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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.
Found in: ključnih besedah
Summary of found: ...cryptoanalysis, cryptography, permutation polynomials, power mappings, APN functions, S-box, CCZ-equivalence, algebraic properties...
Keywords: cryptoanalysis, cryptography, permutation polynomials, power mappings, APN functions, S-box, CCZ-equivalence, algebraic properties
Published: 15.10.2013; Views: 2485; Downloads: 68
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Found in: ključnih besedah
Summary of found: ...artistic gymnastics, rhytmic gymnastics, countermovement jump, explosive power, CMJ, ...
Keywords: artistic gymnastics, rhytmic gymnastics, countermovement jump, explosive power, CMJ
Published: 15.10.2015; Views: 4048; Downloads: 44
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Summary of found: Zadetek v naslovu
Keywords: maximal explosive power, bed rest, diet, lower limbs, nutritional countermeasures
Published: 08.08.2016; Views: 2170; Downloads: 192
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Found in: ključnih besedah
Summary of found: Zadetek v naslovu
Keywords: skeletal muscles, muscle fibers, contractile properties, body-builders, power athletes
Published: 08.08.2016; Views: 3349; Downloads: 191
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Found in: ključnih besedah
Summary of found: ...cutting process, sawing process, cutting power, fracture toughness, drying process, pine wood, beech...
Keywords: cutting process, sawing process, cutting power, fracture toughness, drying process, pine wood, beech wood, shear yield stress
Published: 26.10.2020; Views: 781; Downloads: 57
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