New Automatic Search Tool for Impossible Differentials and Zero-Correlation Linear Approximations

Impossible differential cryptanalysis and zero-correlation linear cryptanalysis are two of the most useful cryptanalysis methods in the field of symmetric ciphers. Until now, there are several automatic search tools for impossible differentials such as U-method and UID-method, which are all independent of the non-linear S-boxes. Since the differential and linear properties can also contribute to the search of impossible differentials and zero-correlation linear approximations respectively, it is meaningful to study the search with considering the properties of nonlinear components. In this paper, we propose an automatic search tool for impossible differentials and zero-correlation linear approximations in both ARX ciphers and ciphers with S-box, which is the first widely applicable one that considers the influence of non-linear operations, especially in ARX ciphers. What’s more, this tool can be used to prove whether there are impossible differentials (zero-correlation linear approximations) in certain rounds of a target cipher, particularly for certain subset of input and output differences (masks) patterns. As applications, we use this automatic tool on HIGHT and LBlock ciphers. Consequently, we find total 4 impossible differentials and 4 zero-correlation linear approximations for 17-round HIGHT which are the longest ones until now, and find six 16-round related-key impossible differentials for LBlock, which are the best ones up to now.