Research On Secure Outsourced Computation Of Matrix Based On Fully Homomorphic Encryption

Matrix computation is one of the most fundamental problems in science and engineering.Matrix computation usually requires a large amount of computing resources,so performing matrix operations on a client with limited computing resources is not a very effective method.With the popularity of cloud computing,we can outsource matrix computing tasks to cloud service providers,thereby reliving the clients from computation costs.However,outsourcing data on cloud servers somewhere could pose a severe threat to users’ privacy as cloud managers are not completely trusted.Fully homomorphic encryption enables us to perform arbitrary computations over encrypted data opening a new avenue for the secure outsourced computation in cloud computing.This paper researches on secure outsourced computation of matrix based on fully homomorphic encryption.The main contributions of this thesis are as follows:1.We investigate the secure outsourced computation of multiple matrix multiplication based on fully homomorphic encryption.The latest Mishra et al.’s work on multiple matrix multiplication method requires huge parameters.Therefore,it will become impractical asymptotically as the number of matrix increases.Firstly,we introduce column-order matrix encoding method,which requires only fixed-size parameters.Secondly,we design a binary multiplication method for multiple matrix multiplication which multiplies pairwise two adjacent matrices in the tree structure.Compared to Mishra et al.’s sequential multiplication,our approach has lower multiplicative circuit depth and thus will be much more efficient.Finally,we introduce a more efficient matrix encoding method based on the hypercube structure,combining it with binary multiplication,to further improve the computational efficiency of secure outsourced computation of multiple matrix multiplication.Experimental results show that compared with the Mishra et al.’s method our proposed methods show excellent computational performance,among which the method based on hypercube structure is the most efficient.2.We investigate the secure outsourced computation of matrix determinant based on fully homomorphic encryption.Most of the existing schemes on secure outsourced computation of matrix determinant are based on the disguise-based technique,but the security is too weak.This paper first proposes a method for secure outsourced computation of matrix determinant based on fully homomorphic encryption which makes use of an efficient matrix encoding method based on the hypercube structure.Experimental results show that our method based on the hypercube structure has a high performace.Compared with the methods based on disguise-based techniques,our method based on fully homomorphic encryption is more secure.