Paper 2011/047

Constructing differential 4-uniform permutations from know ones

Yuyin Yu, Mingsheng Wang, and Yongqiang Li

Abstract

It is observed that exchanging two values of a function over ${\mathbb F}_{2^n}$, its differential uniformity and nonlinearity change only a little. Using this idea, we find permutations of differential $4$-uniform over ${\mathbb F}_{2^6}$ whose number of the pairs of input and output differences with differential $4$-uniform is $54$, less than $63$, which provides a solution for an open problem proposed by Berger et al. \cite{ber}. Moreover, for the inverse function over $\mathbb{F}_{2^n}$ ($n$ even), various possible differential uniformities are completely determined after its two values are exchanged. As a consequence, we get some highly nonlinear permutations with differential uniformity $4$ which are CCZ-inequivalent to the inverse function on $\mathbb{F}_{2^n}$.

Metadata
Available format(s)
PDF
Category
Applications
Publication info
Published elsewhere. Unknown where it was published
Keywords
vectorial boolean functiondifferential uniformitynonlinearityCCZ-equivalencealmost perfect nonlinear (APN)
Contact author(s)
yuyuyin @ 163 com
History
2011-06-17: revised
2011-01-25: received
See all versions
Short URL
https://ia.cr/2011/047
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2011/047,
      author = {Yuyin Yu and Mingsheng Wang and Yongqiang Li},
      title = {Constructing differential 4-uniform permutations from know ones},
      howpublished = {Cryptology ePrint Archive, Paper 2011/047},
      year = {2011},
      note = {\url{https://eprint.iacr.org/2011/047}},
      url = {https://eprint.iacr.org/2011/047}
}
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