599 résultats
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Courbes elliptiques et applications cryptographiques à la diffusion numérique sécurisée
Orateur : Thomas Sirvent - IRMAR
L'objet de cette thèse est la diffusion numérique sécurisée réalisée à l'aide de courbes elliptiques. Elle se compose de quatre chapitres :<br/> Le premier chapitre est consacré au calcul de points de l-torsion sur une courbe elliptique définie sur un corps fini de caractéristique p. Plus précisément, nous combinons un algorithme rapide de calcul d'isogénies dû à Bostan,[…] -
Stream Ciphers - Now and Then
Orateur : Emilia Kasper - Katholieke Universiteit Leuven
In November 2004, the European Network of Excellence for Cryptology (ECRYPT) launched a call for new stream cipher primitives. Authors from academia as well as industry submitted 34 designs, and in May 2008, 8 ciphers were chosen for the eSTREAM final portfolio. In this talk, we look back at the history of stream ciphers to understand the design choices made by cryptographers today. We start by[…] -
The probability that a F_q-hypersurface is smooth
Orateur : Jeroen Demeyer - Universiteit Gent
Consider the projective space P^n over a finite field F_q. A hypersurface is defined by one homogenous equation with coefficients in F_q. For d going to infinity, we show that the probability that a hypersurface of degree d is nonsingular approaches 1/\zeta_{P^n (n+1)}. This is analogous to the well-known fact that the probability that an integer is squarefree equals 1/\zeta(2) = 6/\pi^2. This[…] -
Binary Edwards curves
Orateur : Tanja Lange - Technische Universiteit Eindhoven
The curve shape suggested by Edwards does not define elliptic curves over fields of characteristic 2. We recently generalized the concept of Edwards curves and defined binary Edwards curves. These curves offer complete addition formulas and are the first binary curves with this property. Doubling and differential addition (addition of two points with known difference, like in the Montgomery[…] -
The elliptic-curve zoo
Orateur : Dan Bernstein - Technische Universiteit Eindhoven
The pursuit of speed in elliptic-curve factoring and in elliptic-curve cryptography has led researchers to consider a remarkable variety of curve shapes and point representations. Tanja Lange and I have built an Explicit-Formulas Database, http://hyperelliptic.org/EFD, collecting (and sometimes correcting and often improving) the addition formulas in the literature; EFD now contains 296 computer[…] -
Introduction to Edwards curves
Orateur : Christiane Peters - Technische Universiteit Eindhoven
We present elliptic curves in Edwards form. Using this curve shape we benefit from very fast arithmetic. We will show the affine addition formulas as well as the fast projective formulas. A further speed-up is gained from using inverted coordinates. We will compare these to other coordinate systems which are derived from the Weierstrass normal form. In particular, we will show how Edwards curves[…]