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International Conference on Information and Communications Security

ICICS 2012: Information and Communications Security pp 45–57Cite as

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Implicit Polynomial Recovery and Cryptanalysis of a Combinatorial Key Cryptosystem

Implicit Polynomial Recovery and Cryptanalysis of a Combinatorial Key Cryptosystem

  • Jun Xu18,19,
  • Lei Hu18 &
  • Siwei Sun18 
  • Conference paper
  • 1967 Accesses

  • 3 Citations

Part of the Lecture Notes in Computer Science book series (LNSC,volume 7618)

Abstract

A public key cryptosystem based on factoring and a combinatorial problem of matrices over ℤ N proposed in 2010 is analyzed in this paper. We propose an efficient partial private key recovery attack on it by solving a problem of recovering implicit polynomials with small coefficients given their large roots and deriving the large roots from the public key. From the partial information of private key, we can decrypt any ciphertext of the cryptosystem by a simple computation. Our implicit polynomial recovery is an application of lattice basis reduction.

Keywords

  • Public Key Cryptography
  • Combinatorial Cryptosystem
  • Implicit Polynomial Recovery
  • Lattice
  • LLL Algorithm

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Author information

Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Jun Xu, Lei Hu & Siwei Sun

  2. Graduate University of Chinese Academy of Sciences, Beijing, 100049, China

    Jun Xu

Authors
  1. Jun Xu
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  2. Lei Hu
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  3. Siwei Sun
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Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of Hong Kong, Room 519, 5/F, Haking Building, Pokfulam Road, 852, Hong Kong, China

    Tat Wing Chim

  2. Department of Computer Science, The University of Hong Kong, Room 519, 5/F, Haking Wong Building, Pokfulam Road, 852, Hong Kong, China

    Tsz Hon Yuen

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© 2012 Springer-Verlag Berlin Heidelberg

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Cite this paper

Xu, J., Hu, L., Sun, S. (2012). Implicit Polynomial Recovery and Cryptanalysis of a Combinatorial Key Cryptosystem. In: Chim, T.W., Yuen, T.H. (eds) Information and Communications Security. ICICS 2012. Lecture Notes in Computer Science, vol 7618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34129-8_5

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  • DOI: https://doi.org/10.1007/978-3-642-34129-8_5

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  • Print ISBN: 978-3-642-34128-1

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