Heuristics of the Cocks-Pinch method
Min Sha
TL;DR
This paper heuristically analyzes the Cocks-Pinch method using the Bateman-Horn conjecture, suggesting it can efficiently generate pairing-friendly elliptic curves, supported by numerical evidence.
Contribution
It presents the first heuristic indicating that any efficient pairing-friendly elliptic curve construction can generate such curves over pairing-friendly fields, including Cocks-Pinch.
Findings
Heuristic analysis using Bateman-Horn conjecture.
Cocks-Pinch method can efficiently generate pairing-friendly curves.
Numerical evidence supporting the heuristic.
Abstract
We heuristically analyze the Cocks-Pinch method by using the Bateman-Horn conjecture. Especially, we present the first known heuristic which suggests that any efficient construction of pairing-friendly elliptic curves can efficiently generate such curves over pairing-friendly fields, naturally including the Cocks-Pinch method. Finally, some numerical evidence is given.
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Taxonomy
TopicsCryptography and Residue Arithmetic · Polynomial and algebraic computation · Algebraic Geometry and Number Theory