Quantum Fully Homomorphic Encryption By Integrating Pauli One-time Pad With Quaternions

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Guangsheng Ma^1,2 and Hongbo Li^1,3

¹Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
²School of Mathematics and Physics, North China Electric Power University, Beijing, China
³University of Chinese Academy of Sciences, Beijing, China

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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.

► BibTeX data

@article{Ma2022quantumfully, doi = {10.22331/q-2022-12-01-866}, url = {https://doi.org/10.22331/q-2022-12-01-866}, title = {Quantum {F}ully {H}omomorphic {E}ncryption by {I}ntegrating {P}auli {O}ne-time {P}ad with {Q}uaternions}, author = {Ma, Guangsheng and Li, Hongbo}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {6}, pages = {866}, month = dec, year = {2022} }

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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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

Republished By Plato

Abstract

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