On the Need for Multipermutations: Cryptanalysis of MD4 and SAFER

Cryptographic primitives are usually based on a network with boxes. At EUROCRYPT'94, Schnorr and the author of this paper claimed that all boxes should be multipermutations. Here, we investigate a few combinatorial properties of multipermutations. We argue that boxes which fail to be multipermutations can open the way to unsuspected attacks. We illustrate this statement with two examples.