On Statistical Testing of Block Ciphers

Block ciphers form one of the main classes of cryptographic algorithms. One of the challenges in development of block ciphers, like any other cryptographic algorithms, is the analysis of their cryptographic security. In the course of such analysis, statistical testing of block ciphers is often used. The paper reviews literature on statistical testing of block ciphers. The first section of the paper briefly and informally discusses approaches to the definition of the concept of a random sequence, including the Kolmogorov, von Mises, and Martin-Löf approaches and the unpredictability-related approach. However, all these approaches to the definition of randomness are not directly applicable in practice. The second section describes statistical tests of binary sequences. It provides brief descriptions of the tests included in the DieHard, NIST STS, RaBiGeTe statistical test suites. The third section provides the appropriate information to present further the operation modes of block ciphers. The fourth section deals with techniques for statistical testing of block ciphers. Usually such techniques lie in the fact that based on the block cipher under test, various generators of the pseudorandom sequences are built, with their output sequences being tested using any suite of statistical tests. The approaches to the construction of such generators are given. The paper describes the most known statistical test technique for block ciphers among the submitted for the AES competition. It is a technique the NIST uses for statistical testing of ciphers. In addition, there are other techniques mentioned in the literature. In conclusion the paper states that there is a need to develop new techniques for statistical testing of block ciphers. The paper support was provided from the Russian Foundation for Basic Research in the framework of the research project No. 16-07-00542 supported