Searching all truncated impossible differentials in SPN
Ting Cui, Chenhui Jin, Bin Zhang, Zhuo Chen, Guoshuang Zhang · IET Information Security · 2016
This study concentrates on finding all truncated impossible differentials in substitution–permutation networks (SPNs) ciphers. Instead of using the miss‐in‐the‐middle approach, the authors propose a mathematical description of the truncated impossible differentials. First, they prove that all truncated impossible differentials in an r + 1 rounds SPN cipher could be obtained by searching entry ‘0’ in D ( P ) r , where D ( P ) denotes the differential pattern matrix (DPM) of P ‐layer, thus the length of impossible differentials of an SPN cipher is upper bounded by the minimum integer r such that there is no entry ‘0’ in D ( P ) r . Second, they provide two efficient algorithms to compute the DPMs for both bit‐shuffles and matrices over GF(2 n ). Using these tools they prove that the longest truncated impossible differentials in SPN structure is 2‐round, if the P ‐layer is designed as an maximum distance separable (MDS) matrix. Finally, all truncated impossible differentials of advanced encryption standard (AES), ARIA, AES‐MDS, PRESENT, MAYA and Puffin are obtained.