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The security of block ciphers solely depends on the S-boxes used in their design. Hence, for a secure block cipher, S-boxes should be chosen very thoughtfully.  n -ary quasigroups of different orders and for different values of  n  are being used to design various cryptographic primitives. In the literature, many algorithms based on the quasigroups have been proposed for the generation of S-boxes of order 4. However, in this article, we propose a general method for the construction of symmetric S-boxes of even order using ternary quasigroups of order 4 with certain properties. These S-boxes give strong resistance against linear, differential, algebraic, and DPA attacks and hence provide good cryptographic properties.

Construction of cryptographically strong S-boxes from ternary quasigroups of order 4