Error correctable efficient quantum homomorphic encryption using Calderbank-Shor-Steane codes

TL;DR

This paper introduces an efficient quantum homomorphic encryption scheme leveraging quantum error correction codes, enhancing security and error correction for fault-tolerant quantum cloud computing.

Contribution

It presents a novel scheme that combines encryption and encoding in a single process using Calderbank-Shor-Steane codes, improving security and efficiency over traditional methods.

Findings

Scheme is more secure than permutation-key-based QHE when maximally mixed states are limited.

Uses a longer quantum error correction code to enhance security and error correction.

Demonstrates improved efficiency and security for quantum cloud computing applications.

Abstract

The integration of quantum error correction codes and homomorphic encryption schemes is essential for achieving fault-tolerant secure cloud quantum computing. However, owing to the significant overheads associated with these schemes, their efficiency is paramount. In this study, we develop an efficient quantum homomorphic encryption scheme based on quantum error correction codes that uses a single encoding process to simultaneously perform encryption and encoding. By using a longer quantum error correction code, both the security and error-correction capabilities of the scheme are improved. Through comprehensive evaluations, we demonstrate that the proposed scheme is more secure than the conventional permutation-key-based QHE scheme when the number of maximally mixed states is not more than twice the length of the quantum error-correction code. The proposed scheme offers a more secure and efficient approach to quantum cloud computing, potentially paving the way for more practical and scalable quantum cryptographic protocols.