Implicit Polynomial Recovery and Cryptanalysis of a Combinatorial Key Cryptosystem

  • Jun Xu
  • Lei Hu
  • Siwei Sun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7618)


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.


Public Key Cryptography Combinatorial Cryptosystem Implicit Polynomial Recovery Lattice LLL Algorithm 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jun Xu
    • 1
    • 2
  • Lei Hu
    • 1
  • Siwei Sun
    • 1
  1. 1.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  2. 2.Graduate University of Chinese Academy of SciencesBeijingChina

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