Differential and Linear Attacks on the Full WIDEA-n Block Ciphers (under Weak Keys)

Abstract

We report on differential and linear analysis of the full 8.5-round WIDEA-n ciphers for n ∈ {4,8}, under weak-key assumptions. The novelty in our attacks include the use of differential and linear relation patterns that allow to bypass the diffusion provided by MDS codes altogether. Therefore, we can attack only a single IDEA instance out of n copies, effectively using a narrow trail for the propagation of differences and masks across WIDEA-n. In fact, the higher the value of n, the better the attacks become. Our analyses apply both to particular MDS matrices, such as the one used in AES, as well as general MDS matrices. Our attacks exploit fixed points of MDS matrices. We also observed a curious interaction between certain differential/linear patterns and the coefficients of MDS matrices for non-trivial fixed points. This interaction may serve as an instructive design criterion for block cipher designs such as WIDEA-n. The authors of WIDEA-n suggested a compression function construction using WIDEA-8 in Davies-Meyer mode. In this setting, the weaknesses identified in this paper can lead to free-start collisions and even actual collisions depending on the output transformation of the hash function.