Secure Matrix Computation Based On Full Homomorphic Encryption And Its Applications

Matrix computation is one of the most basic problems in the field of mathematics.It is widely used in science and engineering.Matrix computation often requires a large number of computing resources in applications,local users with limited computing resources may choose to hand over the calculation to the cloud server in order to save local computing resources.Uploading directly to the cloud is obviously unsafe for local privacy data.Full homomorphic encryption technology supports ciphertext computing,which is one of the methods to solve privacy computing.This paper investigates secure matrix computation and its application based on full homomorphic encryption.The main contributions of this paper are as follows:1.We propose a secure matrix multiplication scheme based on fully homomorphic encryption.The existing work supports only the case of the square matrices.This paper investigates secure matrix multiplication for arbitrary matrix based on fully homomorphic encryption.Our proposal is the first secure matrix multiplication scheme for arbitrary matrix based on fully homomorphic encryption.Our method has sufficient security to ensure that matrix information is not leaked in the chosen-plaintext attack(IND-CPA)model.Experimental results show that our scheme has excellent performance for the matrices with different dimensions.To demonstrate the applicability of the proposed matrix multiplication,we further apply it to secure multiple matrices multiplication.Experimental result shows that our solution significantly outperforms the latest secure multiple matrices multiplication scheme.2.Application of security matrix computation to support vector machine encrypted image classification.A naive SVM classification over encrypted data method is encrypting each element of image feature vector into one ciphertext.This method has high time and space complexity.We encrypt the whole feature vector into a single ciphertext based on SIMD technique and save the storage space.We also use SIMD parallel technology to reduce the number of operations between ciphertexts in the process of classification.Our method greatly improves the efficiency of classification calculation.What more,we use the approximate homomorphic comparison method to deal with the final nonlinear computation of classification.Our method significantly improves communication overhead and computational performance compared to the existing work.Experimental results show that our method takes only seconds to classify an encrypted image while the state-of-art work takes several hundred seconds.