Security of the cryptosystems based on ergodic matrices

Hua-wei HUANG; Chang-wen PENG; Yun-yun QU; Chun-hua LI

doi:10.11959/j.issn.1000-436x.2015128

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Security of the cryptosystems based on ergodic matrices

Academic paper | 更新时间：2024-06-05

- Security of the cryptosystems based on ergodic matrices
- Journal on Communications Vol. 36, Issue 8, Pages: 61-67(2015)
- 作者机构：
  
  1. 贵州师范大学数学与计算机科学学院,贵州贵阳 550001
  2. 贵州师范学院数学与计算机科学学院,贵州贵阳 550018
  3. 华东交通大学理学院，江西南昌 330013
- 作者简介：
- 基金信息：
  
  The National Natural Science Foundation of China(61462016);The National Natural Science Foundation of China(11261018);The Doctorial Foundation of Guizhou Normal University([2014]11904-0514021)
- DOI：10.11959/j.issn.1000-436x.2015128
  CLC： TN918
- Online First：2015-08，
  
  Published：25 August 2015
- 稿件说明：
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Hua-wei HUANG, Chang-wen PENG, Yun-yun QU, et al. Security of the cryptosystems based on ergodic matrices[J]. Journal on Communications, 2015, 36(8): 61-67.
DOI：

Hua-wei HUANG, Chang-wen PENG, Yun-yun QU, et al. Security of the cryptosystems based on ergodic matrices[J]. Journal on Communications, 2015, 36(8): 61-67. DOI： 10.11959/j.issn.1000-436x.2015128.

摘要

分析了基于有限域遍历矩阵的公钥密码体制的安全性。根据公钥，采取逆矩阵消去方法得到伪造私钥的线性方程组。从而证明了计算性TEME问题是多项式时间可解的，利用伪造私钥即可破解PZZ1密码体制的密文。在一些情况下，SEME 问题在多项式时间内可归约为离散对数问题，若密钥参数选取不当，PZZ2 密码体制是基于离散对数问题的，并不基于NP困难问题。

Abstract

The security of the public-key cryptosystems based on ergodicmatrices over finite field was analysed.According to the public key

a system of linear equations for the forged secret key bits is obtained by inverse matrix elimination method.It is proved that the computational TEME problem is solvablein polynomial time and the ciphertext of the PZZ1 cryptosystem can be decrypted by the forged secret key.In some case the SEME problem can be reduced to discrete logarithm problem in polynomial time.If the key parameters are chosen improperly

then PZZ2 cryptosystem is based on discrete logarithm problem instead of NP hard problem.

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references

DING J T . Multi-Variate Public Key Cryptosystems [M ] . Berlin : Springer-VerlagPress , 2006 .

MUKESH K S . Public key cryptography with matrices [A ] . Proceedings of the IEEE Workshop on Information Assurance [C ] . United States Military Academy , 2004 . 146 - 152 .

STICKEL E . A new method for exchanging secret keys [A ] . Proc of the Third International Conference on Information Technology and Applications(ICITA05) [C ] . 2005 . 426 - 430 .

SHPILRAIN V . Cryptanalysis of stickel’s key exchange scheme [A ] . Computer Science in Russia 2008,LNCS 5010 [C ] . 2008 . 283 - 288 .

ZHAO Y , WANG L , ZHANG W . Information-exchange using the ergodic matrices in GF(2) [A ] . Proc ACNS 2004 [C ] . Icisa Press , 2004 . 388 - 397 .

赵永皙，黄声烈，姜占华 , 等 . GF(2k)上的遍历矩阵及其特性分析 [J ] . 小型微型计算机系统 , 2005 , 26 ( 12 ): 2135 - 2139 .

ZHAO Y Z , HUANG S L , JIANG Z H , et al . Ergodic matrix over GF(2k)and its properties [J ] . Mini-Micro Systems , 2005 , 26 ( 12 ): 2135 - 2139 .

赵永皙 , 姜占华 , 黄声烈 . 基于 F2 上遍历矩阵的 Shamir 三次传递协议的实现 [J ] . 小型微型计算机系统 , 2006 , 27 ( 6 ): 986 - 991 .

ZHAO Y Z , JIANG Z H , HUANG S L . Implementation of Shamir’s three pass protocol based on ergodic matrix over finite field [J ] . MiniMicro Systems , 2006 , 27 ( 6 ): 986 - 991 .

赵永皙 , 裴士辉 , 王洪军 , 等 . 利用有限域上的遍历矩阵构造动态加密器 [J ] . 小型微型计算机系统 , 2007 , 28 ( 11 ): 2010 - 2014 .

ZHAO Y Z , PEI S H , WANG H J , et al . Using the ergodic matrices over finite field to construct the dynamic encryptor [J ] . Mini-Micro Systems , 2007 , 28 ( 11 ): 2010 - 2014 .

PEI S H , ZHAO Y Z , ZHAO H W . Construct public key encryption scheme using ergodic matrices over GF(2) [A ] . TAMC 2007 [C ] . Berlin,Springer-Verlag , 2007 . 181 - 188 .

PEI S H , ZHAO H W , ZHAO Y Z . Public key cryptography based on ergodic matrices over finite field [J ] . Wuhan University Journal of Natural Sciences , 2006 , 11 ( 6 ): 1525 - 1528 .

裴士辉 , 赵永皙 , 赵宏伟 . 基于遍历矩阵的公钥加密方案 [J ] . 电子学报 , 2010 , 38 ( 8 ): 1908 - 1913 .

PEI S H , ZHAO Y Z , ZHAO H W . Public key encryption scheme based on the ergodic matrices [J ] . Chinese Journal of Electronics , 2010 , 38 ( 8 ): 1908 - 1913 .

赵永皙 , 赵博 , 裴士辉 , 等 . HFEM 公钥密码方案的设计与实现 [J ] . 通信学报 , 2011 , 32 ( 6 ): 24 - 31 .

ZHAO Y Z , ZHAO B , PEI S H , et al . Design and implement on the HFEM public key scheme [J ] . Journal on Communications , 2011 , 32 ( 6 ): 24 - 31 .

赵永皙 , 赵博 , 裴士辉 . 有限域上遍历矩阵的特性研究 [J ] . 数学学报 , 2012 , 55 ( 3 ): 457 - 468 .

ZHAO Y Z , ZHAO B , PEI S H . On the properties of the ergodic matrix over finite field [J ] . ACTA Mathematica Sinica , 2012 , 55 ( 3 ): 457 - 468 .

LIDL R , NIEDERREITER H . Introduction to Finite Fields and Their Applications [M ] . Cambridge : Cambridge University Press , 1986 .

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