An automated model for differential meet in the middle attacks on AndRX ciphers

In recent years, research in block cipher cryptanalysis has been significantly influenced by the development of differential meet in the middle techniques. Originally put forward by Boura et al., this approach has proven to be both adaptable and effective for evaluating modern symmetric-key designs. It has since been successfully employed in the analysis of several block ciphers, including multiple variants of SKINNY, CRAFT, and AES. However, identifying such attacks manually-especially on bit-oriented ciphers with large block sizes-can be a complex and error-prone process, which underscores the growing importance of automated solutions in this domain. To address these challenges, we develop an automated framework that systematically searches for and optimizes differential meet in the middle attacks on bit-oriented block ciphers. Our approach is specifically tailored to AndRX-based constructions, enabling the efficient identification of attack configurations that would be difficult to derive manually. Our method relies on a constraint-based formulation that automatically identifies optimal single-key differential characteristics in AndRX ciphers. Building on this, we propose a unified bitwise CP model to automatically construct optimized differential MITM attacks within the same design framework. Furthermore, we incorporate two dedicated optimization strategies-namely, the equivalent subkey technique and the selective key guessing technique-both of which are tailored to the structural properties of AndRX ciphers and significantly enhance key recovery efficiency. Additionally, we apply two additional optimization techniques: the parallel partitioning technique and reducing data with imposed conditions techniques to further enhance the differential MITM attack on AndRX ciphers. We validate the practicality of our approach through an extensive evaluation on the full SIMON and Simeck families, which are well-known instances of AndRX-based block ciphers. Our analysis leads to enhanced attack results compared to previously reported findings. In particular, our findings extend the round coverage beyond that achieved by previously reported classical meet in the middle and Demirci-Selçuk-type attacks for the respective variants of SIMON and Simeck. These findings highlight the strength and flexibility of our automated tool. Notably, our automated framework for constructing differential meet in the middle attacks works at the bit level and is generic in design, allowing it to be applied to a wide range of bit-oriented block ciphers beyond the AndRX family.