Super Optimal S-boxes Based on Pure Non-linear 3-quasigroups

Abstract

In this paper, we present an approach to construct cryptographically strong 4ï‚´4-bit S-boxes with pure non-linear 3-quasigroups. PRESENT is a light weight block cipher included in ISO and IEC. The S-box used in PRESENT is optimal in linearity, differential uniformity, branch number and algebraic degree. Our methodology is based on 3-quasigroup operations and it enables someone to get 4ï‚´4-bit S-boxes optimal in all the above four properties that PRESENT S-box has.