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Title:
Turning Multiple Key-Dependent Attacks into Universal Attacks
Authors: Hosein Hadipour, Yosuke Todo, Mostafizar Rahman, Maria Eichlseder, Ravi Anand, Takanori Isobe
Abstract:Key-dependent attacks are effective only for specific weak-key classes, limiting their practical impact. We present a generic statistical framework that combines multiple key-dependent distinguishers into universal attacks covering the full key space. Using log-likelihood ratio statistics, our framework tests the secret key against multiple weak-key distinguishers, aggregates their evidence to determine whether the key is weak or strong for each distinguisher, and exploits this classification to reduce the effective key entropy for key recovery.
We apply this to Orthros-PRF, a sum-of-permutations (SoP) design where any differential-based distinguisher holds only for a fraction of keys. This yields the first universal 8-round differential-linear (DL) key-recovery attack with median time complexity 2^{119.58}, whereas prior work reached at most 7 rounds in the weak-key setting. To discover the required distinguishers, we extend the open-source S-box Analyzer tool with MILP support for deterministic propagation and develop a model integrating distinguisher search with key recovery. This enables automated discovery of multidimensional DL distinguishers covering up to 10 rounds in each Orthros branch, improving prior work by 4 rounds.
Our results demonstrate that statistical aggregation of multiple weak-key distinguishers enables effective universal cryptanalysis. Our framework is generic and is applicable to other primitives with multiple identifiable weak-key classes.
ePrint: https://eprint.iacr.org/2025/1996
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