Automatic Search of Differential Characteristics and Improved Differential Cryptanalysis for PRINCE, QARMA, and MANTIS

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.