Classical Cryptographic Protocols in a Quantum World

TL;DR

This paper demonstrates that classical two-party cryptographic protocols for secure function evaluation remain secure against quantum attackers under reasonable computational assumptions, preserving classical cryptography's feasibility in a quantum context.

Contribution

It proves the existence of classical two-party protocols secure against quantum adversaries assuming certain computational hardness, extending classical cryptography into the quantum era.

Findings

Classical protocols remain secure against quantum attacks under certain assumptions.

Secure evaluation of any polynomial-time function is possible with classical protocols.

The classical feasibility paradigm persists in a quantum computational setting.

Abstract

Cryptographic protocols, such as protocols for secure function evaluation (SFE), have played a crucial role in the development of modern cryptography. The extensive theory of these protocols, however, deals almost exclusively with classical attackers. If we accept that quantum information processing is the most realistic model of physically feasible computation, then we must ask: what classical protocols remain secure against quantum attackers? Our main contribution is showing the existence of classical two-party protocols for the secure evaluation of any polynomial-time function under reasonable computational assumptions (for example, it suffices that the learning with errors problem be hard for quantum polynomial time). Our result shows that the basic two-party feasibility picture from classical cryptography remains unchanged in a quantum world.