Orders of Gauss periods in finite fields

DOI10.1007/s002000050093zbMath0931.11057OpenAlexW2914712547WikidataQ56144517 ScholiaQ56144517MaRDI QIDQ1389144

Joachim von zur Gathen, Igor E. Shparlinski

Publication date: 12 August 1998

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002000050093

zbMATH Keywords

algorithmsfinite fieldsnormal basesArtin's conjectureprimitive roots in finite fields

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30)

Related Items (17)

SUM–PRODUCT ESTIMATES AND MULTIPLICATIVE ORDERS OFγANDγ+γ⁻¹IN FINITE FIELDS ⋮ Sparse polynomials, redundant bases, Gauss periods, and efficient exponentiation of primitive elements for small characteristic finite fields ⋮ Generating sets for the multiplicative groups of algebras over finite fields and expander graphs ⋮ LOWER BOUNDS FOR PERIODS OF DUCCI SEQUENCES ⋮ Gauss periods as constructions of low complexity normal bases ⋮ Gauss periods: orders and cryptographical applications ⋮ Elements of high order in Artin-Schreier extensions of finite fields \(\mathbb{F}_q\) ⋮ MULTIPLICATIVE ORDER OF GAUSS PERIODS ⋮ Sharpening of the explicit lower bounds for the order of elements in finite field extensions based on cyclotomic polynomials ⋮ On the multiplicative orders of \(\gamma\) and \(\gamma+\gamma^{-1}\) over finite fields ⋮ Multiplicative orders of Gauss periods and the arithmetic of real quadratic fields ⋮ Finite field elements of high order arising from modular curves ⋮ Unnamed Item ⋮ On the construction of finite field elements of large order ⋮ Efficient polynomial time algorithms computing industrial-strength primitive roots ⋮ Algorithms for exponentiation in finite fields ⋮ Unnamed Item

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