公钥体系中Chebyshev多项式的改进

Improvement and Characteristic Research of Chebyshev Polynomials in PKI

加密算法是当今公钥体系的关键技术.本文在现有Chebyshev多项式基础上进行扩展,提出了有限域Chebyshev多项式的定义,并通过理论证明和编程实验分析总结出它的单向性和带陷门特性等.经过分析这些性质得出,针对实数域Chebyshev多项式提出的破解方法在有限域上不再成立或可以避免.最后指出有限域Chebyshev多项式作为公钥加密体系的基础是可行的.

Encryption algorithm is the key technology of public key infrastructure. By extending the existed Chebyshev Polynomials, this paper proposes the definition of finite fields Chebyshev Polynomials. By theoretical proving and experimental analyzing, some characteristics of it are introduced, such as one-way trapped characteristic. And then it is illustrated that the traditional attack methods are no longer held or could be avoided. Finally, it concludes that the finite fields Chebyshev polynomials used as the base of the public key system is feasible.