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The geometry of some parameterizations and encodings

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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https://hal.archives-ouvertes.fr/hal-00870112
Contributor : Jean-Marc Couveignes Connect in order to contact the contributor
Submitted on : Tuesday, February 16, 2021 - 10:15:23 AM
Last modification on : Wednesday, January 26, 2022 - 5:42:06 PM
Long-term archiving on: : Monday, May 17, 2021 - 6:37:31 PM

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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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