Research On The Theory And Application Of Quantum Homomorphic Encryption

Quantum computation is an emerging computing model that follows the laws of quantum mechanics and performs computation by conducting quantum information units.Depending on the superposition of quantum states and the parallelism of quantum mechanical evolution,the quantum computer exhibits an exponential increase in processing speed compared to the traditional computer.In the context of the current cloud computing era,a large amount of sensitive information and data are transmitted and processed in classical networks using classical cryptographic algorithms.With technique development and increased investments,quantum computers have achieved significant breakthroughs,enabling them to efficiently solve certain hard problems that are challenging for classical cryptographic algorithms.As a result,it is difficult to guarantee the security of private data computed and processed in cloud servers using some classical algorithms.To address this challenge,quantum cryptography has emerged as a crucial approach to protecting sensitive information.Research efforts are being focused on developing quantum encryption algorithms that offer higher security and reliability.The objective is to ensure the confidentiality and integrity of private data by leveraging the unique properties of quantum mechanics.Quantum homomorphic encryption,as an important method that enables quantum computation on ciphertext,shows obvious superiority in privacy protection.It can complete quantum homomorphic evaluation on the private data which is in an encrypted state.And the decryption of the homomorphic evaluation result is consistent with the same homomorphic evaluation conducted on the original quantum plaintext.This delegated computation model allows a client with limited computational power to delegate the secure computation of privacy data to a server with robust computational capabilities,mitigating the risks associated with intermediate decryption.However,researchers have encountered challenges in correcting the errors of nonClifford gate evaluation.The requirement for the quantum channel is relatively high,and there are technical difficulties in the preparation of auxiliary resources.Furthermore,existing quantum homomorphic encryption schemes are limited to two-party delegation only,which have the problem of unidimensionality and are not practical for application in secure multi-party computation scenarios.To address these issues,this thesis makes in-depth research on the quantum homomorphic encryption scheme and its applications in secure multi-party computation.The thesis aims to implement the homomorphic evaluation of universal quantum circuits on encrypted data,leveraging the properties of quantum homomorphic encryption.Additionally,the proposed scheme is extended to multi-party delegation scenarios.A secure multi-party quantum homomorphic encryption scheme is proposed.Moreover,the multi-party quantum private comparison in this thesis is realized with data security and tamper-proof computation results.The main research achievements and innovations of the thesis are as follows.(1)A probabilistic quantum homomorphic encryption scheme for the universal quantum circuit evaluation is proposed to address the difficult problem of errors in non-Clifford gate homomorphic evaluation in quantum homomorphic encryption schemes.Firstly,considering the impact of the open quantum system on the resource states in the quantum homomorphic encryption scheme,the non-maximum entangled states are utilized as auxiliary resources to assist solve the quantum gate errors that occur in the evaluation of nonClifford gate acted on the encrypted quantum states.The homomorphic evaluation of non-Clifford gates is achieved through the application of quantum circuits to a series of quantum gates and joint unitary operation.Secondly,the operations performed by the client and the server are delineated according to the computational power,and the permission to access the data is also clearly pointed out.The client uses the quantum one-time pad to encrypt the private data,and the server loyally executes the homomorphic evaluation algorithm.Finally,the server successively acts on the quantum ciphertext to get the homomorphic computation result according to the order of quantum gates in the universal quantum circuit.Moreover,the client executes the decryption algorithm on the homomorphic computation result to obtain the intended result,which is the same as the homomorphic computation on the original private data.This scheme is true of the homomorphic evaluation of the universal quantum circuit on encrypted data.It can reduce not only the difficulty of preparation techniques but also the requirement for the quantum channel,facilitating the practical implementation of quantum homomorphic encryption.(2)A secure multi-party quantum homomorphic encryption scheme based on ciphertext processing is proposed to solve the singularity problem of the restrictions on the delegate scenario in the quantum homomorphic encryption scheme.Firstly,the encryption keys are distributed to multiple participants and the trusted key center through a measurement device independent quantum key distribution protocol.Each participant encrypts their private data and sends them to the server separately while sending the expected quantum circuits to be executed to the trusted key center and the server.Secondly,a probabilistic quantum homomorphic encryption scheme is adopted,by pre-sharing the non-maximum entangled states between the participants and the server.The correction of quantum gate errors in homomorphic evaluation is completed by applying unitary operators and measurements to achieve arbitrary quantum computation.Later,the evaluation results are returned to the participants.Finally,the trusted key center obtains the decryption key according to the key update rules and sends it to the corresponding participants for decryption.The participants decrypt and obtain the desired outcome that the quantum circuit applied on the quantum plaintext.The proposed scheme not only satisfies the requirements of the ciphertext homomorphic computation of multiple parties,but also improves the universality of the quantum homomorphic encryption scheme.(3)A multi-party quantum privacy comparison protocol based on quantum homomorphic encryption is proposed to make the quantum homomorphic encryption scheme widely applied in secure multi-party quantum computation.Firstly,the multi-party quantum private comparison is reduced to achieving homomorphic evaluation of quantum circuits.A trusted key center is introduced,and a quantum key distribution protocol is used so that each participant gets a secure encryption key.At the same time,the participants encrypt the quantum privacy to be compared using the quantum one-time pad technology and send it to the almost dishonest server with great computing capability.Secondly,by using the quantum homomorphic encryption scheme with perfect security,the server achieves the homomorphic evaluation of the encrypted private data.A non-interactive communication model is established between the participants to accomplish the privacy comparison task of multiple participants.Finally,the comparison results are decrypted and honestly published through the trusted key center.The problem will be resolved which is the malicious tampering of the comparison results.This scheme significantly improves the security of the quantum private comparison protocol and effectively explores the multi-party application scenario of the quantum homomorphic encryption scheme.