Multi-User Security Bound for Mixed Filter Permutators in the Random Oracle Model

At Eurocrypt’16, Méaux et al. designed a construction for symmetric ciphers that can be efficiently evaluated with Fully Homomorphic Encryption, dubbed Filter Permutator. They also specify FLIP, a family of Filter Permutators. Creating FiLIP, they improved their first construction using whitening keys and reduction of the initial key register. Later, Cosseron et al. and Hoffmann et al. proposed successive generalisations of their work, creating the new families of Group Filter Permutators and then Mixed Filter Permutators. In this article, we prove the generic security of Mixed Filter Permutators in the Random Oracle Model. Moreover, we study a derived scheme that avoids using whitening keys. We show that the resulting construction is less secure by providing an attack for some parameter choices that would yield a Mixed Filter Permutator that is secure in the Random Oracle Model. Finally, we prove a security bound for this Mixed Filter Permutators construction without the whitening key.