| Title: | On cryptographically significant mappings over GF(2 [sup] n) |
|---|
| Authors: | ID Pašalić, Enes (Author) |
|---|
| Files: |  http://dx.doi.org/10.1007/978-3-540-69499-1_16
|
|---|
| Language: | English |
|---|
| Work type: | Not categorized |
|---|
| Typology: | 1.08 - Published Scientific Conference Contribution |
|---|
| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
|
|---|
| 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 |
|---|
| Year of publishing: | 2008 |
|---|
| Number of pages: | Str. 189-204 |
|---|
| PID: | 20.500.12556/RUP-3586  |
|---|
| UDC: | 512.624.95 |
|---|
| COBISS.SI-ID: | 15119193 |
|---|
| Publication date in RUP: | 15.10.2013 |
|---|
| Views: | 4313 |
|---|
| Downloads: | 76 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
