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On a conjecture on APN permutations

Cryptography and Communications volume 14, pages 925–931 (2022)Cite this article

Abstract

The single trivariate representation proposed in [C. Beierle, C. Carlet, G. Leander, L. Perrin, A Further Study of Quadratic APN Permutations in Dimension Nine, arXiv:2104.08008] of the two sporadic quadratic APN permutations in dimension 9 found by Beierle and Leander (2020) is further investigated. In particular, using tools from algebraic geometry over finite fields, we prove that such a family does not contain any other APN permutation for larger dimensions.

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Acknowledgements

The research of D. Bartoli and M. Timpanella was partially supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA - INdAM). The second author was supported by the project ”VALERE: VAnviteLli pEr la RicErca” of the University of Campania ”Luigi Vanvitelli”. The authors are grateful to C. Beierle, C. Carlet, G. Leander, and L. Perrin for a number of valuable comments on an earlier draft.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy

    Daniele Bartoli

  2. Dipartimento di Matematica e Fisica, Università degli Studi della Campania “Luigi Vanvitelli”, Caserta, Italy

    Marco Timpanella

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  1. Daniele Bartoli
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  2. Marco Timpanella
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Correspondence to Daniele Bartoli.

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Bartoli, D., Timpanella, M. On a conjecture on APN permutations. Cryptogr. Commun. 14, 925–931 (2022). https://doi.org/10.1007/s12095-022-00558-7

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  • DOI: https://doi.org/10.1007/s12095-022-00558-7

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