Description
I will describe an algorithm for computing the zeta function of an arbitrary hyperelliptic curve in characteristic 2. This is a generalisation of an earlier method of myself and Wan, which tackled a restricted class of curves. The algorithm reduces the problem to that of computing the L-function of an additive character sum over an open subset of the projective line. This latter task can be achieved using the Dwork-Reich trace formula, Dwork's analytic construction of an additive character, and a method for `cohomological reduction' similar to the `Hermite reduction' algorithm used in the symbolic integration of rational functions. The talk is based upon joint work with Daqing Wan. See http://web.comlab.ox.ac.uk/oucl/work/alan.lauder/ for a version of the earlier paper, which has now appeared in LMS JCM, and also two other related papers.
Prochains exposés
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Polytopes in the Fiat-Shamir with Aborts Paradigm
Orateur : Hugo Beguinet - ENS Paris / Thales
The Fiat-Shamir with Aborts paradigm (FSwA) uses rejection sampling to remove a secret’s dependency on a given source distribution. Recent results revealed that unlike the uniform distribution in the hypercube, both the continuous Gaussian and the uniform distribution within the hypersphere minimise the rejection rate and the size of the proof of knowledge. However, in practice both these[…]-
Cryptographie
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Primitive asymétrique
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Mode et protocole
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Post-quantum Group-based Cryptography
Orateur : Delaram Kahrobaei - The City University of New York