Out of Non-linearity: Search Impossible Differentials by the Bitwise Characteristic Matrix

Abstract

In this paper, we propose the M-method which uses the bitwise characteristic matrix to search impossible differentials. M-method exploits not only the linear components but also partial information of non-linear components. According to the principle of miss-in-the-middle, we construct two different types of contradiction to search the impossible differentials with limited time and memory complexity by calculating M r 1 en and M r 2 de which represent r1 rounds encryption and r2 rounds decryption, respectively. Compared with the previous methods, our technique is comprehensible and fast especially for large block size.As a result, we find the 7-round impossible differentials of GIFT-128, the 5-round impossible differentials of PRIDE, and the 4-round impossible differentials of Pyjamask-96. For GIFT-64, PRESENT, RECTANGLE which are well-analyzed by MILP-method or SAT-method, we construct new impossible differentials. Moreover, the efficiency of our method will not be influenced by the block size, which makes us find the new 5-round impossible differentials of the 320-bit permutation of ASCON.