Cryptology ePrint Archive: Report 2016/666

Construction of resilient S-boxes with higher-dimensional vectorial outputs and strictly almost optimal nonlinearity

WeiGuo Zhang and LuYang Li and Enes Pasalic

Abstract: Resilient substitution boxes (S-boxes) with high nonlinearity are important cryptographic primitives in the design of certain encryption algorithms. There are several trade-offs between the most important cryptographic parameters and their simultaneous optimization is regarded as a difficult task. In this paper we provide a construction technique to obtain resilient S-boxes with so-called strictly almost optimal (SAO) nonlinearity for a larger number of output bits $m$ than previously known. This is the first time that the nonlinearity bound $2^{n-1}-2^{n/2}$ of resilient $(n,m)$ S-boxes, where $n$ and $m$ denote the number of the input and output bits respectively, has been exceeded for $m>\lfloor\frac{n}{4}\rfloor$. Thus, resilient S-boxes with extremely high nonlinearity and a larger output space compared to other design methods have been obtained.

Category / Keywords: Boolean functions, nonlinearity, resiliency, S-boxes, stream ciphers

Original Publication (with minor differences): IET Information Security

Date: received 29 Jun 2016, last revised 13 Sep 2016

Contact author: weiguozhang at vip qq com

Available format(s): PDF | BibTeX Citation

Note: The title of this paper is changed

Version: 20160913:061400 (All versions of this report)

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