A New Statistical Approach for Integral Attack

Statistical saturation attack is one of the powerful attacks against block ciphers, however, the requirement of identifying the weak permutation somehow restrict its wide applications. Integral attack can be considered as the deterministic version of the statistical saturation attack, which works by tracing the properties of the integral sets after certain rounds of encryption. It aims to build an integral characteristic path for a large number of rounds. By searching within the message space, it expects to find a characteristic path in a deterministic way assuming the random behavior of the cipher. In this paper, we provide the first study on how to take advantage of the integral attack and apply it to cryptanalysis by using statistical approach, and our new approach does not rely on identifying weak permutations. One of our contributions is to firstly apply the internal collision of a set as the evaluated statistics and show how this property can be efficiently propagated in the General Feistel Structure (GFS) with bijective map S-Box. Secondly, we provide a simple statistical framework to evaluate the data complexity. Finally, we evaluate several GFS and find out for some of the designs, our approach provide a better result compared with other statistical attack such as differential and linear attack.