Hyperbent functions from hyperovals

Kanat Abdukhalikov; Duy Ho

doi:10.1007/s12095-023-00668-w

Hyperbent functions from hyperovals

Kanat Abdukhalikov
, Duy Ho

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Using polar coordinates, we consider descriptions of translation, Subiaco and Adelaide hyperovals in terms of exponential sums and Kloosterman sums. As an application, we describe a new construction of hyperbent functions that belong to the Charpin and Gong’s family. Explicit examples of this construction are provided as functions with multiple trace terms via Dillon-like exponents.

Original language	English
Pages (from-to)	1031-1048
Number of pages	18
Journal	Cryptography and Communications
Volume	15
Issue number	5
DOIs	https://doi.org/10.1007/s12095-023-00668-w
Publication status	Published - Sept 2023

Keywords

Bent functions
Hyperbent functions
Hyperovals
Kloosterman sums

ASJC Scopus subject areas

Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s12095-023-00668-w

Cite this

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abstract = "Using polar coordinates, we consider descriptions of translation, Subiaco and Adelaide hyperovals in terms of exponential sums and Kloosterman sums. As an application, we describe a new construction of hyperbent functions that belong to the Charpin and Gong{\textquoteright}s family. Explicit examples of this construction are provided as functions with multiple trace terms via Dillon-like exponents.",

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AB - Using polar coordinates, we consider descriptions of translation, Subiaco and Adelaide hyperovals in terms of exponential sums and Kloosterman sums. As an application, we describe a new construction of hyperbent functions that belong to the Charpin and Gong’s family. Explicit examples of this construction are provided as functions with multiple trace terms via Dillon-like exponents.

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KW - Hyperbent functions

KW - Hyperovals

KW - Kloosterman sums

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Hyperbent functions from hyperovals

Abstract

Keywords

ASJC Scopus subject areas

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