Research On Publicly Verifiable Delegation Of Matrix Computation

Verifiable delegation computing allows capabilities or resources-limited users outsource complex computing tasks to untrusted server, then verify the result as well as correctness proof computed by server, which should take substantially less computational effort than direct computation by clients. With the development towards multi-polarization of network technology, computing resources are unbalanced distributed. Verifiable computing technology can be more reasonable and flexible to configure resource and solve the problem of task allocation in distributed computing environment. In addition, verifiable computing requires that the server returns calculation results and the proof to prove correctness, which could effectively solve the security problem in cloud computing. As an important outsourcing technology in cloud computing, the verifiable computing has become the focus of many scholars in recent years. However it is still in the stage of theoretical research. More often than not, the research object is general function in private model with poor computational efficiency, especially employing homomorphic encryption scheme. Aim at these shortages,this paper carry out research work based on delegation of the polynomial and matrix operations as follows:(1) This paper considers making use of signature to construct proof for the correctness of results, so that clients could verify without private key. It achieves public delegation as well as public validation, and would be especially practical in multi-user scenarios, which is more adapt to the real production environment leading to a solid foundation for future.(2) This paper introduces algebra single function and homomorphism hash function to encode the input from users. Their one-way property and homomorphic property guarantee data privacy in the transmission, computation and storage process. By means of theoretical analysis and proof, we determine the feasibility of the design.(3) This paper designs a dynamically updatable polynomial evaluation delegation scheme under public model as a basis. Then the matrix is decomposed into vector represented by polynomial, and cooperate with undecomposed matrix to compute matrix multiplication.In addition, according to property of inverse matrix in advanced algebra, we construct inverse matrix outsourcing scheme, which also support public delegation and dynamic update operations.(4) This paper demonstrates the correctness, security and privacy of three schemes according to standard definition. What’s more, different instances are designed such as keyword query, search in encrypted storage of cloud platform and real-time simulation and analysis in portfolio investment, which show the practical value of this research work.