一种新的基于Chebyshev多项式的公钥加密系统(英文)  

A NOVEL PUBLIC KEY CRYPTOGRAPHY USING CHEBYSHEV POLYNOMIALS

作　　者：徐邦海[1] 蒋礼[2] 徐群叁[3] 

机构地区：[1]西北工业大学计算机学院,陕西西安710072 [2]西安财经学院计算机系,陕西西安710061 [3]鲁东大学计算机学院,山东烟台264025

出　　处：《陕西科技大学学报（自然科学版）》2005年第6期48-51,共4页Journal of Shaanxi University of Science & Technology

基　　金：国家863项目(No.2003AA142060);陕西省自然科学基金项目(No.2004A06)

摘　　要：基于Chebyshev多项式和离散对数问题设计了一种新的安全有效的公钥加密系统方案。该方案回避了现有大多数基于混沌的加密系统的实数域问题,即在实数域不存在难解的数学问题,而利用Chebyshev多项式的本群属性,在有限域上实现加密、解密和数字签名操作,而且本方案选择的变量是超过1的正整数,这就避免了不同Chebyshev多项式在|x|≤1区间通过同一点问题。通过深入的性能分析,可以证明本方案在安全性和效率方面都优于ElGamal加密方案。For enjoying some nice chaotic properties and a semi-group property, Chebyshev polynomials have been recently proposed for designing cryptosystem. In this paper, a novel secure and efficient public key cryptosystem based on Chebyshev polynomials and the discrete log problem is presented. Compared with other schemes at present, the improvement of our scheme lies in two aspects： firstly, our scheme does not involve the chaotic properties and only choose the semi-group property since the chaosbased cryptosystems are defined over real number fields which have no intractable problem as number theoretic problems over finite fields. Secondly, the variables in our scheme are picked as positive integers beyond 1 to avoid the insecure situation that different Chebyshev polynomials may pass through a same point when ｜ x ｜≤ 1 . After an in-depth performance analysis, we prove that our scheme excels ElGamal encryption scheme both in security and efficiency.

关 键 词：CHEBYSHEV多项式 公钥加密系统 本群属性 

分 类 号：TN918.1[电子电信—通信与信息系统]