Exploiting Non-full Key Additions: Full-Fledged Automatic Demirci-Selçuk Meet-in-the-Middle Cryptanalysis of SKINNY

The Demirci-Selcuk meet-in-the-middle (DS-MITM) attack is a sophisticated variant of differential attacks. Due to its sophistication, it is hard to efficiently find the best DS-MITM attacks on most ciphers except for AES. Moreover, the current automatic tools only capture the most basic version of DS-MITM attacks, and the critical techniques developed for enhancing the attacks (e.g., differential enumeration and key-dependent-sieve) still rely on manual work. In this paper, we develop a full-fledged automatic framework integrating all known techniques (differential enumeration, key-dependent-sieve, and key bridging, etc) for the DS-MITM attack that can produce key-recovery attacks directly rather than only search for distinguishers. Moreover, we develop a new technique that is able to exploit partial key additions to generate more linear relations beneficial to the attacks. We apply the framework to the SKINNY family of block ciphers and significantly improved results are obtained. In particular, all known DS-MITM attacks on the respective versions of SKINNY are improved by at least 2 rounds, and the data, memory, or time complexities of some attacks are reduced even compared to previous best attacks penetrating less rounds.