Quantifying the Leakage of Quantum Protocols for Classical Two-Party Cryptography
This work addresses security vulnerabilities in quantum cryptographic protocols for distrustful parties, extending impossibility results to all non-trivial primitives, which is incremental but important for foundational security analysis.
The paper tackles the problem of information leakage in quantum protocols for classical two-party cryptography, showing that all non-trivial primitives necessarily leak information to dishonest players, even with a trusted third party, and provides a framework to quantify this leakage with lower bounds for examples like oblivious transfer.
We study quantum protocols among two distrustful parties. By adopting a rather strict definition of correctness - guaranteeing that honest players obtain their correct outcomes only - we can show that every strictly correct quantum protocol implementing a non-trivial classical primitive necessarily leaks information to a dishonest player. This extends known impossibility results to all non-trivial primitives. We provide a framework for quantifying this leakage and argue that leakage is a good measure for the privacy provided to the players by a given protocol. Our framework also covers the case where the two players are helped by a trusted third party. We show that despite the help of a trusted third party, the players cannot amplify the cryptographic power of any primitive. All our results hold even against quantum honest-but-curious adversaries who honestly follow the protocol but purify their actions and apply a different measurement at the end of the protocol. As concrete examples, we establish lower bounds on the leakage of standard universal two-party primitives such as oblivious transfer.