There are several block ciphers designed by using Feistel networks or their generalization, and some of them allow to be represented by using quasigroup transformations, for suitably defined quasigroups. We are interested in those Feistel ciphers and Generalized Feistel ciphers whose round functions in their Feistel networks are bijections. In that case we can define the wanted quasigroups by using suitable orthomorphisms, derived from the corresponding Feistel networks. Quasigroup representations of the block ciphers MISTY1, Camellia, Four-Cell+ and SMS4 are given as examples.
Feistel network Feistel cipher orthomorphism quasigroup MISTY1 Camellia Four-Cell+ SMS4