Constructing an optimum 4×4 S-Box with quasigroup

Abstract

The efficiency of cryptographic algorithms is a problem that is often encountered. One solution of this problem is the use of lightweight cryptography. S-Box is one of the basic non-linear components in a cryptographic algorithm. Among all, 4 × 4 S-Box quasigroup is one kind of S-Box which can be used in lightweight cryptography, that formed by applying quasigroup transformation. The research described in this paper is the construction of the 4 × 4 S-Box using e-transformation of quasigroup as well as to know which leader pattern produces the highest number of optimum S-Box and mostly has higher Robustness value. The construction resulted in 6912 4 × 4 S-Boxes quasigroup by applying for each six leader patterns in four e-transformation rounds of 432 nonlinear quasigroups. The results of 4 × 4 S-Box quasigroup is calculated based on criteria of optimum 4 × 4 S-Box that has higher Robustness value. From all results of the 4 × 4 S-Box quasigroup, it is known that the leader pattern producing S-Box which meet the criteria and all S-Boxes have highest Robustness value are l 1 l 2 l 1 l 2 and l 1 l 2 l 1 l 2. The number of S-Box which meet the criteria is 18,75% of the total 5376 different 4 × 4 S-Boxes quasigroup and the highest Robustness value is 0,75.