The geometry of some parameterizations and encodings | Zendy

Reynald Lercier | Zendy; Jean-Marc Couveignes | Zendy

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The geometry of some parameterizations and encodings

Author(s) -

Reynald Lercier,

Jean-Marc Couveignes

Publication year - 2014

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2014.8.437

Subject(s) - mathematics , modulo , prime (order theory) , parameterized complexity , genus , algebraic curve , finite field , prime power , algebraic number , pure mathematics , combinatorics , discrete mathematics , mathematical analysis , botany , biology

International audienceWe 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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