Composing Quantum Protocols in a Classical Environment

TL;DR

This paper introduces a security framework for quantum protocols implementing classical tasks, demonstrating their composability within classical protocols and verifying the security of specific quantum protocols for oblivious transfer and identification.

Contribution

It defines a universal security criterion for quantum protocols and proves their secure composability within classical protocols, extending the applicability of quantum cryptography.

Findings

Security conditions are uniquely determined by the ideal functionality.

Classical protocols with quantum subroutines remain secure when replacing ideal functionalities with quantum protocols.

Quantum protocols for oblivious transfer and secure identification satisfy the security definition.

Abstract

We propose a general security definition for cryptographic quantum protocols that implement classical non-reactive two-party tasks. The definition is expressed in terms of simple quantum-information-theoretic conditions which must be satisfied by the protocol to be secure. The conditions are uniquely determined by the ideal functionality F defining the cryptographic task to be implemented. We then show the following composition result. If quantum protocols pi_1,...,pi_k securely implement ideal functionalities F_1,...,F_k according to our security definition, then any purely classical two-party protocol, which makes sequential calls to F_1,...,F_k, is equally secure as the protocol obtained by replacing the calls to F_1,...,F_k with the respective quantum protocols pi_1,...,pi_k. Hence, our approach yields the minimal security requirements which are strong enough for the typical use of quantum protocols as subroutines within larger classical schemes. Finally, we show that recently proposed quantum protocols for oblivious transfer and secure identification in the bounded-quantum-storage model satisfy our security definition, and thus compose in the above sense.