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44. Coding theory and applications, solved exercises and problems of linear codesEnes Pašalić, 2013, other educational material Keywords: Gilbert-Eliot channel model, linear code, linear block code, code design, undetected error probability, linear independence, standard form, codeword weight, code rate, systematic code, Binary Hamming code
Published in RUP: 15.10.2013; Views: 5390; Downloads: 95
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47. 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 (S-boxes). An S-box 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 S-box 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.
Keywords: cryptoanalysis, cryptography, permutation polynomials, power mappings, APN functions, S-box, CCZ-equivalence, algebraic properties
Published in RUP: 15.10.2013; Views: 3279; Downloads: 74
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48. Collisions for variants of the BLAKE hash functionJanoš Vidali, Peter Nose, Enes Pašalić, 2010, original scientific article Keywords: BLAKE, BLOKE, BRAKE, collision, cryptography, fixed point, hash functions
Published in RUP: 15.10.2013; Views: 3058; Downloads: 64
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50. 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.
Keywords: Boolean functions, cryptography, optimisation, search problems, stream cipher, attacks, maximum nonlinearity, search algorithm, fixed resiliency
Published in RUP: 15.10.2013; Views: 2960; Downloads: 132
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