Practical and Secure Outsourcing Algorithms of Matrix Operations Based on a Novel Matrix Encryption Method

With the recent growth and commercialization of cloud computing, outsourcing computation has become one of the most important cloud services, which allows the resource-constrained clients to efficiently perform large-scale computation in a pay-per-use manner. Meanwhile, outsourcing large scale computing problems and computationally intensive applications to the cloud has become prevalent in the science and engineering computing community. As important fundamental operations, large-scale matrix multiplication computation (MMC), matrix inversion computation (MIC), and matrix determinant computation (MDC) have been frequently used. In this paper, we present three new algorithms to enable secure, verifiable, and efficient outsourcing of MMC, MIC, and MDC operations to a cloud that may be potentially malicious. The main idea behind our algorithms is a novel matrix encryption/decryption method utilizing consecutive and sparse unimodular matrix transformations. Compared to previous works, this versatile technique can be applied to many matrix operations while achieving a good balance between security and efficiency. First, the proposed algorithms provide robust confidentiality by concealing the local information of the entries in the input matrices. Besides, they also protect the statistic information of the original matrix. Moreover, these algorithms are highly efficient. Our theoretical analysis indicates that the proposed algorithms reduce the time overhead on the client side from O(n 2.3728639 ) to O(n 2 ). Finally, the extensive experimental evaluations demonstrate the practical efficiency and effectiveness of our algorithms

Secure Cloud Computing for Solving Large-Scale Linear Systems of Equations

Solving large-scale linear systems of equations (LSEs) is one of the most common and fundamental problems in big data. But such problems are often too expensive to solve for resource-limited users. Cloud computing has been proposed as an efficient and costeffective way of solving such tasks. Nevertheless, one critical concern in cloud computing is data privacy. Many previous works on secure outsourcing of LSEs have high computational complexity and share a common serious problem, i.e., a huge number of external memory I/O operations, which may render those outsourcing schemes impractical. We develop a practical secure outsourcing algorithm for solving large-scale LSEs, which has both low computational complexity and low memory I/O complexity and can protect clients privacy well. We implement our algorithm on a real-world cloud server and a laptop. We find that the proposed algorithm offers significant time savings for the client (up to 65%) compared to previous algorithms

Noninteractive Verifiable Outsourcing Algorithm for Bilinear Pairing with Improved Checkability

It is well known that the computation of bilinear pairing is the most expensive operation in pairing-based cryptography. In this paper, we propose a noninteractive verifiable outsourcing algorithm of bilinear pairing based on two servers in the one-malicious model. The outsourcer need not execute any expensive operation, such as scalar multiplication and modular exponentiation. Moreover, the outsourcer could detect any failure with a probability close to 1 if one of the servers misbehaves. Therefore, the proposed algorithm improves checkability and decreases communication cost compared with the previous ones. Finally, we utilize the proposed algorithm as a subroutine to achieve an anonymous identity-based encryption (AIBE) scheme with outsourced decryption and an identity-based signature (IBS) scheme with outsourced verification