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首页> 外文期刊>Parallel and Distributed Systems, IEEE Transactions on >Harnessing the Cloud for Securely Outsourcing Large-Scale Systems of Linear Equations
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Harnessing the Cloud for Securely Outsourcing Large-Scale Systems of Linear Equations

机译：利用云安全地外包大型线性方程组

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摘要

Cloud computing economically enables customers with limited computational resources to outsource large-scale computations to the cloud. However, how to protect customers' confidential data involved in the computations then becomes a major security concern. In this paper, we present a secure outsourcing mechanism for solving large-scale systems of linear equations (LE) in cloud. Because applying traditional approaches like Gaussian elimination or LU decomposition (aka. direct method) to such large-scale LEs would be prohibitively expensive, we build the secure LE outsourcing mechanism via a completely different approach—iterative method, which is much easier to implement in practice and only demands relatively simpler matrix-vector operations. Specifically, our mechanism enables a customer to securely harness the cloud for iteratively finding successive approximations to the LE solution, while keeping both the sensitive input and output of the computation private. For robust cheating detection, we further explore the algebraic property of matrix-vector operations and propose an efficient result verification mechanism, which allows the customer to verify all answers received from previous iterative approximations in one batch with high probability. Thorough security analysis and prototype experiments on Amazon EC2 demonstrate the validity and practicality of our proposed design.
机译：云计算可以经济地使计算资源有限的客户将大规模计算外包给云。但是，如何保护计算中涉及的客户机密数据成为主要的安全问题。在本文中，我们提出了一种安全的外包机制，用于解决云中的大型线性方程组（LE）。由于将高斯消除或LU分解（也称为直接方法）之类的传统方法应用于如此大规模的LE会非常昂贵，因此我们通过完全不同的方法（迭代方法）构建安全的LE外包机制，该方法在实施中要容易得多。实际上，仅需要相对简单的矩阵向量运算即可。具体来说，我们的机制使客户能够安全地利用云，以迭代方式找到LE解决方案的连续近似值，同时将敏感的输入和输出保持私有。对于鲁棒的作弊检测，我们进一步探索了矩阵向量运算的代数性质，并提出了一种有效的结果验证机制，该机制使客户能够以较高的概率验证从先前的迭代近似中收到的所有答案。在Amazon EC2上进行的全面安全性分析和原型实验证明了我们提出的设计的有效性和实用性。

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