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

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

 Journal Bull. Pol. Acad. Sci. Math. 59(1) 11 - 18 Bull. Pol. Acad. Sci. Math. 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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