基于有限域GF上圆锥曲线的公钥密码算法

圆锥曲线密码学是一种新型的公钥密码学,迄今对圆锥曲线密码学的研究成果都是以有限域GF(p)上的圆锥曲线为基础的.本文将有限域GF(p)上的圆锥曲线C(GF(p))推广为有限域GF(2ⁿ)上的圆锥曲线C(GF(2ⁿ)),证明了圆锥曲线C(GF(2ⁿ))上的点和加法运算构成有限交换群(C(GF(2ⁿ)),),并给出了圆锥曲线群(C(GF(2ⁿ)),)的阶的计算.此外,提出了使用有限域GF(2ⁿ)上的圆锥曲线群构造公钥密码系统,并给出了ElGamal加密方案和数字签名算法(DSA)在圆锥曲线C(GF(2ⁿ))上模拟的算法,最后分析其安全性.

A Public-Key Cryptosystem Based on Conic Curve in Finite Field GF(2n)

Conic curve cryptosystem was first introduced by CAO Zhenfu in 1998.By now,the previous study on conic curve cryptosystem has been based on conic curve group in finite field GF(p).Since the hardware circuits are suitable for performing addition,multiplication,squaring and the inversion operations in a finite field GF(2~n),the operations in finite field GF(2~n) are typically easier to implement in hardware and software than their counterpart in finite field GF(p).In order to speed up the computation of conic curve cryptosystem,the conic curve group is extended from finite field GF(p) to finite field GF(2~n),and the order of the conic curve group in finite field GF(2~n) is given.In addition,this paper suggests to use conic curve group in finite field GF(2~n) for realizing public-key cryptosystem,and presents the basic ElGamal public-key encryption scheme and the Digital Signature Algorithm(DSA) based on conic curve in finite field GF(2~n).Security of public-key cryptosystem based on conic curve in finite field GF(2~n) is analyzed.