A CRT algorithm for constructing genus 2 curves over finite fields

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We present a new method for constructing genus 2 curves over a finite field with a given number of points on its Jacobian. This method has important applications in cryptography, where groups of prime order are used as the basis for discrete-log based cryptosystems. Our algorithm provides an alternative to the traditional CM method for constructing genus 2 curves. For a quartic CM field K with primitive CM type, we compute the Igusa class polynomials modulo p for certain small primes p and then use the Chinese remainder theorem (CRT) and a bound on the denominators to construct the class polynomials. We also provide an algorithm for determining endomorphism rings of ordinary Jacobians of genus 2 curves over finite fields, generalizing the work of Kohel for elliptic curves.
16 pages. to appear in Proceedings of AGCT-10

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Number Theory, Algebraic Geometry, 11G15; 11G10; 11R37; 14G50

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http://salesiana.dossiersoluciones.com/handle/123456789/121528

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0405305
 http://arxiv.org/abs/math/0405305

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arXiv