New Automatic Search Tool for Searching for Impossible Differentials Using Undisturbed Bits

Abstract

AbstractImpossible differential cryptanalysis is a powerful tool for analyzing the security of symmetric-key primitives. At first, the attacker must finds some impossible differentials as long as possible. There are many tools to automatically search for the longest impossible differentials. In all of these search tools, the input and output differences are fixed before searching, which leads to some limitations. The first limitation is that the number of impossible differentials that can be found is very small. The second limitation is that the existing tools are ineffective in searching for truncated impossible differentials. For some symmetric-key primitives, these tools can only find short round truncated impossible differentials, and for others they can’t even find truncated impossible differentials. As we all know, the number of impossible differentials is also very important because it can improve the data complexity and time complexity of impossible differential cryptanalysis in some cases. In addition, using truncated impossible differentials can usually get better results when impossible differentials are of the same length. In this paper, we propose a new automatic search tool that can overcome the above two limitations. The tool can not only find a large number of impossible differentials in a short time, but also can get truncated impossible differentials of bit-level primitives. It uses undisturbed differential bits, that is, the differential bits with probability 1 in differential propagation, and is based on mixed-integer linear programming (MILP) and meet-in-the-middle technology. We applied the tool to ASCON, SIMON, LBlock and LEA. For each of the four primitives, we found many new impossible differentials. For SIMON and LBlock, we found some related-key impossible differentials longer than the best-known results.KeywordsImpossible differentialUndisturbed bitsMILPASCONSIMONLEALBlockAutomatic search tool