Implicit Computational Complexity of Subrecursive Definitions and Applications to Cryptographic Proofs (Long version)

Patrick Baillot (1) , Gilles Barthe (2) , Ugo Dal Lago (3, 4)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 Institute IMDEA Software [Madrid]
3 DISI - Dipartimento di Scienze dell'Informazione [Bologna]
4 FOCUS - Foundations of Component-based Ubiquitous Systems

We define a call-by-value variant of Gödel 's System T with references, and equip it with a linear dependent type and effect system, called d that can estimate the complexity of programs, as a function of the size of their inputs. We prove that the type system is intentionally sound, in the sense that it over-approximates the complexity of executing the programs on a variant of the CEK abstract machine. Moreover, we define a sound and complete type inference algorithm which critically exploits the subrecursive nature of d Finally, we demonstrate the usefulness of d for analyzing the complexity of cryptographic reductions by providing an upper bound for the constructed adversary of the Goldreich-Levin theorem.

Domaines: Logique en informatique [cs.LO]; Cryptographie et sécurité [cs.CR]

Patrick Baillot, Gilles Barthe, Ugo Dal Lago. Implicit Computational Complexity of Subrecursive Definitions and Applications to Cryptographic Proofs (Long version). [Research Report] ENS Lyon. 2015. ⟨hal-01197456v1⟩