Quantum Fully Homomorphic Encryption by Integrating Pauli One-time Pad with Quaternions

TL;DR

This paper introduces a novel quantum fully homomorphic encryption scheme that enhances efficiency by integrating quaternion representations with Pauli one-time pad encryption, enabling more effective quantum circuit evaluation.

Contribution

The paper presents a new QFHE scheme based on quaternion representation, improving evaluation efficiency and establishing a bridge with previous schemes through a novel encrypted multi-bit control technique.

Findings

More efficient evaluation of 1-qubit gates.

Polynomial complexity improvement for general quantum circuits.

A new encrypted multi-bit control technique for quantum gates.

Abstract

Quantum fully homomorphic encryption (QFHE) allows to evaluate quantum circuits on encrypted data. We present a novel QFHE scheme, which extends Pauli one-time pad encryption by relying on the quaternion representation of SU(2). With the scheme, evaluating 1-qubit gates is more efficient, and evaluating general quantum circuits is polynomially improved in asymptotic complexity. Technically, a new encrypted multi-bit control technique is proposed, which allows to perform any 1-qubit gate whose parameters are given in the encrypted form. With this technique, we establish a conversion between the new encryption and previous Pauli one-time pad encryption, bridging our QFHE scheme with previous ones. Also, this technique is useful for private quantum circuit evaluation. The security of the scheme relies on the hardness of the underlying quantum capable FHE scheme, and the latter sets its security on the learning with errors problem and the circular security assumption.