| Title: | On cryptographically significant mappings over GF(2 [sup] n) |
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| Authors: | ID Pašalić, Enes (Author) |
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| Files: |  http://dx.doi.org/10.1007/978-3-540-69499-1_16
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.08 - Published Scientific Conference Contribution |
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| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
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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. |
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| Keywords: | cryptoanalysis, cryptography, permutation polynomials, power mappings, APN functions, S-box, CCZ-equivalence, algebraic properties |
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| Year of publishing: | 2008 |
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| Number of pages: | Str. 189-204 |
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| PID: | 20.500.12556/RUP-3586  |
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| UDC: | 512.624.95 |
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| COBISS.SI-ID: | 15119193 |
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| Publication date in RUP: | 15.10.2013 |
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| Views: | 5096 |
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| Downloads: | 76 |
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| Metadata: |    |
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