Abelian groups, Gauss periods, and normal bases

DOI10.1006/FFTA.2000.0304zbMath0990.11077OpenAlexW1987107809MaRDI QIDQ5927544

Shuhong Gao

Publication date: 17 August 2002

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/5c6fac3ca18f3f960e7d4ad94d7a453fda70228d

zbMATH Keywords

finite fieldsabelian groupsGauss periodsnormal bases

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Polynomials over finite fields (11T06) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30)

Related Items (6)

Fast arithmetic with general Gauß periods ⋮ Low complexity of a class of normal bases over finite fields ⋮ A new criterion on normal bases of finite field extensions ⋮ On the complexity of the normal bases via prime Gauss period over finite fields ⋮ Normal bases and their dual-bases over finite fields ⋮ Normal bases on Galois ring extensions

Cites Work

• Low complexity normal bases
• Optimal normal bases in \(GF(p^ n)\)
• Optimal normal bases
• Algorithms for exponentiation in finite fields
• An implementation for a fast public-key cryptosystem
• Factoring with Cyclotomic Polynomials
• Normal bases via general Gauss periods
• Normal and Self-Dual Normal Bases from Factorization of $cx^{q + 1} + dx^q - ax - b$
• Gauss periods: orders and cryptographical applications
• On Orders of Optimal Normal Basis Generators
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