【作者】 郝舒欣；

【导师】 赵耿；

【作者基本信息】 西安电子科技大学 ， 密码学， 2011， 硕士

【摘要】 混沌系统因其对初值的敏感性和良好的伪随机性,在密码学方面有着巨大的应用价值。近年来,对混沌系统的研究逐渐成为热点。但是大量的研究成果局限于混沌对称加密范畴,利用混沌来构造公钥密码系统的研究还比较少。目前最具代表性的基于混沌的公钥密码算法是由L.Kocarev提出的基于Chebyshev多项式的公钥密码算法。这种公钥算法思想的提出带动了整个混沌领域对公钥密码体系包括加密算法、数字签名、密钥协商、身份认证等方面的研究热潮。但是该项研究仍然处于初级阶段,存在很多不完善的地方。因此本文针对基于Chebyshev多项式的公钥密码体系的研究是有意义的。在通信技术飞速发展、电子商务日渐广泛应用的今天,身份认证已成为网络中信息安全最重要的一道防线。本文选取了基于有限域的Chebyshev多项式作为研究对象,其所具有的良好的混沌特性、半群特性和单向性可以很好的应用到公钥加密算法、密钥协商及身份认证中去。本文在深入研究基于有限域Chebyshev多项式的类ElGamal算法的基础上,将Chebyshev多项式与身份认证相结合,分析目前已提出的基于Chebyshev多项式的身份认证方案所存在的安全漏洞,并提出新的方案。通过安全性分析和编程实现,证明新方案是安全可行的。更多还原

【Abstract】 Chaotic system has great application value in cryptography because of its sensitive dependence on initial conditions and pseudo-randomness. In recent years, a lot of chaotic cryptosystems have been proposed; however, most of them focus on encryption algorithm of secret key cryptography. Compared with chaotic secret key cryptography, there is much less research on public-key cryptography based on chaos. The most representative public-key cryptography based on chaos is public-key cryptography algorithms based on Chebyshev polynomials, which is proposed by L.Kocarev. The idea lead to the development of public-key cryptosystems based on chaos, which includes encryption algorithms, digital signatures, key agreement, identity authentication and other aspects. But the research is still elementary, many problems still exist. So, research of public-key cryptosystem based on Chebyshev polynomials is meaningful.With the development of communication technology and the widely use of ecommerce, identity authentication has become the most important line of defense in information security of network. Chebyshev polynomials based on finite fields can be used in public-key encryption algorithms, key agreement and identity authentication for its good semi-group property and one-way trapped characteristic. In this paper, an ElGamal-like algorithm using Chebyshev polynomials based on finite fields is deeply researched and the security of the proposed identity authentication scheme based on chebyshev polynomials is also analyzed. According to the above research, the new identity authentication schemes based on chebyshev polynomials are proposed. The program results of the new identity authentication schemes analysis prove the schemes are secure and practical.更多还原