Multimedia Tools and Applications

, Volume 77, Issue 9, pp 11307–11320 | Cite as

Cryptanalysis of an asymmetric cipher protocol using a matrix decomposition problem: revisited

  • Zhimin Yu
  • Chunsheng Gu
  • Zhengjun Jing
  • Qiuru Cai
  • Ye Luo
  • Yao Wang


With the development of quantum computing technology, quantum computers pose a serious threat to the widely used public key cryptography. This is because there are effective quantum algorithms to solve many difficult problems based on commutative algebra structures such as factorization or discrete logarithms. It is generally believed that many public key crytosystems based on non-commutative cryptosystem algebraic structures have the potential to resist quantum computing attacks. Since multiplication of matrices has non-commutative properties, the cryptography based on matrix-based has the potential to resist quantum computing attacks. The security of matrix-based cryptography is closely related to the difficulty of matrix decomposition. An asymmetric cipher protocol based on matrix decomposition problem has been proposed by Raulynaitis et al. to meet the requirements of public key cryptography in the post quantum era. Liu et al. identified some weak keys in this scheme, through which an attacker can solve the equivalent secret key and crack the scheme by solving simultaneous linear equations. Liu et al. proposed an improved scheme to avoid weak keys. However, Raulynaitis and Liu schemes are not fully secured because a special structure of matrix is used to make some matrics commutative. The analysis presented in this paper demostrates that regardless of whether the private key is weak key or not, the equivalent keys from an associated public key can be solved in a reasonable time by a linear algebra attack. For this purpose, the linear equations with coefficients n2 × n2are needed to solve. The equation coefficients are much less than the coefficients 5n2 × 2n2 in the attack methods of Liu et al. Thus, the proposed attack method is not only more general and but also more efficient.


Matrix decomposion Linear equations Cryptanalysis of an asymmetric cipher protocol Equivalent secret key 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Zhimin Yu
    • 1
  • Chunsheng Gu
    • 1
  • Zhengjun Jing
    • 1
  • Qiuru Cai
    • 1
  • Ye Luo
    • 1
  • Yao Wang
    • 1
  1. 1.Key Laboratory of Cloud Computing and Intelligent Information Processing of Changzhou City, School of Computer EngineeringJiangsu University of TechnologyChangzhouChina

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