A Generic Approach to Invariant Subspace Attacks: Cryptanalysis of Robin, iSCREAM and Zorro

Invariant subspace attacks were introduced at CRYPTO 2011 to cryptanalyze

PRINTcipher

. The invariant subspaces for

PRINTcipher

were discovered in an ad hoc fashion, leaving a generic technique to discover invariant subspaces in other ciphers as an open problem. Here, based on a rather simple observation, we introduce a generic algorithm to detect invariant subspaces. We apply this algorithm to the CAESAR candidate iSCREAM, the closely related LS-design Robin, as well as the lightweight cipher Zorro. For all three candidates invariant subspaces were detected, and result in practical breaks of the ciphers. A closer analysis of independent interest reveals that these invariant subspaces are underpinned by a new type of self-similarity property. For all ciphers, our strongest attack shows the existence of a weak key set of density

$$2^{-32}$$

. These weak keys lead to a simple property on the plaintexts going through the whole encryption process with probability one. All our attacks have been practically verified on reference implementations of the ciphers.