基于Chebyshev多项式的公钥密码系统算法

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。

Public-key Cryptosystem Algorithm Based on Chebyshev Polynomial

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.