Cloud Computing Service: The Caseof Large Matrix Determinant Computation

Lei, Xinyu; Liao, Xiaofeng; Huang, Tingwen; Li, Huaqing

doi:10.1109/tsc.2014.2331694

Cited by 89 publications

(38 citation statements)

References 27 publications

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“…Compared with the verification tasks in the existing matrix-related outsourcing frameworks [10,2,11], the challenges in our protocol stem from the fact that the factorization is only an approximation of the original matrix, rather than strict equality. Such approximation nature inherent in NMF computation makes the sampling-based verification approaches, e.g., [2], invalid.…”

Section: Results Verificationmentioning

confidence: 99%

Secure and Verifiable Outsourcing of Nonnegative Matrix Factorization (NMF)

Duan

Zhou

2016

Proceedings of the 4th ACM Workshop on Information Hiding and Multimedia Security

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Cloud computing platforms are becoming increasingly prevalent and readily available nowadays, providing us alternative and economic services for resource-constrained clients to perform large-scale computation. In this work, we address the problem of secure outsourcing of large-scale nonnegative matrix factorization (NMF) to a cloud in a way that the client can verify the correctness of results with small overhead. The input matrix protection is achieved by a lightweight, permutation-based encryption mechanism. By exploiting the iterative nature of NMF computation, we propose a single-round verification strategy, which can be proved to be effective. Both theoretical and experimental results are given to demonstrate the superior performance of our scheme.

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Section: Results Verificationmentioning

confidence: 99%

Secure and Verifiable Outsourcing of Nonnegative Matrix Factorization (NMF)

Duan

Zhou

2016

Proceedings of the 4th ACM Workshop on Information Hiding and Multimedia Security

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“…Zhou et al in [12] pointed out a possible weakness (in the hypothesis of an integer problem). Similar approaches, still based on matrix pre-and post-multiplication, can be found also for matrix product [13,14], determinant computation [15], and singular value decomposition [16].…”

Section: Brief Literature Reviewmentioning

confidence: 92%

Numerical Problem Encryption for High-Performance Computing Applications

Bernardini¹

2019

Modern Cryptography - Theory, Technology, Adaptation and Integration [Working Title]

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Recent years witnessed the diffusion of cloud-based services. Cloud services have the interesting advantage that they can provide resources (CPU, disk space, etc.) that would be too expensive to deploy and maintain in-house. A major drawback of cloud-based services is the problem of handling private data and-possibly-intellectual property to a third party. With some service (e.g., data storage), cryptography can provide a solution; however, there are some services that are more difficult to protect. An example of such services is the renting of CPU to carry out numerical computation such as differential equation solving. In this chapter, we discuss the problem of encrypting numerical problems so that their solution can be safely outsourced. The idea is to transform (encrypt) a given numerical problem into a different one whose solution can be mapped back to the solution of the original problem if the key used at the encryption stage is known.

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“…Since a wide range of applications of linear algebraic operations in various fields, outsourcing linear algebraic operations, such as matrix multiplication computation (MMC) [31], matrix determinant computation (MDC) [32], matrix factorization [33][34][35], and matrix's characteristic polynomial and eigenvalues computation [36] has become a hot topic [8]. Out of which, the closely related operations with our work are matrix inversion computation (MIC) and large-scale system of linear equations (LSLE)solving.…”

Section: Related Workmentioning

confidence: 99%

Publicly verifiable and efficiency/security-adjustable outsourcing scheme for solving large-scale modular system of linear equations

2019

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Solving large-scale modular system of linear equations (LMSLE) is pervasive in modern computer and communication community, especially in the fields of coding theory and cryptography. However, it is computationally overloaded for lightweight devices arisen in quantity with the dawn of the things of internet (IoT) era. As an important form of cloud computing services, secure computation outsourcing has become a popular topic. In this paper, we design an efficient outsourcing scheme that enables the resource-constrained client to find a solution of the LMSLE with the assistance of a public cloud server. By utilizing affine transformation based on sparse unimodular matrices, our scheme has three merits compared with previous work: 1) Our scheme is efficiency/security-adjustable. Our encryption method is dynamic, and it can balance the security and efficiency to match different application scenarios by skillfully control the number of unimodular matrices. 2) Our scheme is versatile. It is suit for generic m-by-n coefficient matrix A, no matter it is square or not. 3) Our scheme satisfies public verifiability and achieves the optimal verification probability. It enables any verifier which is not necessarily the client to verify the correctness of the results returned from the cloud server with probability 1. Finally, theoretical analysis and comprehensive experimental results confirm our scheme's security and high efficiency.

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Cloud Computing Service: The Caseof Large Matrix Determinant Computation

Cited by 89 publications

References 27 publications

Secure and Verifiable Outsourcing of Nonnegative Matrix Factorization (NMF)

Secure and Verifiable Outsourcing of Nonnegative Matrix Factorization (NMF)

Numerical Problem Encryption for High-Performance Computing Applications

Publicly verifiable and efficiency/security-adjustable outsourcing scheme for solving large-scale modular system of linear equations

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