A constant lower bound for any quantum protocol for secure function evaluation

TL;DR

This paper establishes a fundamental limit on the security of quantum protocols for secure function evaluation, showing that perfect security cannot be achieved and that security cannot be arbitrarily amplified.

Contribution

It proves a constant lower bound on cheating probabilities for any quantum protocol in secure function evaluation, extending previous no-go results.

Findings

Constant lower bound on cheating probabilities in quantum protocols

Implication that security amplification is impossible

Applications to oblivious transfer and millionaire's problem

Abstract

Secure function evaluation is a two-party cryptographic primitive where Bob computes a function of Alice's and his respective inputs, and both hope to keep their inputs private from the other party. It has been proven that perfect (or near perfect) security is impossible, even for quantum protocols. We generalize this no-go result by exhibiting a constant lower bound on the cheating probabilities for any quantum protocol for secure function evaluation, and present many applications from oblivious transfer to the millionaire's problem. Constant lower bounds are of practical interest since they imply the impossibility to arbitrarily amplify the security of quantum protocols by any means.