Some classes of complete permutation polynomials in the form of (x p m − x + δ) s + ax p m + bx over F p 2m -Reference-Cited by-同舟云学术

Some classes of complete permutation polynomials in the form of (x ^{p
^m} − x + δ)^s + ax ^{p
^m} + bx over F _{p
^2m}

Published:2022-03-15 Issue:0 Volume:0 Page:
ISSN:2444-8656
Container-title:Applied Mathematics and Nonlinear Sciences
language:en
Short-container-title:

Author:

Xu Xiaofang¹,Fan Jinmei²

Affiliation:

1. School of Mathematics and Physics , Hubei Polytechnic University , Huangshi , , China

2. School of Science , Guilin University of Technology , Guilin , , China

Abstract

Abstract Several classes of complete permutation polynomials (CPPs) in the form of (x p m − x + δ) s + ax p m + bx over F p 2m are described in this paper. For fractional exponent s, the permutation properties of the given polynomials are proved by the AGW criterion and for determining the bijectivity of the corresponding piecewise functions. For exponent s satisfying s = i(p m − 1) + p j , the main proofs here depend on the AGW criterion and the quantity of solutions for certain linearised equations. Several results generalise some earlier results on permutation polynomials (PPs).

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science

Link

https://www.sciendo.com/pdf/10.2478/amns.2021.2.00132

Reference27 articles.

1. Akbary, A., Ghioca, D., & Wang, Q. (2011). On constructing permutations of finite fields. Finite Fields Appl. 17, 51–67.

2. Bartoli, D., Giulietti, M., Quoos, L., & Zini, G. (2017). Complete permutation polynomials from exceptional polynomials. J. Number Theory. 176, 46–66.

3. Diffie, W., & Ledin, G. (translators). (2008). SMS4 encryption algorithm for wireless networks. From https://eprint.iacr.org/2008/329.pdf.

4. Feng, D., Feng, X., & Zhang, W., et al. (2011). Loiss: a byte-oriented stream cipher. IWCC’11 Proceedings of the Third international conference on Coding and Cryptology, Springer, 109–125.

5. Gupta, R., & Sharma, R. K. (2018). Further results on permutation polynomials of the form (xpm − x + δ)s + x over Fp2m. Finite Fields Appl. 50, 196–208.