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The authors present cryptanalytic results of an exhaustive search of all 16! bijective 4-bit S-Boxes. Previously affine equivalence classes have been exhaustively analyzed in 2007 work by Leander and Poschmann. They extend on this work by giving further properties of the optimal S-Box linear equivalence classes. In the main analysis they consider two S-Boxes to be cryptanalytically equivalent if they are isomorphic up to the permutation of input and output bits and a XOR of a constant in the input and output. They have enumerated all such equivalence classes with respect to their differential and linear properties. These equivalence classes are equivalent not only in their differential and linear bounds but also have equivalent algebraic properties, branch number and circuit complexity.
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