Séminaire de Cryptographie

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Robert Carls

Explicit higher dimensional 3-adic canonical lifting

Our talk is about joint work with D. Kohel and D. Lubicz. We prove equations having as solutions the theta null points of canonical lifts of ordinary abelian varieties over finite fields of characteristic 3. We describe an algorithm for 3-adic canonical lifting of ordinary abelian surfaces based on our formulas. The algorithm has been implemented in MAGMA. Examples of canonically lifted theta null points are given whose coordinates generate the ray class field modulo 2 of the reflex field of the endomorphism algebra.