627 results
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The probability that a F_q-hypersurface is smooth
Speaker : 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[…] -
Introduction to Edwards curves
Speaker : 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[…] -
The elliptic-curve zoo
Speaker : 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[…] -
Binary Edwards curves
Speaker : 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[…] -
Treatment of the Initial Value in Time-Memory-Data Tradeoff Attacks on Stream Ciphers
Speaker : Orr Dunkelman - ENS-chaire France Telecom
Time-Memory Tradeoff (TMTO) attacks on stream ciphers are a serious security threat and the resistance to this class of attacks is an important criterion in the design of a modern stream cipher. TMTO attacks are especially effective against stream ciphers where a variant of the TMTO attack can make use of multiple data to reduce the off-line and the on-line time complexities of the attack (given a[…] -
Les suites elliptiques à divisibilité.
Speaker : Valery Mahé - University of East Anglia
Les suites elliptiques à divisibilité sont un analogue, dans le cadre de la théorie des courbes elliptiques, des suites de Lucas et de Mersenne. De part leurs liens étroits avec les polynômes de division, les suites elliptiques à divisibilité et leurs généralisations ont des applications en cryptographie : étude par Shipsey du probleme du logarithme discret, algorithme de Stange pour le calcul[…]