The three low complexity bases and their dual bases
Suppose that N={α0,α1,···,αn-1} is a basis of E over F,some low complexity normal ba-ses with complexity 3n-2 was constructed and multiplication table was given.According to the relat-ed concepts of the trace function and multiplication table,it proved that the form of the generator of their dual basis and their dual bases has complexity 3n-2 or 3n-3.Furthermore,it calculated the complexity of the pseudo-self-dual polynomial bases and the weak self-dual polynomial bases of E o-ver F.This provides a theoretical basis for finding optimized algorithms and selecting appropriate ba-ses in the field of cryptography.
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