On the c-differential uniformity of certain maps over finite fields
| Autor: | Sartaj Ul Hasan, Pantelimon Stanica, Mohit Pal, Constanza Riera |
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| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Polynomial Pure mathematics Class (set theory) 12E20 06E30 11T06 94A60 94C10 Computer Science - Information Theory Information Theory (cs.IT) Applied Mathematics Differential uniformity Process (computing) Function (mathematics) Computer Science Applications Power (physics) Finite field FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) Affine transformation Mathematics |
| Zdroj: | Designs, Codes and Cryptography. 89:221-239 |
| ISSN: | 1573-7586 0925-1022 |
| DOI: | 10.1007/s10623-020-00812-0 |
| Popis: | We give some classes of power maps with low $c$-differential uniformity over finite fields of odd characteristic, {for $c=-1$}. Moreover, we give a necessary and sufficient condition for a linearized polynomial to be a perfect $c$-nonlinear function and investigate conditions when perturbations of perfect $c$-nonlinear (or not) function via an arbitrary Boolean or $p$-ary function is perfect $c$-nonlinear. In the process, we obtain a class of polynomials that are perfect $c$-nonlinear for all $c\neq 1$, in every characteristic. The affine, extended affine and CCZ-equivalence is also looked at, as it relates to $c$-differential uniformity. Comment: Revised version; 22 pages; to appear in Des. Codes Cryptogr |
| Databáze: | OpenAIRE |
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