On the Security of Public-key Cryptosystems Based on the Third-order LFSR Sequences over Finite Field GF(p)

Dezhi Gao

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On the Security of Public-key Cryptosystems Based on the Third-order LFSR Sequences over Finite Field GF(p)

机译：基于有限域GF（p）上三阶LFSR序列的公钥密码系统的安全性

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摘要

The security of a public key system whose trapdoor is based on the defined third-order Linear Feedback Shift-Register(LFSR) sequences over finite field GF(p) are investigated. It shows that the security of LFSR is polynomial-time equivalent to the generalized discrete logarithm problems. Thus, the security of a public-key encryption distribution scheme which proposed by Guang G. and Lein H. should be considered to be as secure as the Diffie-Hellman scheme.

机译：研究了其活门基于有限域GF（p）上定义的三阶线性反馈移位寄存器（LFSR）序列的公钥系统的安全性。结果表明，LFSR的安全性是多项式时间，等同于广义离散对数问题。因此，应当认为，Guang G.和Lein H.提出的公钥加密分发方案的安全性与Diffie-Hellman方案一样安全。

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来源
《Journal of systems science & information》 |2010年第2期|P.115-121|共7页
作者
Dezhi Gao;
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作者单位

Information Science and Engineering College, Shandong University of Science and Technology, Qingdao 266510, China;

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原文格式 PDF
正文语种 eng
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关键词
cryptography; security; LFSR system; discrete logarithm problem;

机译：密码学安全;LFSR系统;离散对数问题;

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1. Two methods of directly constructing probabilistic public-key encryption primitives based on third-order LFSR sequences [J] . Jiang ZT, Zhan Y, Chen D, Applied mathematics and computation . 2005,第2期

机译：基于三阶LFSR序列直接构造概率公共密钥加密原语的两种方法
2. Public-key cryptosystems based on cubic finite field extensions [J] . Guang Gong, Lein Harn IEEE Transactions on Information Theory . 1999,第7期

机译：基于三次有限域扩展的公钥密码系统
3. On the Security of Public-Key Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$ [J] . Liao Xiaofeng, Chen Fei, Wong Kwok-wo Computers, IEEE Transactions on . 2010,第10期

机译：有限域$ Z_N $上基于Chebyshev多项式的公钥算法的安全性
4. Security of Public-key Cryptosystems Based on Chebyshev Polynomials over Prime Finite Fields [C] . J. B. Lima, R. M. Campello de Souza, D. Panario IEEE International Symposium on Information Theory . 2008

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5. Algorithms for Finite Field Arithmetics and Their Applications to Public-key Cryptosystems [D] . 伊東利哉. 1988

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7. ElGamal Public-Key cryptosystem in multiplicative groups of quotient rings of polynomials over finite fields [O] . El-Kassar A. N., Haraty Ramzi A. 2005

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8. Public-Key Cryptosystems Based on Linear Codes [R] . Gabidulin, E. M. 1995

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On the Security of Public-key Cryptosystems Based on the Third-order LFSR Sequences over Finite Field GF(p)

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