The Research On Secure Outcourcing Computation Based On Threshold Cryptography

With the development of modern society,the complexity of computing tasks is getting higher and higher,the client's computing tasks become more and more heavy.But the client's computing power is affected by the hardware device,the client's computing power can not meet the level of modern computing.Therefore,how to outsource client's computing tasks to the cloud server to calculate,has become a problem.The development of secure outsourcing compution is to solve the contradiction between the lack of client computing power and the complexity of computing tasks.The general secure outsourcing compution protocol needs to satisfy three properties,respectively,they are outsourceable,security and verifiable.Most of the current secure outsourcing compution can only outsource limited functions,can not outsource any functions.The complexity of the secure outsourcing compution,which can outsource any functions,is too high.Therefore,this thesis constructs a secure outsourcing compution protocol that can outsource general function.Based on the threshold cryptography,this thesis constructs a secure outsourcing compution protocol for general functions by using the homomorphism of the encryption algorithm,and propose the corresponding verification method.The main contents and innovations of this thesis are as follows:1.Starting from the threshold cryptography,we first propose a(2-3)threshold encryption algorithm.After that,this thesis uses(2-3)threshold encryption algorithm to construct a correct outsourcing compution protocol.In this thesis,we construct the addition algorithm and the multiplication algorithm on the(2-3)threshold ciphertext,so that to construct a secure outsourcing compution protocol for general functions by using the homomorphism of the encryption algorithm.At the same time,this thesis proves the correctness,outsourceable and verifiable of the agreement.2.This thesis proposes two methods to achieve the verifiable of the above protocol.The first method is to outsource the computational tasks to two servers,which are not colluded.The client check whether the two results are equal to verify the result.The second method is that the client performs a preprocessing algorithm to obtain the authentication key,and the result of the server can be verified by the verification key,which proves that the result is correct.In this thesis,the security,outsourceable,verifiable of both methods are proven.3.In this thesis,we propose a secure outsourcing compution protocol for solving large-scale linear equations by using the properties of elementary transformation matrices.The protocol is a non-interactive protocol,is more effective than previous protocol.