SoK: Robust properties, robust abstractions and back-translations

Many formal security criteria in fields like secure compilation (e.g. full abstraction and robust hyperproperty preservation), cryptography (e.g. security games, reduction proofs, and universal composability), and information flow control share a fundamental underlying structure. This underlying structure and related concepts also appear in broader contexts like denotational semantics and computational expressiveness, yet their connections are often overlooked. This paper identifies and systematizes this structure through robust properties (criteria holding in any context), robust abstractions (ensuring preservation of robust properties from abstract to concrete systems) and the new notion of non-degrading abstractions, which guarantees that the concrete system only exhibits concrete violations that are also present in the corresponding abstract system, thereby ensuring no new violations are introduced by the abstraction. By unifying concepts from different areas into a common framework, we highlight existing but underexplored connections, provide new insights and general results, and introduce a valuable perspective for understanding and advancing formal security.