Paper 2020/357 Original: eprint.iacr.org/2020/357 ↗

Quasigroups and Substitution Permutation Networks: A Failed Experiment

Abstract

We introduce a generalization of substitution permutation networks using quasigroups. Then, we prove that for quasigroups isotopic with a group $\mathbb{G}$, the complexity of mounting a differential attack against our generalization is the same as attacking a substitution permutation network based on $\mathbb{G}$. Although the result is negative, we believe that the design can be instructional for teaching students that failure is a natural part of research. Also, we hope to prevent others from making the same mistake by showing where such a path leads.