On the Differential Spectrum of a Differentially $3$-Uniform Power Function

Tingting Pang; Nian Li; Xiangyong Zeng

Paper 2022/610

On the Differential Spectrum of a Differentially -Uniform Power Function

Tingting Pang, Nian Li, and Xiangyong Zeng

Abstract

In this paper, we investigate the cardinality, denoted by , of the intersection of for , where are the cyclotomic classes of order two over the finite field , is an odd prime and is a positive integer. By making most use of the results on cyclotomic classes of orders two and four as well as the cardinality of the intersection , we compute the values of in the case of , where . As a consequence, the power function over is shown to be differentially -uniform and its differential spectrum is also completely determined.

Metadata

Available format(s): PDF
Publication info: Preprint. MINOR revision.
Keywords: Power function differential spectrum cyclotomic number
Contact author(s): ttingpang @ 163 com
History: 2022-05-23: received
Short URL: https://ia.cr/2022/610
License: CC BY

BibTeX

@misc{cryptoeprint:2022/610,
      author = {Tingting Pang and Nian Li and Xiangyong Zeng},
      title = {On the Differential Spectrum of a Differentially $3$-Uniform Power Function},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/610},
      year = {2022},
      url = {https://eprint.iacr.org/2022/610}
}