用分布式并行算法选取GF〔p〕上椭圆曲线的基点

Selection of Base Point of Elliptic Curve over GF(P) Using Distributed Parallel Arithmetic

椭圆曲线密码体制 (ECC)的研究与实现已逐渐成为公密码体制研究的主流 ,适用于密码的安全椭圆曲线及其基点的选取 ,是椭圆曲线密码实现的基础 ,而高效性是椭圆曲线密码系统得以广泛应用的重要因素。该文首先介绍有限域上定义的椭圆曲线及点群运算规则 ,给出椭圆曲线点群的阶。其次 ,就大素数域上安全椭圆曲线的基点的选取算法作了讨论 ,采用分布式并行算法 ,进一步改进优化 ,并借助于MIRACL系统利用标准C语言对它们成功实现 .实际测试结果表明 ,该工作确实加快了安全椭圆曲线基点的选取。

The study and realization of elliptic curve cryptography have become the mainstream of the study on public cryptography ,and the selection of secure elliptic curves in cipher and their base points is the basis of implementing the elliptic curve cryptography.But high efficiency is the important factor to make the elliptic curve cryptosystem widely used. This paper ,firstly introduces the elliptic curve in finite field and algebraic law of its point group,gives the order of the group.Secondly the selection algorithm of the base point about secure elliptic curves over large prime number is discussed, and optimized resorting to distributed parallel algorithm,futher more the algorithm is implemented successfully in C language using the MIRACL system.The actual test results indicate that our work really enhances the selection efficiency of the base point about secure elliptic curves.