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Secure outsourcing of large matrix determinant computation

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Abstract

Cloud computing provides the capability to connect resource-constrained clients with a centralized and shared pool of resources, such as computational power and storage on demand. Large matrix determinant computation is almost ubiquitous in computer science and requires large-scale data computation. Currently, techniques for securely outsourcing matrix determinant computations to untrusted servers are of utmost importance, and they have practical value as well as theoretical significance for the scientific community. In this study, we propose a secure outsourcing method for large matrix determinant computation. We employ some transformations for privacy protection based on the original matrix, including permutation and mix-row/mix-column operations, before sending the target matrix to the cloud. The results returned from the cloud need to be decrypted and verified to obtain the correct determinant. In comparison with previously proposed algorithms, our new algorithm achieves a higher security level with greater cloud efficiency. The experimental results demonstrate the efficiency and effectiveness of our algorithm.

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Acknowledgements

This study was partially supported by the National Natural Science Foundation of China (Grant No. 61502269), National Key Research and Development Program of China (2017YFA0303903), and Zhejiang Province Key R&D Project (2017C01062).

Author information

Authors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua University, Beijing, 100084, China

    Jiayang Liu

  2. Beijing Research Institute of Telemetry, Beijing, 100094, China

    Jingguo Bi

  3. Institute for Advanced Study, Tsinghua University, Beijing, 100084, China

    Jingguo Bi

  4. Space Star Technology Co., Ltd, Beijing, 100086, China

    Mu Li

Authors
  1. Jiayang Liu
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  2. Jingguo Bi
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  3. Mu Li
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Corresponding author

Correspondence to Jingguo Bi.

Additional information

Jiayang Liu received the BS degree in mathematics from Tsinghua University, China in 2012. He is a PhD candidate in information security in Department of Computer Science and Technology of Tsinghua University, China.

Jingguo Bi received the BS and PhD degree in information security from Shandong University, China in 2007 and 2012, respectively. He was an associate researcher in Tsinghua University, China. He is currently a researcher in Beijing Research Institute of Telemetry, China. His research interests are public key cryptosystems.

Mu Li is a senior engineer of Spacestar Technology Co., Ltd, China. His research interests include cyber security, satellite communication and VLSI design.

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Liu, J., Bi, J. & Li, M. Secure outsourcing of large matrix determinant computation. Front. Comput. Sci. 14, 146807 (2020). https://doi.org/10.1007/s11704-019-9189-7

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