20.500.12556/RUP-3586 On cryptographically significant mappings over GF(2 [sup] n) 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. cryptoanalysis cryptography permutation polynomials power mappings APN functions S-box CCZ-equivalence algebraic properties kriptoanaliza kriptografija algebraične lastnosti true true false Angleški jezik Angleški jezik Delo ni kategorizirano 2013-10-15 12:08:51 2013-10-15 12:08:51 2024-03-01 12:11:16 0000-00-00 00:00:00 2008 0 0 Str. 189-204 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.624.95 15118937 15119193 http://dx.doi.org/10.1007/978-3-540-69499-1_16 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=3586 Fakulteta za matematiko, naravoslovje in informacijske tehnologije 0 0 0