On the Efficiency of Classical and Quantum Secure Function Evaluation

TL;DR

This paper analyzes the efficiency bounds of classical and quantum protocols for secure function evaluation, highlighting new quantum protocols that outperform classical bounds and establishing fundamental limitations.

Contribution

It introduces a quantum protocol that surpasses classical efficiency bounds for OT and provides new lower bounds for quantum reductions of OT.

Findings

Classical bounds on OT efficiency are extended to the statistical quantum setting.

A quantum protocol for OT that violates classical efficiency bounds by an arbitrarily large factor.

Established lower bounds for quantum reductions of OT to commitments.

Abstract

We provide bounds on the efficiency of secure one-sided output two-party computation of arbitrary finite functions from trusted distributed randomness in the statistical case. From these results we derive bounds on the efficiency of protocols that use different variants of OT as a black-box. When applied to implementations of OT, these bounds generalize most known results to the statistical case. Our results hold in particular for transformations between a finite number of primitives and for any error. In the second part we study the efficiency of quantum protocols implementing OT. While most classical lower bounds for perfectly secure reductions of OT to distributed randomness still hold in the quantum setting, we present a statistically secure protocol that violates these bounds by an arbitrarily large factor. We then prove a weaker lower bound that does hold in the statistical quantum setting and implies that even quantum protocols cannot extend OT. Finally, we present two lower bounds for reductions of OT to commitments and a protocol based on string commitments that is optimal with respect to both of these bounds.