Distinguishing Attack on NORX Permutation
NORX is a permutation-based authentication scheme which is currently a third-round candidate of the ongoing CAESAR competition. The security bound of NORX is derived from the sponge construction applied to an ideal underlying permutation. In this paper, we show that the NORX core permutation is non-ideal with a new distinguishing attack. More specifically, we can distinguish NORX64 permutation with 248.5 queries and distinguish NORX32 permutation with 264.7 queries using carefully crafted differential-linear attacks. We have experimentally verified the distinguishing attack on NORX64 permutation. Although the distinguishing attacks reveal the weakness of the NORX permutation, it does not directly threat the security of the NORX authenticated encryption scheme.
A Security Analysis of Deoxys and its Internal Tweakable Block Ciphers
In this article, we provide the first independent security analysis of Deoxys, a third-round authenticated encryption candidate of the CAESAR competition, and its internal tweakable block ciphers Deoxys-BC-256 and Deoxys-BC-384. We show that the related-tweakey differential bounds provided by the designers can be greatly improved thanks to a Mixed Integer Linear Programming (MILP) based search tool. In particular, we develop a new method to incorporate linear incompatibility in the MILP model. We use this tool to generate valid differential paths for reduced-round versions of Deoxys-BC-256 and Deoxys-BC-384, later combining them into broader boomerang or rectangle attacks. Here, we also develop a new MILP model which optimises the two paths by taking into account the effect of the ladder switch technique. Interestingly, with the tweak in Deoxys-BC providing extra input as opposed to a classical block cipher, we can even consider beyond full-codebook attacks. As these primitives are based on the TWEAKEY framework, we further study how the security of the cipher is impacted when playing with the tweak/key sizes. All in all, we are able to attack 10 rounds of Deoxys-BC-256 (out of 14) and 13 rounds of Deoxys-BC-384 (out of 16). The extra rounds specified in Deoxys-BC to balance the tweak input (when compared to AES) seem to provide about the same security margin as AES-128. Finally we analyse why the authenticated encryption modes of Deoxys mostly prevent our attacks on Deoxys-BC to apply to the authenticated encryption primitive.