New classes of p-ary bent functions

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.

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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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Correspondence to Pantelimon Stănică.

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This article is part of the Topical Collection on Special Issue on Boolean Functions and Their Applications

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Mandal, B., Stănică, P. & Gangopadhyay, S. New classes of p-ary bent functions. Cryptogr. Commun. 11, 77–92 (2019). https://doi.org/10.1007/s12095-018-0290-9

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Keywords

  • Subspace sum
  • p-ary bent functions
  • Affine invariance

Mathematics Subject Classification (2010)

  • 06E30
  • 94C10