Tenth Algorithmic Number Theory Symposium ANTS-X University of California, San Diego July 9 – 13, 2012 Tenth Algorithmic Number Theory Symposium (ANTS-X) July 9 – 13, 2012

Isogeny volcanoes: a computational perspective

Andrew Sutherland

Abstract: The elegant structure and computationally explicit form of isogeny graphs of elliptic curves over a finite field has made them an increasingly important tool for computational number theorists and practitioners of elliptic curve cryptography. In this talk I will briefly review the theory that determines the structure of these graphs, and then provide several examples of algorithms that are able to realize substantial (often dramatic) performance gains by exploiting this knowledge.

Files available: slides (PDF)