Generating pairing-friendly parameters for the CM construction of genus 2 curves over prime fields

• Published in: Designs, codes, and cryptography Vol. 67; no. 3; pp. 341 - 355
• Main Authors: Lauter, Kristin, Shang, Ning
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.06.2013; Springer
• Subjects: Algebra; Algebraic geometry; Applied sciences; Circuits; Coding and Information Theory; Computer Science; Cryptography; Cryptology; Data Structures and Information Theory; Discrete Mathematics in Computer Science; Exact sciences and technology; Field theory and polynomials; Information and Communication; Information, signal and communications theory; Mathematics; Number theory; Sciences and techniques of general use; Signal and communications theory; Telecommunications and information theory; Pairing-friendly parameters; 11T71; Public-key cryptography; Hyperelliptic curve cryptography; 14H45; Finite field; Elliptic curve; Bilinear form; Modeling; Pairing-based cryptography; Efficiency; Public key; Classification; Hyperelliptic curve; Algebraic curve; Quantitative analysis
• ISSN: 0925-1022; 1573-7586
• DOI: 10.1007/s10623-012-9611-8

We present two contributions in this paper. First, we give a quantitative analysis of the scarcity of pairing-friendly genus 2 curves. This result is an improvement relative to prior work which estimated the density of pairing-friendly genus 2 curves heuristically. Second, we present a method for generating pairing-friendly parameters for which , where ρ is a measure of efficiency in pairing-based cryptography. This method works by solving a system of equations given in terms of coefficients of the Frobenius element. The algorithm is easy to understand and implement.