An Efficient Affine Equivalence Algorithm for Multiple S-Boxes and a Structured Affine Layer

An affine equivalence problem is to find affine mappings A and B such that \(F=B\circ S\circ A\) for given two permutations F and S, which was first studied by Biryukov et al. Their algorithm for solving an affine equivalence problem is quite efficient and has been used in the cryptanalytic toolbox for many cryptographic schemes. Recently, Baek et al. presented a specialized affine equivalence algorithm (SAEA), which solves an affine equivalence problem in the case that S is a concatenation of several smaller S-boxes. The SAEA is more efficient than the affine equivalence algorithm for special cases, but its complexity mainly depends on the entire input size of F.

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