Analyzing Permutations for AES-like Ciphers: Understanding ShiftRows.

摘要: Designing block ciphers and hash functions in a manner that resemble the AES many aspects has been very popular since Rijndael was adopted as Advanced Encryption Standard. However, sharp contrast to MixColumns operation, security implications of way state is permuted by operation resembling ShiftRows never studied depth. Here, we provide first structured study influence ShiftRows-like operations, or more generally, word-wise permutations, AES-like with respect diffusion properties resistance towards differentialand linear attacks. After formalizing concept guaranteed trail weights, show range equivalence results for permutation layers this context. We prove weight analysis when using arbitrary rotations special case, reduces consideration specific normal form. Using mixed-integer programming approach, obtain optimal parameters wide ciphers, improvements on Rijndael-192, Rijndael-256, PRIMATEs-80 Prost-128. As separate result, cases geometry seemingly bound can be obtained cyclic only layer, i.e. implementation friendly way.