Public-key Cryptosystem Algorithm Based on Chebyshev Polynomial

doi:10.3969/j.issn.1000-3428.2008.24.047

Computer Engineering ›› 2008, Vol. 34 ›› Issue (24): 137-139. doi: 10.3969/j.issn.1000-3428.2008.24.047

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Public-key Cryptosystem Algorithm Based on Chebyshev Polynomial

ZHAO Geng1,2, YAN Hui1,2, TONG Zong-ke1,2

(1. Department of Computer Science and Technology, Beijing Electronic Science and Technology Institute, Beijing 100070;2. College of Communication Engineering, Xidian University, Xi’an 710071)

Received:1900-01-01 Revised:1900-01-01 Online:2008-12-20 Published:2008-12-20

基于Chebyshev多项式的公钥密码系统算法

赵耿1,2，闫慧1,2，童宗科1,2

(1. 北京电子科技学院计算机科学与技术系，北京 100070；2. 西安电子科技大学通信工程学院，西安 710071)

Abstract

Abstract: This paper introduces the definiteness and properties of Chebyshev polynomial based on finite fields. It studies the security of the ElGamal-like cryptosystem based on Chebyshev polynomial of finite fields, and proposes a modified public-key cryptosystem. In the modified public-key cryptosystem, the secret key is hidden from public key, and it can not be calculated by public key. Analysis shows that the modified system is accurate and doable, and it is better than the ElGamal public-key cryptosystem based on finite fields Chebyshev polynomial.

Key words: Chebyshev polynomial, ElGamal public-key cryptosystem, semi-group property

摘要： 介绍有限域Chebyshev多项式的定义和性质。针对基于有限域Chebyshev多项式的类ElGamal公钥密码系统存在的弱点，提出一个新的公钥密码算法。该算法的公开密钥隐藏了求秘密密钥的信息，即已知该算法的公开密钥求秘密密钥，在计算上几乎是不可行的。通过理论分析和编程实现，证明该算法是正确可行的，其安全性高于同类算法。

关键词: Chebyshev多项式, ElGamal公钥密码系统, 半群特性

CLC Number:

TP301.6

ZHAO Geng; YAN Hui; TONG Zong-ke;. Public-key Cryptosystem Algorithm Based on Chebyshev Polynomial[J]. Computer Engineering, 2008, 34(24): 137-139.

赵耿;闫慧;童宗科;. 基于Chebyshev多项式的公钥密码系统算法[J]. 计算机工程, 2008, 34(24): 137-139.

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