基于有限域上圆锥曲线的公钥密码系统

随着Internet的迅猛发展，公钥密码系统以其算法简单、安全性高已经成为密码学领域的一个非常重要的研究课题。为了更加方便地构建公钥密码系统，文中在介绍了有限域上的圆锥曲线C(Fp)及其离散对数问题、明文嵌入与译码算法的基础上，给出了公钥密码系统在圆锥曲线C(Fp)上的模拟，这里p是奇素数，Fp为p元有限域。这些圆锥曲线密码系统的安全性是基于C(Fp)上离散对数的计算，较椭圆曲线密码系统更易于设计与实现。

A Public Key Cryptosystem Based on a Conic Curve over Finite Fields

With the rapid development of Internet,public key cryptosystem has become a very important research topic in cryptography field for its simple algorithm and high security.To build public key cryptosystem more conveniently,on the basis of the introduction of the conic curve over a finite field C(F_p) and the discrete logarithm problem,plaintext embedding and decoding algorithm,the paper presents a conic curve analog of public key cryptosystem inC(F_p),here p is an odd prime and F_p a finite field of p elements.The security of these conic curve cryptosystem based on the discrete logarithm problem on conic curve over C(F_p) and it is much easier to design and realize than elliptic curve cryptosystem.