Permutation polynomials of the form (xp - x + δ)s + L (x)

Jin Yuan; Cunsheng Ding; Huaxiong Wang; Josef Pieprzyk

doi:10.1016/j.ffa.2007.05.003

Permutation polynomials of the form (xp - x + δ)^s + L (x)

Jin Yuan^*, Cunsheng Ding, Huaxiong Wang, Josef Pieprzyk

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

65 Citations (Scopus)

Abstract

Recently, several classes of permutation polynomials of the form (x² + x + δ)^s + x over F_2m have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (x^p - x + δ)^s + L (x) over F_pm is investigated, where L (x) is a linearized polynomial with coefficients in F_p. Six classes of permutation polynomials on F_2m are derived. Three classes of permutation polynomials over F_3m are also presented.

Original language	English
Pages (from-to)	482-493
Number of pages	12
Journal	Finite Fields and their Applications
Volume	14
Issue number	2
DOIs	https://doi.org/10.1016/j.ffa.2007.05.003
Publication status	Published - Apr 2008

Keywords

permutation polynomials
kloosterman polynomials

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10.1016/j.ffa.2007.05.003

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abstract = "Recently, several classes of permutation polynomials of the form (x2 + x + δ)s + x over F2m have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (xp - x + δ)s + L (x) over Fpm is investigated, where L (x) is a linearized polynomial with coefficients in Fp. Six classes of permutation polynomials on F2m are derived. Three classes of permutation polynomials over F3m are also presented.",

keywords = "permutation polynomials, kloosterman polynomials",

author = "Jin Yuan and Cunsheng Ding and Huaxiong Wang and Josef Pieprzyk",

year = "2008",

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T1 - Permutation polynomials of the form (xp - x + δ)s + L (x)

AU - Yuan, Jin

AU - Ding, Cunsheng

AU - Wang, Huaxiong

AU - Pieprzyk, Josef

PY - 2008/4

Y1 - 2008/4

N2 - Recently, several classes of permutation polynomials of the form (x2 + x + δ)s + x over F2m have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (xp - x + δ)s + L (x) over Fpm is investigated, where L (x) is a linearized polynomial with coefficients in Fp. Six classes of permutation polynomials on F2m are derived. Three classes of permutation polynomials over F3m are also presented.

AB - Recently, several classes of permutation polynomials of the form (x2 + x + δ)s + x over F2m have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (xp - x + δ)s + L (x) over Fpm is investigated, where L (x) is a linearized polynomial with coefficients in Fp. Six classes of permutation polynomials on F2m are derived. Three classes of permutation polynomials over F3m are also presented.

KW - permutation polynomials

KW - kloosterman polynomials

UR - https://www.scopus.com/pages/publications/40749134215

U2 - 10.1016/j.ffa.2007.05.003

DO - 10.1016/j.ffa.2007.05.003

M3 - Article

AN - SCOPUS:40749134215

SN - 1071-5797

VL - 14

SP - 482

EP - 493

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

IS - 2

ER -

Permutation polynomials of the form (xp - x + δ)^s + L (x)

Abstract

Keywords

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