SATOH算法及快速实现技术研究

Study on SATOH Algorithm and Its Fast Implementation

随着椭圆曲线公钥密码的广泛应用,怎样生成安全的椭圆曲线是椭圆曲线密码的研究重点,而怎样快速计算椭圆曲线的阶(有理点的个数)是椭圆曲线密码的关键,安全的椭圆曲线密码参数是椭圆曲线密码本身安全的基础,否则会遭受基于Pollard-ρ攻击,反常曲线等安全隐患。公开的文献上主要介绍了SATOH算法的原理,对具体的实现和算法的提升没有做详细的介绍,这里详细介绍了SATOH算法的原理和快速实现方法。

With the extensive use of ECC,how to generate secure eciptlic curve is very important to ECC research. While how to fast compute the order（number of rational point） is the key to ECC. The secure ECC parameter is the foundation of ECC, or otherwise it would suffer Pollard-ρ attack,abnormal curve attack and so on. Public papers mainly describe the theory of SATOH algorithm,but give no detailed introduction of its implementation and fast computation. This paper treats of in detail the theory and implementation of SATOH algorithm.