Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic encryption

TL;DR

This paper explores the fundamental privacy and correctness trade-offs in quantum homomorphic encryption, establishing definitions for circuit privacy, and demonstrating how these trade-offs impact the design of secure quantum computation protocols.

Contribution

It introduces a formal definition of quantum circuit privacy, and reveals inherent trade-offs between privacy and correctness in quantum homomorphic encryption schemes.

Findings

Established a definition of quantum circuit privacy.

Reduced quantum oblivious transfer to quantum homomorphic encryption.

Uncovered fundamental privacy-correctness trade-offs in quantum protocols.

Abstract

Quantum homomorphic encryption, which allows computation by a server directly on encrypted data, is a fundamental primitive out of which more complex quantum cryptography protocols can be built. For such constructions to be possible, quantum homomorphic encryption must satisfy two privacy properties: data privacy which ensures that the input data is private from the server, and circuit privacy which ensures that the ciphertext after the computation does not reveal any additional information about the circuit used to perform it, beyond the output of the computation itself. While circuit privacy is well-studied in classical cryptography and many homomorphic encryption schemes can be equipped with it, its quantum analogue has received little attention. Here we establish a definition of circuit privacy for quantum homomorphic encryption with information-theoretic security. Furthermore, we reduce quantum oblivious transfer to quantum homomorphic encryption. By using this reduction, our work unravels fundamental trade-offs between circuit privacy, data privacy and correctness for a broad family of quantum homomorphic encryption protocols, including schemes that allow only the computation of Clifford circuits.