On k-Switching of Mappings on Finite Fields
Keywords:
Mappings of finite fields, switching, permutationAbstract
The switching construction was used in several recent papers to construct special mappings on finite fields. In this paper we generalize the concept of switching to a k-switching with 1 ≤ k ≤ n. We present some general properties of k-switching and describe permutations produced using k-switching.
References
A. Akbary, D. Ghioca and Q. Wang, “On constructing permutations of finite fields”, Finite Fields Appl., vol. 17, pp. 51-67, 2011.
L. Budaghyan, C. Carlet and G. Leander, “Constructing new APN functions from known ones”, Finite Fields Appl., vol. 15, pp. 150-159, 2009.
P. Charpin and G. Kyureghyan, “When does G(x) + °Tr(H(x)) permute Fpn?”, Finite Fields Appl., vol. 15, pp. 615-632, 2009.
Y. Edel and A. Pott, “A new almost perfect nonlinear function which is not quadratic”, Adv. Math. Commun., vol. 3, pp. 59-81, 2009.
G. Kyureghyan, “Constructing permutations of finite fields via linear translators”, J. Combin. Theory Ser. A, vol. 118, pp. 1052-1061, 2011.
G. Kyureghyan and Yin Tan, “On a family of planar mappings”, Enhancing crypto¬graphic primitives with techniques from error correcting codes, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur. 23, IOS, Amsterdam, pp. 175-178, 2009.
M. Kyureghyan and S. Abrahamyan, “A method of constructing permutation polyno¬mials over finite fields”, Int. J. Information Theories and Applications, vol. 17, pp. 328-334, 2010.
A. Pott and Y. Zhou, “Switching construction of planar functions on finite fields”, Arithmetic of finite fields, Lecture Notes in Comput. Sci. 6087, Springer, Berlin, pp. 135¬150, 2010.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.