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Cryptography and Communications

, Volume 11, Issue 1, pp 77–92 | Cite as

New classes of p-ary bent functions

  • Bimal Mandal
  • Pantelimon Stănică
  • Sugata Gangopadhyay
Article
  • 88 Downloads
Part of the following topical collections:
  1. Special Issue on Boolean Functions and Their Applications

Abstract

In this paper, we consider the p-ary functions from \({\mathbb {F}_{p}^{n}}\) to \(\mathbb {F}_{p}\), where p is an odd prime. We characterize the subspace sum concept (depending upon the derivative) and give many of its properties. In particular, we show that the subspace sum of p-ary functions with respect to a subspace of \({\mathbb {F}_{p}^{n}}\) is an affine invariant. Further, we construct two new classes of p-ary bent functions, which do not contain one another.

Keywords

Subspace sum p-ary bent functions Affine invariance 

Mathematics Subject Classification (2010)

06E30 94C10 

Notes

Acknowledgments

We thank the referees for the very useful comments that has immensely helped us to significantly improve both technical and editorial quality of the paper. The first two authors thank the Centre of Excellence in Cryptology (CoEC) and R. C. Bose Centre for Cryptology and Security of Indian Statistical Institute, Kolkata, for supporting their visits at the Indian Statistical Institute, Kolkata, during which period the above work was carried on.

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Copyright information

© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.Department of Applied MathematicsNaval Postgraduate SchoolMontereyUSA
  3. 3.Department of Computer Science and EngineeringIndian Institute of Technology RoorkeeRoorkeeIndia

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