Computational Security of Quantum Encryption

TL;DR

This paper explores the foundational aspects of encrypting quantum data securely in the computational setting, establishing definitions, equivalences, and constructions that extend classical cryptography into the quantum realm.

Contribution

It introduces quantum analogues of classical encryption notions, proves their equivalence, and constructs secure quantum encryption schemes from basic quantum primitives.

Findings

Quantum-secure one-way functions imply IND-CCA1-secure symmetric-key encryption.

Quantum-secure trapdoor permutations imply semantically-secure public-key encryption.

Established foundational definitions and equivalences for quantum encryption security.

Abstract

Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes against quantum attacks. In this work, we initiate the study of another relevant topic: the encryption of quantum data in the computational setting. In this direction, we establish quantum versions of several fundamental classical results. First, we develop natural definitions for private-key and public-key encryption schemes for quantum data. We then define notions of semantic security and indistinguishability, and, in analogy with the classical work of Goldwasser and Micali, show that these notions are equivalent. Finally, we construct secure quantum encryption schemes from basic primitives. In particular, we show that quantum-secure one-way functions imply IND-CCA1-secure symmetric-key quantum encryption, and that quantum-secure trapdoor one-way permutations imply semantically-secure public-key quantum encryption.