Elliptic curves in
connection with applications to cryptology
(Un exposé de R. Balasubramanian au séminaire de théorie
des nombres de Jussieu le 11 octobre 1999)
Résumé :
With the advent of Public system Cryptography,
the algorithms for primality testing and factorisation have become popular.
The classical algorithms depend on the multiplicative group
mod p and as such on the number theoretic properties of p-1. However the
algorithms based on elliptic curves depend upon the group E over the finite
field with p elements and thus on the number theoretic properties of
p+1-a .This allows for a substantial improvement over the classical
methods for primality testing and factorisation.