Description
This talk is about joint work with David Lubicz. By a classical result of Serre and Tate the deformation space of an ordinary abelian variety is given by a formal torus. In Serre-Tate coordinates the problem of canonical lifting is trivial. Unfortunately, in general it is difficult to compute the Serre-Tate parameters of a given abelian variety. Alternatively, one may use canonical coordinates which are induced by a canonical theta structure. Mumford introduced theta structures in order to construct an arithmetic moduli space of abelian varieties. We apply a multi-variate Hensel lifting procedure to a certain set of p-adic theta identities which are obtained using Mumford's formalism of algebraic theta functions. As an application we give a point counting algorithm for ordinary abelian varieties over a finite field which is quasi-quadratic in the degree of the finite field.
Next sessions
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Polytopes in the Fiat-Shamir with Aborts Paradigm
Speaker : 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[…]-
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Post-quantum Group-based Cryptography
Speaker : Delaram Kahrobaei - The City University of New York