Blend Arithmetic Operations on Tensor-Based Fully Homomorphic Encryption Over Real Numbers

Recent booming growth of networking-based solutions have brought numerous challenges to security and privacy from both perspectives of insider and outsider threats. The encrypted data are relatively considered a safe storage status; however, the process of encrypting data is still facing adversarial actions and data process generally is inapplicable over ciphertexts. As a type of the encryption approach allowing computations over ciphertexts, a fully homomorphic encryption (FHE) can concurrently deal with the adversarial hazards and support computations on ciphertexts. This paper focuses on the issue of blend arithmetic operations over real numbers and proposes a novel tensor-based FHE solution. The proposed approach is called a FHE for blend operations model that uses tensor laws to carry the computations of blend arithmetic operations over real numbers. In our paper, we provide both theoretical proof and experimental evaluations in order to evince the adoptability of the proposed approach.

I. Introduction

Contemporary data usage lifecycle is generally more complicated than it was before due to the interconnected stakeholders and untrusted service vendors in the system, such as the Internet-of-Things and cloud computing [1]–[3]. Data owners are unaware of the real service providers behind the mask of the service presentation when computing resources are offered as a manner of the service [4], [5]. This security concern is commonly caused by the loss of control over the data from the data owner side [6], [7]. Thus, there has been an urgent demand for finding out an approach that proactively prevents data from unexpected usage on the remotes, which forms the major motivation of this work. A fully homomorphic encryption (FHE) solution is an ideal conceptual alternative. For example, an FHE application scenario can be that a financial service institution can prevent cloud providers from touching sensitive data but still can use cloud services. However, there is no practicable FHE application yet in the market due to technical obstacles.