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arXiv · 1701.06477

Proving uniformity and independence by self-composition and coupling

Gilles Barthe·Thomas Espitau·Benjamin Grégoire·Justin Hsu·Pierre-Yves Strub
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Abstract

Proof by coupling is a classical proof technique for establishing probabilistic properties of two probabilistic processes, like stochastic dominance and rapid mixing of Markov chains. More recently, couplings have been investigated as a useful abstraction for formal reasoning about relational properties of probabilistic programs, in particular for modeling reduction-based cryptographic proofs and for verifying differential privacy. In this paper, we demonstrate that probabilistic couplings can be used for verifying non-relational probabilistic properties. Specifically, we show that the program logic pRHL---whose proofs are formal versions of proofs by coupling---can be used for formalizing uniformity and probabilistic independence. We formally verify our main examples using the EasyCrypt proof assistant.

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Gilles Barthe, Thomas Espitau, Benjamin Grégoire, Justin Hsu, Pierre-Yves Strub. 2017-04-01. Proving uniformity and independence by self-composition and coupling. https://arxiv.org/abs/1701.06477

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