An Equivalent Condition on the Switching Construction of Differentially $4$-uniform Permutations on $\gf_{2^{2k}}$ from the Inverse Function

Xi Chen; Yazhi Deng; Min Zhu; Longjiang Qu

Paper 2014/648

An Equivalent Condition on the Switching Construction of Differentially $4$-uniform Permutations on $\gf_{2^{2k}}$ from the Inverse Function

Xi Chen, Yazhi Deng, Min Zhu, and Longjiang Qu

Abstract

Differentially $4$-uniform permutations on $\gf_{2^{2k}}$ with high nonlinearity are often chosen as substitution boxes in block ciphers. Recently, Qu et al. used the powerful switching method to construct permutations with low differential uniformity from the inverse function \cite{QTTL, QTLG} and proposed a sufficient but not necessary condition for these permutations to be differentially $4$-uniform. In this paper, a sufficient and necessary condition is presented. We also give a compact estimation for the number of constructed differentially $4$-uniform permutations. Comparing with those constructions in \cite{QTTL, QTLG}, the number of functions constructed here is much bigger. As an application, a new class of differentially $4$-uniform permutations is constructed. The obtained functions in this paper may provide more choices for the design of substitution boxes.

Note: International Journal of Computer Mathematics, to appear

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Minor revision. International Journal of Computer Mathematics, to appear
Keywords: Differentially $4$-uniform permutation Substitution box $4$-Uniform BFI Preferred Boolean function APN function
Contact author(s): 1138470214 @ qq com
History: 2016-02-15: revised; 2014-08-27: received; See all versions
Short URL: https://ia.cr/2014/648
License: CC BY

BibTeX

@misc{cryptoeprint:2014/648,
      author = {Xi Chen and Yazhi Deng and Min Zhu and Longjiang Qu},
      title = {An Equivalent Condition on the Switching Construction of Differentially $4$-uniform Permutations on $\gf_{2^{2k}}$ from the Inverse Function},
      howpublished = {Cryptology {ePrint} Archive, Paper 2014/648},
      year = {2014},
      url = {https://eprint.iacr.org/2014/648}
}