## Section: New Results

### Relational Reasoning via Probabilistic Coupling

Participants : Gilles Barthe [IMDEA Software, Madrid] , Thomas Espitau [ENS Cachan] , Benjamin Grégoire, Justin Hsu [University of Pennsylvania] , Léo Stefanesco [ENS Lyon] , Pierre-Yves Strub [IMDEA Software, Madrid] .

Probabilistic coupling is a powerful tool for analyzing pairs of probabilistic processes. While the mathematical definition of coupling looks rather complex and cumbersome to manipulate, we show that the relational program logic pRHL—the logic underlying the EasyCrypt cryptographic proof assistant—already internalizes a generalization of probabilistic coupling. With this insight, constructing couplings is no harder than constructing logical proofs. We demonstrate how to express and verify classic examples of couplings in pRHL, and we mechanically verify several couplings in EasyCrypt. This work is described in [9] .