# The geometry of some parameterizations and encodings

* Corresponding author
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We report on current work on parameterization of low genera algebraic curves. For example, we prove that for $q$ a prime power that is large enough and prime to 6, a fixed positive proportion of all genus two curves over the field with $q$ elements can be parameterized by 3-radicals. This results in the existence of a deterministic encoding into these curves when $q$ is congruent to 2 modulo 3. Abstract of a talk given at GEOCRYPT 2013, Papeete.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-00870112
Contributor : Jean-Marc Couveignes <>
Submitted on : Saturday, October 5, 2013 - 10:16:39 AM
Last modification on : Monday, July 8, 2019 - 4:56:07 PM

### Citation

Jean-Marc Couveignes, Reynald Lercier. The geometry of some parameterizations and encodings. Advances in Mathematics of Communications, AIMS, 2014, 8 (4), pp.22. ⟨10.3934/amc.2014.8.437⟩. ⟨hal-00870112⟩

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