We study the complexity (that is, the weight of the multiplication table) of the elliptic normal bases introduced by Couveignes and Lercier. We give an upper bound on the complexity of these elliptic normal bases, and we analyze the weight of some special vectors related to the multiplication table of those bases. This analysis leads us to some perspectives on the search for low complexity normal bases from elliptic periods.

翻译：我们研究了由Couveignes和Lercier引入的椭圆正规基的复杂性（即乘法表的权重）。我们给出了这些椭圆正规基复杂性的上界，并分析了与该基乘法表相关的若干特殊向量的权重。这一分析为我们从椭圆周期中寻找低复杂性正规基提供了若干展望。