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Gauss sums of the cubic character over {${\rm GF}(2^m)$}}: an elementary derivation

Type of publication Peer-reviewed
Publikationsform Original article (peer-reviewed)
Author Schipani D., Elia M.,
Project New Cryprosystems based on Algebra
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Original article (peer-reviewed)

Journal Bull. Pol. Acad. Sci. Math.
Volume (Issue) 59(1)
Page(s) 11 - 18
Title of proceedings Bull. Pol. Acad. Sci. Math.
DOI 10.4064/ba59-1-2

Abstract

An elementary approach is shown which derives the value of the Gauss sum of a cubic character over a finite field $\mathbb F_{2^s}$ without using Davenport-Hasse's theorem (namely, if $s$ is odd the Gauss sum is -1, and if $s$ is even its value is $-(-2)^{s/2}$).
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