Paper 2019/079

New Results about the Boomerang Uniformity of Permutation Polynomials

Kangquan Li, Longjiang Qu, Bing Sun, and Chao Li

Abstract

In EUROCRYPT 2018, Cid et al. introduced a new concept on the cryptographic property of S-boxes: Boomerang Connectivity Table (BCT for short) for evaluating the subtleties of boomerang-style attacks. Very recently, BCT and the boomerang uniformity, the maximum value in BCT, were further studied by Boura and Canteaut. Aiming at providing new insights, we show some new results about BCT and the boomerang uniformity of permutations in terms of theory and experiment in this paper. Firstly, we present an equivalent technique to compute BCT and the boomerang uniformity, which seems to be much simpler than the original definition. Secondly, thanks to Carlet's idea, we give a characterization of functions $f$ from $\mathbb{F}_{2}^n$ to itself with boomerang uniformity $\delta_{f}$ by means of the Walsh transform. Thirdly, by our method, we consider boomerang uniformities of some specific permutations, mainly the ones with low differential uniformity. Finally, we obtain another class of $4$-uniform BCT permutation polynomials over $\mathbb{F}_{2^n}$, which is the first binomial.

Metadata
Available format(s)
PDF
Publication info
Preprint. Minor revision.
Keywords
Finite FieldBoomerang Connectivity TableBoomerang UniformityPermutation Polynomial
Contact author(s)
likangquan11 @ nudt edu cn
History
2019-01-28: received
Short URL
https://ia.cr/2019/079
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2019/079,
      author = {Kangquan Li and Longjiang Qu and Bing Sun and Chao Li},
      title = {New Results about the Boomerang Uniformity of Permutation Polynomials},
      howpublished = {Cryptology ePrint Archive, Paper 2019/079},
      year = {2019},
      note = {\url{https://eprint.iacr.org/2019/079}},
      url = {https://eprint.iacr.org/2019/079}
}
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