Division polynomials for twisted Edwards curves
Richard Moloney, Laura Hitt, Gary McGuire
TL;DR
This paper introduces division polynomials for twisted Edwards curves, which characterize their torsion points and may facilitate computational applications in elliptic curve cryptography.
Contribution
It provides the first explicit division polynomials for twisted Edwards curves and analyzes their coefficients for potential computational benefits.
Findings
Division polynomials characterize n-torsion points.
Coefficients of these polynomials have properties useful for computation.
The results may improve algorithms involving twisted Edwards curves.
Abstract
This paper presents division polynomials for twisted Edwards curves. Their chief property is that they characterise the -torsion points of a given twisted Edwards curve. We also present results concerning the coefficients of these polynomials, which may aid computation.
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Taxonomy
TopicsCryptography and Residue Arithmetic · Algebraic Geometry and Number Theory · Advanced Numerical Analysis Techniques