A Probabilistic Separation Logic
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 probabilistic 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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2019
- DOI:
- 10.48550/arXiv.1907.10708
- arXiv:
- arXiv:1907.10708
- Bibcode:
- 2019arXiv190710708B
- Keywords:
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- Computer Science - Programming Languages;
- Computer Science - Logic in Computer Science
- E-Print:
- doi:10.1145/3371123