Public Key Cryptosystem for Conic Curve over Eisenstein Ring
Li Xu · Jisuanji gongcheng · 2009
In order to realize secure and effective curves cryptosystem over curves, this paper introduces Eisenstein ring Z [ω]. It discusses some basic properties of conic curve C r(a,b)over the residue class ring Z [ω]/(r). It is proved that the two kinds of addition algorithms respectively defined by mapping manner and coordinate manner are consistent with each other. A limited Abel group is composed by (C r(a,b),⊕). It validates that the algorihtm which is used for finding a base point over C n(a,b) is suitable for C r(a,b). Numerical simulation of ElGamal cryptosystem over C r(a,b)is given, and the results show that the improved conic curve cryptosystem has several merits such as being easy to embed plaintext, high computing speed and easy to be implemented.