As an access control technology of digital material, digital rights management systems have a profound effect on the copyright protection of digital content. To address the threat of key exposure, applying white‐box ciphers is effective to provide a security guarantee for digital rights management systems. SPNbox, proposed at Asiacrypt’16 is such a white‐box cipher that fulfils comprehensive resistance against key exposure for digital rights management systems, including black‐box security on the server‐side and white‐box security on the client‐side. So far, the previous integral cryptanalysis of SPNbox employs a general 2‐round distinguisher without considering the details of SPNbox. The properties of SPNbox are carefully explored and a novel 2‐round integral distinguisher is introduced. On this basis, we propose new competitive 3‐round key recovery attacks with lower complexities. Particularly, the improved attack on 3‐round SPNbox‐32 only requires 232 chosen plaintexts, whereas the current best attack necessitates 262 chosen plaintexts. In addition, integral attacks on 4‐ and 5‐round SPNbox‐8 are presented for the first time. Thus, the security margin of SPNbox‐8 is narrowed by two rounds. These results indicate that the capability of SPNbox resisting integral cryptanalysis is inferior to the designers' claim.

In Addition-Rotation-Xor (ARX) ciphers, the large domain size obstructs the application of the boomerang connectivity table. In this paper, we explore the problem of computing this table for a modular addition and the automatic search of boomerang characteristics for ARX ciphers. We provide dynamic programming algorithms to efficiently compute this table and its variants. These algorithms are the most efficient up to now. For the boomerang connectivity table, the execution time is 42(n − 1) simple operations while the previous algorithm costs 82(n − 1) simple operations, which generates a smaller model in the searching phase. After rewriting these algorithms with boolean expressions, we construct the corresponding Boolean Satisfiability Problem models. Two automatic search frameworks are also proposed based on these models. This is the first time bringing the SAT-aided automatic search techniques into finding boomerang attacks on ARX ciphers. Finally, under these frameworks, we find out the first verifiable 10-round boomerang trail for SPECK32/64 with probability 2−29.15 and a 12-round trail for SPECK48/72 with probability 2−44.15. These are the best distinguishers for them so far. We also perceive that the previous boomerang attacks on LEA are constructed with an incorrect computation of the boomerang connection probability. The result is then fixed by our frameworks.

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Format-preserving encryption (FPE) allows encrypting plaintexts while preserving a specific format. In Selected Areas in Cryptography 2018, two targeted ciphers were proposed as new FPE schemes. The second scheme was designed with an algorithm called Mix-Swap-Unmix that is shown to be equivalent to a particular matching exchange process under a specific setting. In this comment paper, we prove that the matching exchange process is invalid. As a result, this equivalence does not exist. The matching exchange process is proposed by Czumaj and Kutyłowski to permute items at random in parallel andThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.