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Key Recovery on Several Matrix Public-Key Encryption Schemes
WANG Hou-Zhen 1,ZHANG Huan-Guo 1, TANG Shao-Hua 2
1. Key Laboratory of Aerospace Information Security and Trusted Computing,Ministry of Education, School of Computer, Wuhan University, Wuhan 430079, China
2. South China University of Technology, Guangzhou, 510006, China
*Correspondence author
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Funding: This work was supported by the Ph.D. Programs Foundation of Ministry of Education of China（No.No. 20120141120007）, the Foundation of Science and Technology on Information Assurance Laboratory （No.No. KJ-14-002）
Opened online:12 June 2016
Accepted by: none
Citation: WANG Hou-Zhen,ZHANG Huan-Guo, TANG Shao-Hua.Key Recovery on Several Matrix Public-Key Encryption Schemes[OL]. [12 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4692635
 
 
Eight years ago, Pei emph{et. al} described a matrix public-key encryption scheme based on the matrix factorization over a finite field. Recently, Gu and Zheng also proposed a similar scheme based on the nonabelian factorization (NF) assumption. The security of these schemes is essentially based on a two-sidematrices exponentiation (TSME) problem. In this paper, we show that the TSME problem is susceptible to a very efficient linearization equations attack. Regardless of the public key parameters, we can easily find an equivalent key only in polynomial time $mathcal{O}ig(2n^5(log n+1)ig)$ from the public key alone, and thus it is very practical and can be implemented within less than 1/20 of a second on the recommended system parameters of the schemes.
Keywords:public key cryptosystem, linearization equations attack, equivalent key, matrix factorization
 
 
 

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