Quantum entropic security and approximate quantum encryption

TL;DR

This paper generalizes entropic security concepts to quantum encryption, establishing equivalences, security proofs for specific ciphers, and a lower bound on key length, advancing quantum cryptography theory.

Contribution

It introduces quantum entropic security and indistinguishability, proves their equivalence, and extends encryption schemes within this new security framework.

Findings

Proves equivalence of quantum entropic security and indistinguishability

Provides security proofs for two quantum cipher schemes

Establishes a lower bound on key length for quantum encryption

Abstract

We present full generalisations of entropic security and entropic indistinguishability to the quantum world where no assumption but a limit on the knowledge of the adversary is made. This limit is quantified using the quantum conditional min-entropy as introduced by Renato Renner. A proof of the equivalence between the two security definitions is presented. We also provide proofs of security for two different cyphers in this model and a proof for a lower bound on the key length required by any such cypher. These cyphers generalise existing schemes for approximate quantum encryption to the entropic security model.