Concept

Accouplement de Weil

Publications associées (7)

Isogeny graphs of ordinary abelian varieties

Dimitar Petkov Jetchev, Benjamin Pierre Charles Wesolowski, Ernest Hunter Brooks

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse gr ...

Springer Heidelberg2017

Prym varieties of spectral covers

Tamás Hausel

Given a possibly reducible and non-reduced spectral cover pi: X -> C over a smooth projective complex curve C we determine the group of connected components of the Prym variety Prym(X/C). As an immediate application we show that the finite group of n-torsi ...

Geometry & Topology Publications2012

Signatures for Multisource Network Coding

László Czap

We consider the problem of securing inter-ﬂow network coding with multiple sources. We present a practical homomorphic signature scheme that makes possible to verify network coded packets composed of data originating from diﬀerent sources. The multi-source ...

ArXiv2010

Categorical Foundations for K-theory

Nicolas Mathieu Michel

K-Theory was originally defined by Grothendieck as a contravariant functor from a subcategory of schemes to abelian groups, known today as K0. The same kind of construction was then applied to other fields of mathematics, like spaces and (not necessarily c ...

EPFL2010

Ate Pairing on Hyperelliptic Curves

Robert Granger

In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller’s algorithm can be up t ...

Springer-Verlag Berlin Heidelberg2007

High Security Pairing-Based Cryptography Revisited

Robert Granger

The security and performance of pairing based cryptography has provoked a large volume of research, in part because of the exciting new cryptographic schemes that it underpins. We re-examine how one should implement pairings over ordinary elliptic curves f ...

Springer Berlin Heidelberg2006

On Small Characteristic Algebraic Tori in Pairing-Based Cryptography

Robert Granger, Martijn Stam

The value of the Tate pairing on an elliptic curve over a finite field may be viewed as an element of an algebraic torus. Using this simple observation, we transfer techniques recently developed for torus-based cryptography to pairing-based cryptography, r ...

2006

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