Secure Tensor Decomposition for Big Data Using Transparent Computing Paradigm

The exponential growth of big data places a great burden on current computing environment. However, there exists a vast gap in the approaches that can securely and efficiently process the large scale heterogeneous data. This paper, on the basis of transparent computing paradigm, presents a unified approach that coordinates the transparent servers and transparent clients to decompose tensor, a mathematical model widely used in data intensive applications, to a core tensor multiplied with a number of truncated orthogonal bases. The structured, semi-structured as well as structured data are transformed to low-order sub-tensors, which are then encrypted using the Paillier homomorphic encryption scheme on the transparent clients. The cipher sub-tensors are transported to the transparent servers for carrying out the integration and decomposition operations. Three secure decomposition algorithms, namely secure bidiagonalization algorithm, secure singular value decomposition algorithm, and secure mode product algorithm, are presented to generate the bidiagonal matrices, truncated orthogonal bases, and core tensor respectively. The homomorphic operations of the three algorithms are carried out on the transparent servers, while the non-homomorphic operations, namely division and square root, are performed on the transparent clients. Experimental results indicate that the proposed method is promising for secure tensor decomposition for big data.