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Journal Articles Journal of Automated Reasoning Year : 2019

Implicit Computational Complexity of Subrecursive Definitions and Applications to Cryptographic Proofs

Abstract

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.
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Dates and versions

hal-01197456 , version 1 (11-09-2015)
hal-01197456 , version 2 (03-10-2016)
hal-01197456 , version 3 (06-12-2019)

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Patrick Baillot, Gilles Barthe, Ugo Dal Lago. Implicit Computational Complexity of Subrecursive Definitions and Applications to Cryptographic Proofs. Journal of Automated Reasoning, 2019, 63 (4), pp.813-855. ⟨10.1007/978-3-662-48899-7_15⟩. ⟨hal-01197456v3⟩
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