亏格为2的超椭圆曲线上的二分算法及其优化  

A HALVING ALGORITHM FOR HYPERELLIPTIC CURVE OF GENUS TWO AND ITS OPTIMIZATION

作　　者：陈玉春[1] 朱艳琴[1] 刘月琴[1] 王振中[1] 

机构地区：[1]苏州大学计算机科学与技术学院,江苏苏州215006

出　　处：《计算机应用与软件》2008年第7期94-95,111,共3页Computer Applications and Software

基　　金：江苏省研究生创新计划项目(2005055)资助

摘　　要：相对于椭圆曲线密码体制而言,超椭圆曲线密码体制(HECC)具有许多优势,如更短的操作数,更小的带宽,在同等安全条件下所用的基域小,在同样的定义域上亏格越大、曲线越多,等等。HECC中最重要且最耗时的运算是标量乘,二分法是一种比常用的倍点法更为有效的算法。对二分法作了进一步的优化,通过选择合适的曲线参数,减少二分法中域操作运算量,降低其运算复杂度,从而有效地提高了实现效率。Compared with ECC, HECC has more advantages, such as shorter operand, smaller bandwidth, smaller field under the same secu- rity,larger genus and more curves on the same definition area. In hyperelliptic curve cryptosystem, the most important and costliest operation is the scalar multiplication, and the halving algorithm is more effective than the doubling algorithm. The halving algorithm is optimized. The ap- propriate curve parameters are selected, and the field operations are simplified. The operation complexity is reduced, and the efficiency of the algorithm is improved.

关 键 词：超椭圆曲线 亏格 二分算法 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构] TP303[自动化与计算机技术—计算机科学与技术]