F2上安全的Edwards曲线  

Secure Edwards Curves over F2

作　　者：李静[1] 彭国华[1] 

机构地区：[1]四川大学数学学院,四川成都610064

出　　处：《信息安全与通信保密》2009年第8期293-296,共4页Information Security and Communications Privacy

摘　　要：Edwards曲线提供了大量的可以抵挡旁道攻击的椭圆曲线，因此引起了人们特别的关注。最近Bernstein、Lange和Farashahi将一般的Edwards曲线推广到了特征为2的域上，并认为这类椭圆曲线必将会有广泛的应用。但是这类曲线的安全性却仍然是一个值得商榷的问题。文中通过双有理等价映射讨论了F2上的Edwards曲线与Koblitz曲线之间的关系，并由此推出这类Edwards曲线会在一些扩域上具有安全性。The invention of Edwards curves has attracted much attention from the cryptologists, because they provide a large amount of elliptic curves which are possible to resist the side-channel attack. Recently, Bemstein, Lange and Farashahi generalize Edwards curves to binary field and recommend their wide applications. However, the security of these curves is open to question. In this paper the relation between an ordinary Edwards curve over F2 and one kind of Koblitz curve is discussed, in virtue of the birationally equivalence map, and form this, it is deduced that this Edwards curve is secure in some extension fields.

关 键 词：椭圆曲线 二元椭圆曲线 KOBLITZ曲线 双有理等价 

分 类 号：O187.1[理学—数学]