The trace of an optimal normal element and low complexity normal bases

DOI10.1007/s10623-008-9195-5zbMath1196.12001OpenAlexW2076436757MaRDI QIDQ1009092

Maria Christopoulou, Theo Garefalakis, Daniel Panario, David Thomson

Publication date: 31 March 2009

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-008-9195-5

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Finite fields (field-theoretic aspects) (12E20)

Related Items (11)

A class of Gaussian normal bases and their dual bases ⋮ On the bound of the complexity of the normal basis generated by the trace of the dual element of a Type I optimal normal element ⋮ Normal bases from 1-dimensional algebraic groups ⋮ Low complexity of a class of normal bases over finite fields ⋮ The Gaussian normal basis and its trace basis over finite fields ⋮ Gauss periods as constructions of low complexity normal bases ⋮ On the complexity of the normal bases via prime Gauss period over finite fields ⋮ Elliptic periods for finite fields ⋮ AFFINE TRANSFORMATION OF A NORMAL ELEMENT AND ITS APPLICATION ⋮ Construction of self-dual normal bases and their complexity ⋮ Complexities of self-dual normal bases

Cites Work

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• Low complexity normal bases
• On the complexity of the dual basis of a type I optimal normal basis
• Optimal normal bases in \(GF(p^ n)\)
• Optimal normal bases
• On Artin's conjecture and Euclid's algorithm in global fields
• On primes in arithmetic progression having a prescribed primitive root
• Low complexity normal bases in \(\mathbb F_{2^n}\)
• Normal and Self-Dual Normal Bases from Factorization of $cx^{q + 1} + dx^q - ax - b$

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