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

Authors:
Jin Yuan;Cunsheng Ding;Huaxiong Wang;Josef Pieprzyk
Affiliations:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia;Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China;Division of Mathematical Sciences, Nanyang Technological University, Singapore and Centre for Advanced Computing---Algorithms and Cryptography, Department of Computing, Macquarie University, Austr ...;Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
Venue:
Finite Fields and Their Applications
Year:
2008

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Abstract

Recently, several classes of permutation polynomials of the form (x^2+x+@d)^s+x over F"2"^"m have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (x^p-x+@d)^s+L(x) over F"p"^"m is investigated, where L(x) is a linearized polynomial with coefficients in F"p. Six classes of permutation polynomials on F"2"^"m are derived. Three classes of permutation polynomials over F"3"^"m are also presented.