Automatic link establishment (ALE) was developed to establish a simplified connection in high-frequency (HF) radio system. As a family of tweakable block ciphers, HALFLOOP was standardized by the U.S. Department of Defense to protect the transmitted messages during ALE. According to existing attacks of HALFLOOP, there is a pending search for stronger non-generic attacks against the structure of ciphers itself. To solve the problems, a research team led by Shaozhen CHEN published their new progress on 15 April 2026 in Frontiers of Computer Science co-published by Higher Education Press and Springer Nature.
Observing that HALFLOOP has a property of smaller internal states compared to master keys, causing a low diffusion in the key schedule, the team proposed powerful related-key boomerang attacks on two larger variants of HALFLOOP. The relevant results highlight urgent concerns about the design of cryptographic standards and underscore the need for stronger key schedule algorithms.
In the research, they combined theoretical analysis with automated tools to propose a more efficient model to search for sandwich distinguishers of ciphers with non-linear key schedules. On the one hand, rather than simple relationships, more constraints in the internal linear layer were derived to improve efficiency. On the other hand, they overcame the limitations of non-linear key schedule and avoided possible weak-key attacks or invalid trails. Then, applying the model to two larger variants of HALFLOOP, they got appropriate sandwich distinguishers for subsequent key recovery attacks and validated the correctness experimentally.
Finally, they executed nearly full-round related-key boomerang attacks on HALFLOOP. For HALFLOOP-48, the time complexity of the full-round attack is significantly improved compared with previous non-generic methods. Moreover, they achieved a breakthrough on HALFLOOP-96, i.e. not a weak-key attack for the 9-round attack. Future work can focus on investigating additional ciphers with similar structures and addressing the identified flaws brought by key schedule algorithms.
DOI:10.1007/s11704-025-40755-0