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A probabilistic separation logic

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Kevin LiaoAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 4, Issue POPL

Article No.: 55, Pages 1 - 30

https://doi.org/10.1145/3371123

Published: 20 December 2019 Publication History

Abstract

Probabilistic independence is a useful concept for describing the result of random sampling—a basic operation in all probabilistic languages—and for reasoning about groups of random variables. Nevertheless, existing verification methods handle independence poorly, if at all. We propose a probabili stic separation logic PSL, where separation models probabilistic independence. We first give a new, probabilistic model of the logic of bunched implications (BI). We then build a program logic based on these assertions, and prove soundness of the proof system. We demonstrate our logic by verifying information-theoretic security of cryptographic constructions for several well-known tasks, including private information retrieval, oblivious transfer, secure multi-party addition, and simple oblivious RAM. Our proofs reason purely in terms of high-level properties, like independence and uniformity.

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Index Terms

A probabilistic separation logic
1. Security and privacy
  1. Formal methods and theory of security
    1. Logic and verification
2. Theory of computation
  1. Logic
    1. Separation logic

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 4, Issue POPL

January 2020

1984 pages

EISSN:2475-1421

DOI:10.1145/3377388

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Published: 20 December 2019

Published in PACMPL Volume 4, Issue POPL

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Cited By

Bao JD'Osualdo EFarzan A(2025)Bluebell: An Alliance of Relational Lifting and Independence for Probabilistic ReasoningProceedings of the ACM on Programming Languages10.1145/37048949:POPL(1719-1749)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704894
Haselwarter PLi KAguirre AGregersen STassarotti JBirkedal L(2025)Approximate Relational Reasoning for Higher-Order Probabilistic ProgramsProceedings of the ACM on Programming Languages10.1145/37048779:POPL(1196-1226)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704877
Haselwarter PLi Kde Medeiros MGregersen SAguirre ATassarotti JBirkedal L(2024)Tachis: Higher-Order Separation Logic with Credits for Expected CostsProceedings of the ACM on Programming Languages10.1145/36897538:OOPSLA2(1189-1218)Online publication date: 8-Oct-2024
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