Formalize the FHE security bound using EasyCrypt reflection machinery

Determine whether EasyCrypt’s reflection machinery suffices to formalize the sublinear security bound for approximate fully homomorphic encryption obtained through adaptive noise-flooding composition.

Background

The paper develops a Rocq and SSProve formalization of the adaptive noise-flooding reduction for approximate fully homomorphic encryption. Its verified selected-call compiler exposes adaptive oracle calls in concrete SSProve program syntax, enabling conditional Kullback–Leibler costs to be accumulated and converted to statistical distance only once, thereby obtaining a square-root dependence on the number of decryption queries.

The authors contrast this trace-based SSProve approach with EasyCrypt, where adversaries are treated as opaque modules and reflection techniques can extract adversary semantics. They explicitly leave unresolved whether EasyCrypt’s reflection machinery can support formalization of the same FHE security argument with its sublinear, square-root composition loss.