Formalized Information-Theoretic Proofs of Privacy Using the HOL4 Theorem-Prover

Authors:
Aaron R. Coble
Affiliations:
University of Cambridge Computer Laboratory, Cambridge, UK CB3 0FD
Venue:
PETS '08 Proceedings of the 8th international symposium on Privacy Enhancing Technologies
Year:
2008

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Abstract

Below we present an information-theoretic method for proving the amount of information leaked by programs formalized using the HOL4 theorem-prover. The advantages of this approach are that the analysis is quantitative, and therefore capable of expressing partial leakage, and that proofs are performed using the HOL4 theorem-prover, and are therefore guaranteed to be logically and mathematically consistent with the formalization. The applicability of this methodology to proving privacy properties of Privacy Enhancing Technologies is demonstrated by proving the anonymity of the Dining Cryptographers protocol. To the best of the author's knowledge, this is the first machine-verified proof of privacy of the Dining Cryptographers protocol for an unbounded number of participants and a quantitative metric for privacy.