Extending Higher-Order Integral: An Efficient Unified Algorithm of Constructing Integral Distinguishers for Block Ciphers

摘要

In this paper, we give an extension of the concept of higher-order integral, which can make us design better higher-order integral distinguishers for some block ciphers (structures). Using the new extension, we present a unified algorithm of searching for the best possible higher-order integral distinguishers for block ciphers. We adopt the inside-out approach, trying to predict the behavior of a set of carefully chosen data, not only along encryption direction, but also along decryption direction. Applying the unified algorithm, we search for the best possible higher-order integral distinguishers of Gen-SMS4 structure, Gen-Fourcell structure and Present. For Gen-SMS4 structure and Present, the best higher-order integral distinguishers given by our algorithm are better than the best results known so far. For Gen-Fourcell structure, the best higher-order integral distinguishers given by our algorithm are the same as the best results known so far. We expect that the inside-out method is helpful to understand higher-order integral of block ciphers better, and the unified algorithm presented in this paper can be used as a tool for efficiently evaluating the security of a block cipher against integral cryptanalysis.