Elliptic butterflies
Jean-Marc Couveignes, Reynald Lercier

TL;DR
This paper explores recursive algorithms for elliptic functions, enabling efficient evaluation and interpolation with applications in finite fields, coding, and cryptography.
Contribution
It introduces a recursive approach based on elliptic butterflies, extending classical methods to elliptic functions with complexity scaling as d log d.
Findings
Existence of straight-line programs with complexity d log d
Applications to finite field arithmetic, coding theory, cryptography
Extension of classical butterfly algorithms to elliptic functions
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 for these problems and present applications to finite field arithmetic, coding theory and cryptography.
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Taxonomy
TopicsPolynomial and algebraic computation · Cryptography and Residue Arithmetic · Complexity and Algorithms in Graphs
