Symmetric quantum fully homomorphic encryption with perfect security

TL;DR

This paper introduces a symmetric quantum fully homomorphic encryption scheme based on quantum one-time pad, enabling secure quantum computations on encrypted data with perfect security, a significant advancement over classical methods.

Contribution

It presents the first symmetric QFHE scheme with perfect security and constructs a QOTP-based symmetric QHE scheme with key-independent evaluation.

Findings

Allows any unitary transformation on encrypted quantum data

Achieves perfect security unlike classical schemes

Includes a QOTP-based QHE scheme with key-independent evaluation

Abstract

Suppose some data have been encrypted, can you compute with the data without decrypting them? This problem has been studied as homomorphic encryption and blind computing. We consider this problem in the context of quantum information processing, and present the definitions of quantum homomorphic encryption (QHE) and quantum fully homomorphic encryption (QFHE). Then, based on quantum one-time pad (QOTP), we construct a symmetric QFHE scheme, where the evaluate algorithm depends on the secret key. This scheme permits any unitary transformation on any $n$-qubit state that has been encrypted. Compared with classical homomorphic encryption, the QFHE scheme has perfect security. Finally, we also construct a QOTP-based symmetric QHE scheme, where the evaluate algorithm is independent of the secret key.