On Equivalences, Metrics, and Polynomial Time [chapter]

Alberto Cappai, Ugo Dal Lago
2015 Lecture Notes in Computer Science  
Interactive behaviors are ubiquitous in modern cryptography, but are also present in λcalculi, in the form of higher-order constructions. Traditionally, however, typed λ-calculi simply do not fit well into cryptography, being both deterministic and too powerful as for the complexity of functions they can express. We study interaction in a λ-calculus for probabilistic polynomial time computable functions. In particular, we show how notions of context equivalence and context metric can both be
more » ... racterized by way of traces when defined on linear contexts. We then give evidence on how this can be turned into a proof methodology for computational indistinguishability, a key notion in modern cryptography. We also hint at what happens if a more general notion of a context is used.
doi:10.1007/978-3-319-22177-9_24 fatcat:4wzjikkktjhddbinn4qx5tndzy