Quelques mathématiques de la cryptographie à clés publiques
I present examples of mathematical objects that are of interest for public key cryptography. Text for the Journée Annuelle 2007 of the SMF.
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arXiv subjects
Jean-Marc Couveignes
Publications and source records attributed to Jean-Marc Couveignes.
Bases invariantes de friabilité
Given a finite residue field $k$, one looks for a smoothness basis that is invariant under the automorphism group of $k$. We construct models for some finite fields that admit such a basis. This work aims at accelerating algorithms for computing discrete logarithms in some finite residue fields.
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Jacobiens, jacobiennes et stabilité numérique
This paper is concerned with the complexity and stability of arithmetic operations in the jacobian variety of curves over the field of complex numbers, as the genus grows to infinity. We focus on modular curves. Efficient and stable computation in the jacobian of modular curves is useful for computing coefficients of modular forms in deterministic polynomial time. This work is part of my contribution to Edixhoven's program for solving this problem.
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