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

Yongqiang Li; Mingsheng Wang

Paper 2011/642 Original: eprint.iacr.org/2011/642 ↗

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

Yongqiang Li

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: Preprint.
History: 2011-11-30: last updated; 2011-11-30: published
Short URL: https://ia.cr/2011/642
License: https://creativecommons.org/licenses/by/4.0/

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}
}