%0 Journal Article
%T Fast Arithmetic in Generalized Optimal Extension Fields<br>广义最优扩域上的快速运算
%A Wang Qing-xian
%A Sun Shi-xin
%A <br>王庆先
%A 孙世新
%J 电子与信息学报
%D 2006
%I 
%X In Elliptic Curves Cryptosystems (ECC), the optimal extension fields is preferable to others method, whether concerns performance or memory request. But, it is very difficult to choose pseudo-Mersenne prime numbers, and satisfy the condition that p just is presented by a register of processor. This paper replaces pseudo-Mersenne numbers by generalized Mersenne numbers, provides a new notation-Generalized Optimal Extension Fields(GOEFs), and studies the fast arithmetic about multiplication and modular reduction in GOEFs, finally, deduces common formulas for multiplication and some more general formulas for modular reduction in GOEFs. The results in this paper extend the corresponding work on arithmetic of Bailey, Mihailescu, and Woodbury in OEFs.
%K Private communication
%K Elliptic curves cryptosystems
%K Generalized optimal extension fields
%K Multiplication
%K Modular reduction<br>保密通信
%K 椭圆曲线密码体制
%K 广义最优扩域
%K 乘法运算
%K 模约简运算
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=1319827C0C74AAE8D654BEA21B7F54D3&jid=EFC0377B03BD8D0EF4BBB548AC5F739A&aid=8ECCEF904175CF5B&yid=37904DC365DD7266&vid=D3E34374A0D77D7F&iid=38B194292C032A66&sid=B79ACB6EBBFC9730&eid=DA74B62FE4348759&journal_id=1009-5896&journal_name=电子与信息学报&referenced_num=0&reference_num=9