Cryptanalysis of the full MMB block cipher

The block cipher MMB was designed by Daemen, Govaerts and Vandewalle, in 1993, as an alternative to the IDEA block cipher. We exploit and describe unusual properties of the modular multiplication in $Z_{2^{32} - 1}$, which lead to a differential attack on the full 6-round MMB cipher (both versions 1.0 and 2.0). Further contributions of this paper include detailed square and linear cryptanalysis of MMB. Concerning differential cryptanalysis (DC), we can break the full MMB with 2^118 chosen plaintexts, 2^95.91 6-round MMB encryptions and 2^64 counters, effectively bypassing the cipher's countermeasures against DC. For the square attack, we can recover the 128-bit user key for 4-round MMB with 2^34 chosen plaintexts, 2^126.32 4-round encryptions and 2^64 memory blocks. Concerning linear cryptanalysis, we present a key-recovery attack on 3-round MMB requiring 2^114.56 known-plaintexts and 2^126 encryptions. Moreover, we detail a ciphertext-only attack on 2-round MMB using 2^93.6 ciphertexts and 2^93.6 parity computations. These attacks do not depend on weak-key or weak-subkey assumptions, and are thus independent of the key schedule algorithm

On a Generalization of Substitution-Permutation Networks: The HADES Design Strategy

Keyed and unkeyed cryptographic permutations often iterate simple round functions. Substitution-permutation networks (SPNs) are an approach that is popular since the mid 1990s. One of the new directions in the design of these round functions is to reduce the substitution (S-Box) layer from a full one to a partial one, uniformly distributed over all the rounds. LowMC and Zorro are examples of this approach. A relevant freedom in the design space is to allow for a highly non-uniform distribution of S-Boxes. However, choosing rounds that are so different from each other is very rarely done, as it makes security analysis and implementation much harder. We develop the design strategy Hades and an analysis framework for it, which despite this increased complexity allows for security arguments against many classes of attacks, similar to earlier simpler SPNs. The framework builds upon the wide trail design strategy, and it additionally allows for security arguments against algebraic attacks, which are much more of a concern when algebraically simple S-Boxes are used. Subsequently, this is put into practice by concrete instances and benchmarks for a use case that generally benefits from a smaller number of S-Boxes and showcases the diversity of design options we support: A candidate cipher natively working with objects in GF(p), for securing data transfers with distributed databases using secure multiparty computation (MPC). Compared to the currently fastest design MiMC, we observe significant improvements in online bandwidth requirements and throughput with a simultaneous reduction of preprocessing effort, while having a comparable online latency