I‑AIMS Institute for Artificial Intelligence
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The case for superelliptic curves

Lubjana Beshaj, Tanush Shaska, Eustrat Zhupa

I-AIMS paper 2015-1 · Published in NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur. 41 (2015), 1–14 · 2015

There is a natural question to ask whether the rich mathematical theory of the hyperelliptic curves can be extended to all superelliptic curves. Moreover, one wonders if all of the applications of hyperelliptic curves such as cryptography, mathematical physics, quantum computation, diophantine geometry, etc. can carry over to the superelliptic curves. In this short paper we make the case that the superelliptic curves are exactly the curves that one should study.

MSC classes: Primary 11G05; Secondary 14H45, 14H30, 14G50

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References

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