Generalizing Vélu's formulas and some applications

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Microsoft Research
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Published on ● Video Link: https://www.youtube.com/watch?v=6Sa6l3c8ssI


Duration: 57:48
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Vélu's formulas allow to compute an isogeny between elliptic curves from the coordinates of the points in the kernel. In this talk, I describe an algorithm using theta functions to compute an isogeny from its kernel on any abelian variety. I will give specific timings of a genus 2 implementation, and describe some applications. This is a joint work with Romain Cosset and David Lubicz.



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