Implicit Computational Complexity of Subrecursive Definitions and Applications to Cryptographic Proofs

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 ℓ T , that can estimate the time complexity of programs, as a function of the size of their inputs. We prove that the type system is intentionally sound, in th...

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Bibliographic Details
Published in:Journal of automated reasoning Vol. 63; no. 4; pp. 813 - 855
Main Authors: Baillot, Patrick, Barthe, Gilles, Dal Lago, Ugo
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.12.2019
Springer Nature B.V
Subjects:
Abstract machines
Algorithms
Artificial Intelligence
Complexity
Computer Science
Cryptography
Mathematical Logic and Formal Languages
Mathematical Logic and Foundations
Sound
Symbolic and Algebraic Manipulation
Upper bounds
Complexity analysis
Cryptographic proofs
Linear dependent types
Implicit computational complexity
ISSN:0168-7433, 1573-0670
Online Access:Get full text
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Summary: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 ℓ T , that can estimate the time 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 ℓ T . Finally, we demonstrate the usefulness of d ℓ T 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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ISSN:0168-7433
1573-0670
DOI:10.1007/s10817-019-09530-2