Paper 2011/642

Constructing differentially 4-uniform permutations over $\mbf_{2^{2m}}$ from quadratic APN permutations over $\mbf_{2^{2m+1}}$

Yongqiang Li and Mingsheng Wang

Abstract

In this paper, by means of the idea proposed in \cite{carlet4uniformpermu}, differentially 4-uniform permutations with the best known nonlinearity over $\mbf_{2^{2m}}$ can be constructed by using quadratic APN permutations over $\mbf_{2^{2m+1}}$. Special emphasis is given for the Gold functions. The algebraic degree of the constructions and their compositional inverse is also investigated. One of the constructions and its compositional inverse have both algebraic degree $m+1$ over $\mbf_2^{2m}$.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
PermutationDifferential uniformityNonlinearityAlgebraic degree
Contact author(s)
liyongqiang @ is iscas ac cn
History
2011-11-30: received
Short URL
https://ia.cr/2011/642
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2011/642,
      author = {Yongqiang Li and Mingsheng Wang},
      title = {Constructing differentially 4-uniform permutations over $\mbf_{2^{2m}}$ from quadratic {APN} permutations over $\mbf_{2^{2m+1}}$},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/642},
      year = {2011},
      url = {https://eprint.iacr.org/2011/642}
}
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