ON ORDERS OF OPTIMAL NORMAL BASIS GENERATORS

被引:39
作者
GAO, SH [1 ]
VANSTONE, SA [1 ]
机构
[1] UNIV WATERLOO,DEPT COMBINATOR & OPTIMIZAT,WATERLOO,ON N2L 3G1,CANADA
关键词
FINITE FIELDS; PRIMITIVE ELEMENTS; NORMAL BASES;
D O I
10.2307/2153492
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we give some experimental results on the multiplicative orders of optimal normal basis generators in F(2)n over F-2 for n less than or equal to 1200 whenever the complete factorization of 2(n) - 1 is known. Our results show that a subclass of optimal normal basis generators always have high multiplicative orders, at least O((2(n) - 1)/n), and are very often primitive. For a given optimal normal basis generator alpha in F(2)n and an arbitrary integer e, we show that alpha(e) can be computed in O(n . v(e)) bit operations, where v(e) is the number of 1's in the binary representation of e.
引用
收藏
页码:1227 / 1233
页数:7
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