Research On (k,n) Threshold Quantum Homomorphic Encryption Protocols

Today,with the rapid development of Internet technology,people’s life gradually relies on network..However,cloud servers are used as intermediate nodes for most information storage and transmission,so users’ private information may be leaked.In recent years,quantum computer technology develops fast and its high speed of computing makes some classical encryption methods insecure.In order to seek a more secure encryption method,quantum cryptography was born.Quantum cryptography is a discipline based on the principle of quantum mechanics to complete corresponding cryptographic tasks.And quantum homomorphic encryption is one of the important directions of quantum cryptography.If the client with limited quantum capacity wants to delegate private information to the server with full quantum capacity for calculation without leaking the information,it allows the client to conduct the calculation on the encrypted information and still get the desired result after decryption.This paper mainly studies the quantum homomorphic encryption and obtains the following results:1.It is observed that the number of calculators in the quantum homomorphic encryption protocol proposed by Chen is d and it is flexible.However,this protocol can only complete some single-qubit gates and the ability of the evaluators are high.In this paper,we improve this protocol.Firstly,we extend the computational scope of the protocol,so that it can realize arbitrary single-qubit computation.Then by changing the positions of some quantum gates in the computation process,the quantum power required by most calculators is reduced although at the cost of a little flexibility;2.A way to construct quantum fully homomorphic encryption protocols is proposed,which is feasible for most (k，n) threshold quantum state sharing protocols.Then,based on Song’s quantum state sharing protocol,a quantum fully homomorphic encryption protocol is proposed to realize any quantum computation.The universal set of quantum gates used is {(X,Y,Z,H,S,T,CNOT,U(θ)}.