Paper 2012/443

Improved CRT Algorithm for Class Polynomials in Genus 2

Kristin Lauter and Damien Robert


We present a generalization to genus~2 of the probabilistic algorithm of Sutherland for computing Hilbert class polynomials. The improvement over the Bröker-Gruenewald-Lauter algorithm for the genus~2 case is that we do not need to find a curve in the isogeny class whose endomorphism ring is the maximal order; rather, we present a probabilistic algorithm for ``going up'' to a maximal curve (a curve with maximal endomorphism ring), once we find any curve in the right isogeny class. Then we use the structure of the Shimura class group and the computation of $(\ell,\ell)$-isogenies to compute all isogenous maximal curves from an initial one. This is an extended version of the article published at ANTS~X.

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Published elsewhere. Published at ANTS X
Class polynomialsgenus 2CRT
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damien robert @ inria fr
2013-05-07: last of 3 revisions
2012-08-06: received
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      author = {Kristin Lauter and Damien Robert},
      title = {Improved CRT Algorithm for Class Polynomials in Genus 2},
      howpublished = {Cryptology ePrint Archive, Paper 2012/443},
      year = {2012},
      note = {\url{}},
      url = {}
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