| 关于遍历矩阵密码体制的安全性 |
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| 引用本文： | 黄华伟,彭长文,瞿云云,李春华. 关于遍历矩阵密码体制的安全性[J]. 通信学报, 2015, 36(8): 61-67. DOI: 10.11959/j.issn.1000-436x.2015128 |
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| 作者姓名： | 黄华伟 彭长文 瞿云云 李春华 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金资助项目(61462016,11261018)；贵州省科学技术基金资助项目([2014]2125, 2142)；贵州师范大学博士基金资助项目([2014]11904-0514021) |
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| 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。
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| 关 键 词： | 遍历矩阵；公钥密码；计算复杂度；有限域；算法 |
| 收稿时间： | 2014-06-01 |
Security of the cryptosystems based on ergodic matrices |
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| Hua-wei HUANG,Chang-wen PENG,Yun-yun QU,Chun-hua LI. 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 |
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| Authors: | Hua-wei HUANG Chang-wen PENG Yun-yun QU Chun-hua LI |
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| Affiliation: | 1. School of Mathematics and Computer Science,Guizhou Normal University,Guiyang 550001,China;2. School of Mathematics and Computer Sciences,Guizhou Normal College,Guiyang 550018,China;3. School of Science,East China Jiaotong University,Nanchang 330013,China |
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| 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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| Keywords: | ergodic matrix public-key cryptography computational complexity finite field algorithm |
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