Quantifying the Leakage of Quantum Protocols for Classical Two-Party Cryptography

TL;DR

This paper proves that any strictly correct quantum protocol for non-trivial classical two-party primitives inevitably leaks information, extending impossibility results and providing a framework to quantify this leakage, even with trusted third parties.

Contribution

It introduces a framework to quantify information leakage in quantum protocols for classical primitives, showing all such protocols leak information regardless of third-party assistance.

Findings

All strictly correct quantum protocols for non-trivial primitives leak information.

Leakage quantification framework applies even with trusted third parties.

Lower bounds established for leakage in oblivious transfer and other primitives.

Abstract

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.