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 1 - 2 / 21 1.On cryptographically significant mappings over GF(2 [sup] n)Enes Pašalić, 2008, published scientific conference contributionAbstract: 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.Found in: ključnih besedahSummary of found: ...cryptographic property known as APN (AlmostPerfect Nonlinear) permutations. On the other hand, when ▫$n$▫ is... ...1\$▫. Some theoretical results related to permutation polynomials and algebraic properties of the functions in...Keywords: cryptoanalysis, cryptography, permutation polynomials, power mappings, APN functions, S-box, CCZ-equivalence, algebraic propertiesPublished: 15.10.2013; Views: 1366; Downloads: 27 Full text (0,00 KB) 2.On derivatives of planar mappings and their connections to complete mappingsAmela Muratović-Ribić, Enes Pašalić, 2018, original scientific articleAbstract: Given are necessary conditions for a permutation polynomial to be the derivative of a planar mapping. These conditions are not sufficient and there might exist permutation polynomials which are not derivatives of some planar mapping satisfying these conditions. For the first time we show that there is a close connection between two seemingly unrelated structures, namely planar and complete mappings. It is shown that any planar mapping induces a sequence of complete mappings having some additional interesting properties. Furthermore, a class of almost planar mappings over extension fields is introduced having the property that its derivatives are permutations in most of the cases. This class of functions then induces many infinite classes of complete mappings (permutations) as well.Found in: ključnih besedahSummary of found: ...Given are necessary conditions for a permutation polynomial to be the derivative of a... ...not sufficient and there might exist permutation polynomials which are not derivatives of some planar...Keywords: planar mapping, derivatives, complete mappings, permutation polynomialsPublished: 19.12.2018; Views: 523; Downloads: 104 Full text (0,00 KB)
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