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International Conference on Information Security and Cryptology

Inscrypt 2016: Information Security and Cryptology pp 343–354Cite as

A Linear Algebra Attack on the Non-commuting Cryptography Class Based on Matrix Power Function

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10143))

Abstract

Advances in quantum computers threaten to break public key cryptosystems such as RSA, ECC, and EIGamal on the hardness of factoring or taking a discrete logarithm, while no quantum algorithms are found to solve certain mathematical problems on non-commutative algebraic structures until now. Under this background, a non-commuting cryptography class based on matrix power function has been given. In this paper we show that the non-commuting cryptography class based on MPF is vulnerable to a linear algebra attack which only requires polynomial time to achieve the equivalent keys respectively. In addition, we conduct an analysis on the flaws in this schemes and propose an improved scheme that remedies the weakness of their schemes.

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Acknowledgments

We want to thank the anonymous reviewers for their comments which helped to improve the paper. This work is supported by the National Natural Science Foundation of China (Grant Nos. 61303212, 61170080), the State Key Program of National Natural Science of China(Grant Nos. 61332019, U1135004), the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91018008), the Hubei Natural Science Foundation of China (Grant Nos. 2011CDB453, 2014CFB440).

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Authors and Affiliations

  1. Computer School of Wuhan University, Wuhan, 430072, Hubei, China

    Jinhui Liu, Huanguo Zhang & Jianwei Jia

  2. Key Laboratory of Aerospace Information Security and Trusted Computing Ministry of Education, Wuhan, 430072, Hubei, China

    Jinhui Liu, Huanguo Zhang & Jianwei Jia

Authors
  1. Jinhui Liu
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  2. Huanguo Zhang
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  3. Jianwei Jia
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Corresponding author

Correspondence to Huanguo Zhang .

Editor information

Editors and Affiliations

  1. School of Science, Hangzhou Normal University, Hangzhou, China

    Kefei Chen

  2. Institute of Information Engineering, SKLOIS, Beijing, China

    Dongdai Lin

  3. Snapchat Inc., Columbia University, New York, New York, USA

    Moti Yung

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Liu, J., Zhang, H., Jia, J. (2017). A Linear Algebra Attack on the Non-commuting Cryptography Class Based on Matrix Power Function. In: Chen, K., Lin, D., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2016. Lecture Notes in Computer Science(), vol 10143. Springer, Cham. https://doi.org/10.1007/978-3-319-54705-3_21

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  • DOI: https://doi.org/10.1007/978-3-319-54705-3_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54704-6

  • Online ISBN: 978-3-319-54705-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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