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arXiv · 2510.27375

Elliptic butterflies

Jean-Marc Couveignes·Reynald Lercier
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Abstract

We study natural evaluation and interpolation problems for elliptic functions and prove that they allow a recursive treatment using a variant of classical butterflies first introduced by Gauss. We deduce the existence of straight-line programs with complexity scaling with $d\log(d)$ for these problems and present applications to finite field arithmetic, coding theory and cryptography.

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Jean-Marc Couveignes, Reynald Lercier. 2025-10-31. Elliptic butterflies. https://arxiv.org/abs/2510.27375

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