ELEMENTS OF HIGH ORDER ON FINITE FIELDS FROM ELLIPTIC CURVES
2010 ◽
Vol 81
(3)
◽
pp. 425-429
◽
Keyword(s):
AbstractWe discuss the problem of constructing elements of multiplicative high order in finite fields of large degree over their prime field. We obtain such elements by evaluating rational functions on elliptic curves, at points whose order is small with respect to their degree. We discuss several special cases, including an old construction of Wiedemann, giving the first nontrivial estimate for the order of the elements in this construction.
2007 ◽
Vol 75
(1)
◽
pp. 135-149
◽
Keyword(s):
2006 ◽
Vol 73
(2)
◽
pp. 245-254
◽
Keyword(s):