%0 Journal Article
%T Fast Multiplication on a Family of Koblitz Elliptic Curves<br>一类Koblitz椭圆曲线的快速点乘
%A HU Lei
%A FENG Deng-Guo
%A WEN Tie-Hua
%A <br>胡磊
%A 冯登国
%A 文铁华
%J 软件学报
%D 2003
%I 
%X Fast point multiplication on a family of Koblitz elliptic curves in characteristic 3 is considered. Such curves are suitable for establishing provable secure cryptographic schemes with low bandwidth. By utilizing the complex multiplication property of the curves and using a modulo reduction and Frobenius expansion technique, it is shown that there is a fast point multiplication method without precomputation on the curves, which is 6 times faster than the ordinary repeated-double-add method. The idea of the fast method is independent of the optimization of finite field arithmetic and the choice of coordinate expression for points of the elliptic curves.
%K elliptic curve
%K point multiplication
%K Frobenius expansion
%K modulo reduction
%K fast algorithm<br>椭圆曲线
%K 点乘
%K Frobenius展开式
%K 模约减
%K 快速算法
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=8240383F08CE46C8B05036380D75B607&jid=7735F413D429542E610B3D6AC0D5EC59&aid=FBD1C9980B82B9F8&yid=D43C4A19B2EE3C0A&vid=F3583C8E78166B9E&iid=708DD6B15D2464E8&sid=DA7B73AC3A57CF54&eid=B37991020B552F70&journal_id=1000-9825&journal_name=软件学报&referenced_num=7&reference_num=14