On Statistically-Secure Quantum Homomorphic Encryption

TL;DR

This paper investigates the possibility of information-theoretically secure quantum homomorphic encryption (QHE), proving limitations for its existence and proposing a scheme for IQP circuits based on the one-time pad.

Contribution

It establishes that ITS quantum FHE must have exponential overhead and introduces a QHE scheme for IQP circuits using the one-time pad.

Findings

ITS quantum FHE incurs exponential overhead

Proposed QHE scheme for IQP circuits

Limitations on ITS quantum FHE existence

Abstract

Homomorphic encryption is an encryption scheme that allows computations to be evaluated on encrypted inputs without knowledge of their raw messages. Recently Ouyang et al. constructed a quantum homomorphic encryption (QHE) scheme for Clifford circuits with statistical security (or information-theoretic security (IT-security)). It is desired to see whether an information-theoretically-secure (ITS) quantum FHE exists. If not, what other nontrivial class of quantum circuits can be homomorphically evaluated with IT-security? We provide a limitation for the first question that an ITS quantum FHE necessarily incurs exponential overhead. As for the second one, we propose a QHE scheme for the instantaneous quantum polynomial-time (IQP) circuits. Our QHE scheme for IQP circuits follows from the one-time pad.