Yuling Luo
Abstract
Large-scale matrix determinants and linear equations are two basic computational tools in science and engineering fields. However, it is difficult for a resource-constrained client to solve large-scale computational tasks. Cloud computing service provides additional computing resources for resource-constrained clients. To solve the problem of large-scale computation, in this article, a secure and efficient framework is proposed to outsource large-scale matrix determinants and linear equations to a cloud. Specifically, the proposed framework contains two protocols, which solve large-scale matrix determinant and linear equations, respectively. In the outsourcing protocols of large-scale matrix determinants and linear equations, the task matrix is encrypted and sent to the cloud by the client. The encrypted task matrix is directly computed by using LU factorization in the cloud. The computed result is returned and verified by the cloud and the client, respectively. The computed result is decrypted if it passes the verification. Otherwise, it is returned to the cloud for recalculation. The framework can protect the input privacy and output privacy of the client. The framework also can guarantee the correctness of the result and reduce the local computational complexity. Furthermore, the experimental results show that the framework can save more than 70% of computing resources after outsourcing computing. Thus, this article provides a secure and efficient alternative for solving large-scale computational tasks.
- [1] . 2010. Cloud computing: The next revolution in information technology. In 1st International Conference on Parallel, Distributed and Grid Computing (PDGC’10). 2–3.Google Scholar
Cross Ref
- [2] . 2014. Highly efficient linear regression outsourcing to a cloud. IEEE Trans. Cloud Comput. 2, 4 (2014), 499–508.Google ScholarCross Ref
- [3] . 2014. Privacy-preserving and verifiable protocols for scientific computation outsourcing to the cloud. J. Parallel Distrib. Comput. 74, 3 (2014), 2141–2151.Google ScholarDigital Library
- [4] . 2015. New algorithms for secure outsourcing of large-scale systems of linear equations. IEEE Trans. Inf. Forens. Secur. 10, 1 (2015), 69–78.Google ScholarCross Ref
- [5] . 2018. Efficient and secure outsourcing of large-scale linear system of equations. IEEE Trans. Cloud Comput. 9, 2 (2018), 587–597.Google ScholarCross Ref
- [6] . 2022. Secure distributed outsourcing of large-scale linear systems. Proc. Int. Conf. Distrib. Comput. Syst. 1, 1 (2022), 1110–1121.Google Scholar
- [7] . 2019. Cloud-based outsourcing for enabling privacy-preserving large-scale non-negative matrix factorization. IEEE Trans. Serv. Comput. 15, 1 (2019), 1–13.Google Scholar
- [8] . 2017. Practical privacy-preserving outsourcing of large-scale matrix determinant computation in the cloud. In Cloud Computing and Security Conference. 3–15.Google ScholarCross Ref
- [9] . 2020. Secure outsourcing algorithm of BTC feature extraction in cloud computing. IEEE Access 8, 1 (2020), 106958–106967.Google ScholarCross Ref
- [10] . 2014. Achieving security, robust cheating resistance, and high-efficiency for outsourcing large matrix multiplication computation to a malicious cloud. Inf. Sci. 280, 1 (2014), 205–217.Google ScholarCross Ref
- [11] . 2015. Cloud computing service: The case of large matrix determinant computation. IEEE Trans. Serv. Comput. 8, 5 (2015), 688–700.Google ScholarCross Ref
- [12] . 2013. Outsourcing large matrix inversion computation to a public Cloud. IEEE Trans. Cloud Comput. 1, 1 (2013), 78–87.Google Scholar
- [13] . 2018. Privacy-preserving large-scale systems of linear equations in outsourcing storage and computation. Sci. China Inf. Sci. 61, 3 (2018), 1–9.Google ScholarCross Ref
- [14] . 2011. Secure multiparty computation for privacy preserving data mining. Encyc. Data Warehous. Mining 1, 1 (2011), 1–39.Google Scholar
- [15] . 2020. Secure outsourcing of large matrix determinant computation. Front. Comput. Sci. 14, 6 (2020), 146807–146819.Google ScholarDigital Library
- [16] . 2014. Efficient and verifiable algorithm for secure outsourcing of large-scale linear programming. In Proceedings of the International Conference on Advanced Information Networking and Applications (AINA’14). 591–596.Google ScholarDigital Library
- [17] . 2012. Security challenges for the public cloud. IEEE Internet Comput. 16, 1 (2012), 69–73.Google ScholarDigital Library
- [18] . 2022. Outsourcing LDA-based face recognition to an untrusted cloud. IEEE Trans. Depend. Sec. Comput. 1, 1 (2022), 1–12.Google Scholar
- [19] . 2015. Efficient secure outsourcing of large-scale linear systems of equations. In Proceedings of the IEEE INFOCOM Conference. 1035–1043.Google ScholarCross Ref
- [20] . 2019. Practical secure computation outsourcing. Comput. Surv. 51, 2 (2019), 1–40.Google ScholarDigital Library
- [21] . 2013. Cloud-based software platform for big data analytics in smart grids. Comput. Sci. Eng. 15, 4 (2013), 38–47.Google ScholarDigital Library
- [22] . 2021. Secure outsourcing of matrix determinant computation under the malicious cloud. Sensors 21, 20 (2021), 1–20.Google ScholarCross Ref
- [23] . 2011. Secure and practical outsourcing of linear programming in cloud computing. In Proceedings of the IEEE INFOCOM Conference. 820–828.Google ScholarCross Ref
- [24] . 2016. Secure optimization computation outsourcing in cloud computing: a case study of linear programming. IEEE Trans. Comput. 65, 1 (2016), 216–229.Google ScholarDigital Library
- [25] . 2013. Harnessing the cloud for securely outsourcing large-scale systems of linear equations. IEEE Trans. Parallel Distrib. Syst. 24, 6 (2013), 1172–1181.Google ScholarDigital Library
- [26] . 2013. Privacy-assured outsourcing of image reconstruction service in cloud. IEEE Trans. Emerg. Topics Comput. 1, 1 (2013), 166–177.Google ScholarCross Ref
- [27] . 2005. On the Euclidean distance of images. IEEE Trans. Pattern Anal. Mach. Intell. 27, 8 (2005), 1334–1339.Google ScholarDigital Library
- [28] . 2019. Efficient and secure outsourcing of DFT, IDFT, and circular convolution. IEEE Access 7, 1 (2019), 60126–60133.Google ScholarCross Ref
- [29] . 2020. Secure and efficient outsourcing computation on large-scale linear regressions. Inf. Sci. 522, 1 (2020), 134–147.Google ScholarCross Ref
- [30] . 2022. Machine learning on cloud with blockchain: A secure, verifiable and fair approach to outsource the linear regression. IEEE Trans. Netw. Sci. Eng. 9, 6 (2022), 3956–3967.Google ScholarCross Ref
- [31] . 2019. A low-overhead, confidentiality-assured, and authenticated data acquisition framework for IoT. IEEE Trans. Industr. Inform. 16, 12 (2019), 7566–7578.Google ScholarCross Ref
- [32] . 2017. Harnessing the hybrid cloud for secure big image data service. IEEE Internet Things J. 4, 5 (2017), 1380–1388.Google ScholarCross Ref
- [33] . 2020. Cloud-assisted privacy-conscious large-scale Markowitz portfolio. Inf. Sci. 527, 1 (2020), 548–559.Google ScholarCross Ref
- [34] . 2020. Secure transmission of compressed sampling data using edge clouds. IEEE Trans. Industr. Inform. 16, 10 (2020), 6641–6651.Google ScholarCross Ref
- [35] . 2020. Privacy-assured FogCS: Chaotic compressive sensing for secure industrial big image data processing in fog computing. IEEE Trans. Industr. Inform. 3203, 4 (2020), 1–11.Google Scholar
- [36] . 2019. Efficiently and securely outsourcing compressed sensing reconstruction to a cloud. Inf. Sci. 496, 1 (2019), 150–160.Google ScholarDigital Library
- [37] . 2020. Secure and efficient outsourcing of PCA-based face recognition. IEEE Trans. Inf. Forens. Secur. 15, 4 (2020), 1683–1695.Google ScholarDigital Library
- [38] . 2020. How to securely outsource finding the min-cut of undirected edge-weighted graphs. IEEE Trans. Inf. Forens. Secur. 15, 1 (2020), 315–328.Google ScholarDigital Library
- [39] . 2015. Outsourcing large-scale quadratic programming to a public cloud. IEEE Access 3, 1 (2015), 2581–2589.Google ScholarCross Ref
- [40] . 2016. Outsourcing eigen-decomposition and singular value decomposition of large matrix to a public cloud. IEEE Access 4, 1 (2016), 869–879.Google ScholarCross Ref
- [41] . 2018. Efficiently and securely harnessing cloud to solve linear regression and other matrix operations. Fut. Gen. Comput. Syst. 81, 1 (2018), 404–413.Google ScholarDigital Library
Index Terms
- A Secure and Efficient Framework for Outsourcing Large-scale Matrix Determinant and Linear Equations
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