## Construction of secure random curves of genus 2 over prime fields (2004)

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Venue: | Advances in Cryptology – EUROCRYPT 2004, volume 3027 of Lecture Notes in Comput. Sci |

Citations: | 37 - 12 self |

### BibTeX

@INPROCEEDINGS{Gaudry04constructionof,

author = {Pierrick Gaudry and Éric Schost},

title = {Construction of secure random curves of genus 2 over prime fields},

booktitle = {Advances in Cryptology – EUROCRYPT 2004, volume 3027 of Lecture Notes in Comput. Sci},

year = {2004},

pages = {239--256},

publisher = {Springer-Verlag}

}

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### Abstract

Abstract. For counting points of Jacobians of genus 2 curves defined over large prime fields, the best known method is a variant of Schoof’s algorithm. We present several improvements on the algorithms described by Gaudry and Harley in 2000. In particular we rebuild the symmetry that had been broken by the use of Cantor’s division polynomials and design a faster division by 2 and a division by 3. Combined with the algorithm by Matsuo, Chao and Tsujii, our implementation can count the points on a Jacobian of size 164 bits within about one week on a PC. 1