Limitations on information theoretically secure quantum homomorphic encryption

TL;DR

This paper demonstrates that achieving information-theoretically secure, deterministic, fully homomorphic encryption with perfect security in a quantum setting requires exponential overhead, highlighting fundamental limitations.

Contribution

It provides a fundamental impossibility result for quantum fully homomorphic encryption under perfect security constraints.

Findings

Deterministic fully homomorphic encryption with perfect security requires exponential overhead.

Quantum mechanics does not enable information-theoretically secure fully homomorphic encryption without exponential costs.

The proof uses an information localisation argument to establish the limitation.

Abstract

Homomorphic encryption is a form of encryption which allows computation to be carried out on the encrypted data without the need for decryption. The success of quantum approaches to related tasks in a delegated computation setting has raised the question of whether quantum mechanics may be used to achieve information theoretically secure fully homomorphic encryption. Here we show, via an information localisation argument, that deterministic fully homomorphic encryption necessarily incurs exponential overhead if perfect security is required.