions, Sbox, CCZequivalence, algebraic properties Published: 15.10.2013; Views: 1452; Downloads: 28 Full text (0,00 KB) 
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