Cryptography and Communications

, Volume 9, Issue 6, pp 693–705 | Cite as

Several classes of permutation trinomials from Niho exponents

  • Nian Li
  • Tor Helleseth


Motivated by recent results on the constructions of permutation polynomials with few terms over the finite field \({\mathbb F}_{2^n}\), where n is a positive even integer, we focus on the construction of permutation trinomials over \({\mathbb F}_{2^n}\) from Niho exponents. As a consequence, several new classes of permutation trinomials over \({\mathbb F}_{2^n}\) are constructed from Niho exponents based on some subtle manipulation of solving equations with low degrees over finite fields.


Finite field Niho exponent Permutation trinomial 

Mathematics Subject Classification (2010)

05A05 11T06 11T55 



The authors would like to thank the editor and reviewers for their comments that improved the quality of this paper. This work was supported by the Norwegian Research Council.


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of InformaticsUniversity of BergenBergenNorway

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