Abelian surfaces with a given number of points

  • Peter Stevenhagen | Mathematical Institute, Leiden University, Netherlands

This is a report on joint work with Everett Howe and Kristin Lauter.

I will discuss the genus 2 analogue of the problem of efficiently constructing an elliptic curve over a finite field with a prescribed number N of points. If N is provided with its prime factorization, the elliptic construction I gave with Broker is heuristically polynomial time outside a zero density subset of input values N. I will explain why the analogous construction to obtain abelian surfaces of given order N is intrinsically exponential.

Speaker Details

Peter Stevenhagen is professor of mathematics at the Universiteit Leiden. His research concerns problems and algorithms in algebraic number theory. He is proud to be advisor of both a postdoc and an intern at Microsoft Research.

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