On Session Typing, Probabilistic Polynomial Time, and Cryptographic Experiments (Long Version). (arXiv:2207.03360v1 [cs.LO])

A system of session types is introduced as induced by a Curry Howard
correspondence applied to Bounded Linear Logic, and then extending the thus
obtained type system with probabilistic choices and ground types. The obtained
system satisfies the expected properties, like subject reduction and progress,
but also unexpected ones, like a polynomial bound on the time needed to reduce
processes. This makes the system suitable for modelling experiments and proofs
from the so-called computational model of cryptography.

session version