Paper 2017/197

A Construction of Bent Functions with Optimal Algebraic Degree and Large Symmetric Group

Wenying Zhang, Zhaohui Xing, and Keqin Feng

Abstract

We present a construction of bent function $f_{a,S}$ with $n=2m$ variables for any nonzero vector $a\in \mathbb{F}_{2}^{m}$ and subset $S$ of $\mathbb{F}_{2}^{m}$ satisfying $a+S=S$. We give the simple expression of the dual bent function of $f_{a,S}$. We prove that $f_{a,S}$ has optimal algebraic degree $m$ if and only if $|S|\equiv 2 (\bmod 4) $. This construction provides series of bent functions with optimal algebraic degree and large symmetric group if $a$ and $S$ are chosen properly.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Preprint.
Contact author(s)
wzhang @ esat kuleuven be
History
2017-02-28: received
Short URL
https://ia.cr/2017/197
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2017/197,
      author = {Wenying Zhang and Zhaohui Xing and Keqin Feng},
      title = {A Construction of Bent Functions with Optimal Algebraic Degree and Large Symmetric Group},
      howpublished = {Cryptology ePrint Archive, Paper 2017/197},
      year = {2017},
      note = {\url{https://eprint.iacr.org/2017/197}},
      url = {https://eprint.iacr.org/2017/197}
}
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