Cryptology ePrint Archive: Report 2010/294

Computing genus 2 curves from invariants on the Hilbert moduli space

Kristin Lauter and Tonghai Yang

Abstract: We give a new method for generating genus 2 curves over a finite field with a given number of points on the Jacobian of the curve. We define two new invariants for genus 2 curves as values of modular functions on the Hilbert moduli space and show how to compute them. We relate them to the usual three Igusa invariants on the Siegel moduli space and give an algorithm to construct curves using these new invariants. Our approach simplifies the complex analytic method for computing genus 2 curves for cryptography and reduces the amount of computation required.

Category / Keywords: public-key cryptography / Hyperelliptic curve cryptography

Date: received 17 May 2010

Contact author: klauter at microsoft com

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Version: 20100518:040850 (All versions of this report)

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