Cryptography and Communications

, Volume 3, Issue 1, pp 1–16 | Cite as

New commutative semifields defined by new PN multinomials

Article

Abstract

We introduce two infinite classes of quadratic PN multinomials over \(\textbf{F}_{p^{2k}}\) where p is any odd prime. We prove that for k odd one of these classes defines a new family of commutative semifields (in part by studying the nuclei of these semifields). After the works of Dickson (Trans Am Math Soc 7:514–522, 1906) and Albert (Trans Am Math Soc 72:296–309, 1952), this is the firstly found infinite family of commutative semifields which is defined for all odd primes p. These results also imply that these PN functions are CCZ-inequivalent to all previously known PN mappings.

Keywords

Commutative semifield Equivalence of functions Perfect nonlinear Planar function 

Notes

Acknowledgements

This work was supported by Norwegian Research Council and partly by the grant NIL-I-004 from Iceland, Liechtenstein and Norway through the EEA and Norwegian Financial Mechanisms.

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Copyright information

© Springer Science + Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of InformaticsUniversity of BergenBergenNorway

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