Cryptology ePrint Archive: Report 2010/344

Generating more Kawazoe-Takahashi Genus 2 Pairing-friendly Hyperelliptic Curves.

Ezekiel J Kachisa

Abstract: Constructing pairing-friendly hyperelliptic curves with small $\rho$-values is one of challenges for practicability of pairing-friendly hyperelliptic curves. In this paper, we describe a method that extends the Kawazoe-Takahashi method of generating families of genus $2$ ordinary pairing-friendly hyperelliptic curves by parameterizing the parameters as polynomials. With this approach we construct genus $2$ ordinary pairing-friendly hyperelliptic curves with $2 <\rho \le 3$.

Category / Keywords: pairing-friendly curves, hyperelliptic curves, pairings

Date: received 15 Jun 2010, last revised 3 Oct 2010

Contact author: ezekiel at live ie

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Version: 20101003:103230 (All versions of this report)

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