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Implicit Computational Complexity of Subrecursive Definitions and Applications to Cryptographic Proofs

  • Patrick Baillot
  • Gilles Barthe
  • Ugo Dal Lago
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9450)

Abstract

We define a call-by-value variant of Gödel’s System \(\mathsf {T} \) with references, and equip it with a linear dependent type and effect system, called \(\mathsf {d}\ell \mathsf {T} \), 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 \(\mathsf {d}\ell \mathsf {T} \). Finally, we demonstrate the usefulness of \(\mathsf {d}\ell \mathsf {T} \) for analyzing the complexity of cryptographic reductions by providing an upper bound for the constructed adversary of the Goldreich-Levin theorem.

Keywords

Type System Function Symbol Typing Rule Type Inference Typing Judgement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Patrick Baillot
    • 1
  • Gilles Barthe
    • 2
  • Ugo Dal Lago
    • 1
    • 3
  1. 1.INRIA, UCBL, Université de Lyon, LIPLyonFrance
  2. 2.IMDEA Software InstituteMadridSpain
  3. 3.INRIA, Università di BolognaBolognaItaly

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