Reflection structure has a significant advantage that realizing decryption and encryption results in minimum additional costs, and many block ciphers tend to adopt such structure to achieve the requirement of low overhead. PRINCE, MANTIS, QARMA, and PRINCEv2 are lightweight block ciphers with reflection feature proposed in recent years. In this paper, we consider the automatic differential cryptanalysis of reflection block ciphers based on Boolean satisfiability (SAT) method. Since reflection block ciphers have different round functions, we extend forward and backward from the middle structure and achieve to accelerate the search of the optimal differential characteristics for such block ciphers with the Matsui’s bounding conditions. As a result, we present the optimal differential characteristics for PRINCE up to 12 rounds (full round), and they are also the optimal characteristics for PRINCEv2. We also find the optimal differential characteristics for MANTIS, QARMA‐64, and QARMA‐128 up to 10, 12, and 8 rounds, respectively. To mount an efficient differential attack on such block ciphers, we present a uniform SAT model by combining the differential characteristic searching process and the key recovery process. With this model, we find two sets of 7‐round differential characteristics for PRINCE with less guessed key bits and use them to present a multiple differential attack against 11‐round PRINCE, which improves the known single‐key attack on PRINCE by one round to our knowledge.

Abstract Deoxys‐BC is the internal tweakable block cipher of the authenticated encryption (AE) Deoxys family, in which Deoxys‐II is the primary choice for the use case of ‘Defence in depth’ among the portfolio of CAESAR competition. Improvements of the related‐tweakey rectangle attacks on round‐reduced Deoxys‐BC using the known distinguishers is focussed in this study. Under the new related‐key rectangle attack framework proposed by Dong et al. in EUROCRYPT 2022, we present three kinds of precomputed tables to further reduce the time complexity in the key‐recovery phase. In the related‐tweakey rectangle attack, the invalid quartets are filtered or the subtweakey candidates are obtained by lookup the precomputed tables without more computation. Based on the precomputed table technique, we improved the related‐tweakey rectangle attacks on 11‐round Deoxys‐BC‐256, 13‐round and 14‐round Deoxys‐BC‐384. Furthermore, we reduce the time complexity of the 13‐round related‐tweakey rectangle attack on Deoxys AE scheme Deoxys‐I‐256‐128 by a factor of 2 24 compared with the best previous attack.