A Probabilistic Separation Logic

07/24/2019
by   Gilles Barthe, et al.
0

Probabilistic independence is a fundamental tool for reasoning about randomized programs. Independence describes the result of drawing a fresh random sample—a basic operation in all probabilistic languages—and greatly simplifies formal reasoning about collections of random samples. Nevertheless, existing verification methods handle independence poorly, if at all. In this paper, we propose a probabilistic separation logic where separation models probabilistic independence. We first give a new, probabilistic model of the logic of bunched implications (BI), the logic of assertions in separation logic. Then, we introduce a program logic based on these assertions and prove soundness of the proof system. We demonstrate our logic by verifying security properties of several cryptographic constructions, including simple ORAM, secure multi-party addition, oblivious transfer, and private information retrieval. Our logic is able to state and verify two different forms of the standard cryptographic security property, while proofs work in terms of high-level properties like independence and uniformity.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/29/2021

A Separation Logic for Negative Dependence

Formal reasoning about hashing-based probabilistic data structures often...
research
08/20/2020

A Logic to Reason about Dependence and Independence

Independence and conditional independence are fundamental concepts for r...
research
08/09/2021

Probabilistic annotations for protocol models

We describe how a probabilistic Hoare logic with localities can be used ...
research
04/03/2023

Lilac: A Modal Separation Logic for Conditional Probability

We present Lilac, a separation logic for reasoning about probabilistic p...
research
08/20/2020

DataProVe: A Data Protection Policy and System Architecture Verification Tool

In this paper, we propose a tool, called DataProVe, for specifying high-...
research
04/11/2018

Constraint-Based Synthesis of Coupling Proofs

Proof by coupling is a classical technique for proving properties about ...
research
08/30/2023

On the Independencies Hidden in the Structure of a Probabilistic Logic Program

Pearl and Verma developed d-separation as a widely used graphical criter...

Please sign up or login with your details

Forgot password? Click here to reset