In this paper, a security evaluation framework for AND-RX ciphers against impossible differential cryptanalysis is proposed. This framework is constructed based on three different methods towards finding the theoretical upper boundary, theoretical lower boundary, and practical boundary of impossible differential distinguishers (short for ID) respectively. The provable security boundary (upper boundary) can be calculated with two round-function-related matrices through a few matrix multiplications, this calculation is beyond actual input and output differences. For searching longer IDs (lower boundary), an automatic method is proposed. With this method, given the input and output difference, all the possible direct and indirect contradictions are detected. For the practical boundary, a method of approximating all the potential longest IDs with concrete differential trails is introduced. The three boundaries validate the correctness from each other. According to our result, on the one hand, the boundaries derived with well-designed ID-construction methods can already reach the practical boundary for some block ciphers and it is unlikely to be improved based on known construction methods or future unknown construction methods. On the other hand, for those ciphers whose current best result does not reach our boundary, longer IDs can be discovered with this framework. The correctness is validated by a series of applications. For the provable security boundary, four family ciphers-SIMON, Simeck, Friet-PC and SAND are investigated. For SIMON and Simeck, the lengths of current longest IDs have reached their provable security boundaries. For Friet-PC and SAND, there is a gap between the provable security boundary and current best results. With the automatic searching method, some longer IDs on Friet-PC and SAND are discovered. For Friet-PC, 128 11-round IDs are discovered, while the previous best differential distinguisher is 9-round. For SAND64, 256 11-round IDs are propose...