## Cryptology ePrint Archive: Report 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.

Category / Keywords: Differentially $4$-uniform permutation, Substitution box, $4$-Uniform BFI, Preferred Boolean function, APN function

Original Publication (with minor differences): International Journal of Computer Mathematics, to appear

Date: received 21 Aug 2014, last revised 15 Feb 2016

Contact author: 1138470214 at qq com

Available format(s): PDF | BibTeX Citation

Note: International Journal of Computer Mathematics, to appear

Short URL: ia.cr/2014/648

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