Jean-Marc Couveignes
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Jean-Marc Couveignes has a total of 4 co-authors. Here are the top co-authors by number of shared publications:
- Reynald Lercier
DGA & Univ Rennes, CNRS, IRMAR - UMR 6625, Rennes, France
3 shared publications - Tony Ezome
Université des Sciences et Techniques de Masuku
2 shared publications - Bas Edixhoven
Universiteit Leiden, Leiden, Netherlands
1 shared publication - Emmanuel Hallouin
Institut de Mathématiques de Toulouse UMR 5219
1 shared publication
Latest Publications
- Open Access
The geometry of some parameterizations and encodings
We explore parameterizations by radicals of low genera algebraic curves. We prove that for $q$ a prime power that is large enough and prime to $6$, a fixed positive proportion of all genus 2 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 $3$. We extend this construction to parameterizations by $\ell$-radicals for small odd integers $\ell$, and make it explicit for $\ell=5$.Open AccessThe geometry of some parameterizations and encodings
We explore parameterizations by radicals of low genera algebraic curves. We prove that for $q$ a prime power that is large enough and prime to $6$, a fixed positive proportion of all genus 2 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 $3$. We extend this construction to parameterizations by $\ell$-radicals for small odd integers $\ell$, and make it explicit for $\ell=5$. - Open Access
A faster pseudo-primality test
We propose a pseudo-primality test using cyclic extensions of $\mathbb Z/n \mathbb Z$. For every positive integer $k \leq \log n$, this test achieves the security of $k$ Miller-Rabin tests at the cost of $k^{1/2+o(1)}$ Miller-Rabin tests.Open AccessA faster pseudo-primality test
We propose a pseudo-primality test using cyclic extensions of $\mathbb Z/n \mathbb Z$. For every positive integer $k \leq \log n$, this test achieves the security of $k$ Miller-Rabin tests at the cost of $k^{1/2+o(1)}$ Miller-Rabin tests. - Open Access
Approximate computations with modular curves
This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations with modular curves and their Jacobians. These approximations are done in polynomial time in the dimension and the required number of significant digits. We explain the main ideas of how the approximations are done, illustrating them with examples, and we sketch some applications in number theory.
Open AccessApproximate computations with modular curves
This article gives an introduction for mathematicians interested in numerical computations in algebraic geometry and number theory to some recent progress in algorithmic number theory, emphasising the key role of approximate computations with modular curves and their Jacobians. These approximations are done in polynomial time in the dimension and the required number of significant digits. We explain the main ideas of how the approximations are done, illustrating them with examples, and we sketch some applications in number theory.
- 16 May 2012
- Published by Springer Nature in Rendiconti del Circolo Matematico di Palermo Series 2
- Vol. 61 (2) , 261-278
A faster pseudo-primality test
- 16 May 2012
- Published by Springer Nature in Rendiconti del Circolo Matematico di Palermo Series 2
- Vol. 61 (2) , 261-278
A faster pseudo-primality test
- 21 December 2011
- Published by Mathematical Sciences Publishers in Algebra & Number Theory
- Vol. 5 (4) , 431-463
Global descent obstructions for varieties
- 21 December 2011
- Published by Mathematical Sciences Publishers in Algebra & Number Theory
- Vol. 5 (4) , 431-463
Global descent obstructions for varieties