Upper bounding the number of bent functions using 2-row bent rectangles

Sergey Agievich

Paper 2023/497

Upper bounding the number of bent functions using 2-row bent rectangles

Sergey Agievich

, Belarusian State University

Abstract

Using the representation of bent functions by bent rectangles, that is, special matrices with restrictions on columns and rows, we obtain an upper bound on the number of bent functions that improves previously known bounds in a practical range of dimensions. The core of our method is the following fact based on the recent observation by Potapov (arXiv:2107.14583): a 2-row bent rectangle is completely determined by one of its rows and the remaining values in slightly more than half of the columns.

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Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint.
Keywords: bent function bent rectangle near-bent function number of bent functions Walsh–Hadamard spectrum
Contact author(s): agievich @ bsu by
History: 2023-06-01: revised; 2023-04-05: received; See all versions
Short URL: https://ia.cr/2023/497
License: CC BY

BibTeX

@misc{cryptoeprint:2023/497,
      author = {Sergey Agievich},
      title = {Upper bounding the number of bent functions using 2-row bent rectangles},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/497},
      year = {2023},
      url = {https://eprint.iacr.org/2023/497}
}