On the Power of Quantum Encryption Keys

TL;DR

This paper explores quantum encryption schemes with quantum keys, establishing bounds on message size and key sharing, and demonstrating that quantum keys do not outperform classical keys in these aspects.

Contribution

It introduces a model of quantum encryption keys, extends to an asymmetric setting, and proves bounds showing quantum keys offer no advantage over classical keys.

Findings

Quantum keys do not allow larger messages than classical keys.

Bounds relate message size and key copies to the entropy of the decryption key.

Classical keys can asymptotically achieve optimal bounds.

Abstract

The standard definition of quantum state randomization, which is the quantum analog of the classical one-time pad, consists in applying some transformation to the quantum message conditioned on a classical secret key $k$. We investigate encryption schemes in which this transformation is conditioned on a quantum encryption key state $\rho_k$ instead of a classical string, and extend this symmetric-key scheme to an asymmetric-key model in which copies of the same encryption key $\rho_k$ may be held by several different people, but maintaining information-theoretical security. We find bounds on the message size and the number of copies of the encryption key which can be safely created in these two models in terms of the entropy of the decryption key, and show that the optimal bound can be asymptotically reached by a scheme using classical encryption keys. This means that the use of quantum states as encryption keys does not allow more of these to be created and shared, nor encrypt larger messages, than if these keys are purely classical.