Vol. 1, No. 1, 2013

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Isogeny volcanoes

Andrew V. Sutherland

Vol. 1 (2013), No. 1, 507–530
Abstract

The remarkable structure and computationally explicit form of isogeny graphs of elliptic curves over a finite field have made these graphs an important tool for computational number theorists and practitioners of elliptic curve cryptography. This expository paper recounts the theory behind isogeny graphs and examines several recently developed algorithms that realize substantial (and often dramatic) performance gains by exploiting this theory.

Keywords
elliptic curves, isogeny graphs
Mathematical Subject Classification 2010
Primary: 11G07, 11Y16
Secondary: 11G15, 11G20
Milestones
Published: 14 November 2013
Authors
Andrew V. Sutherland
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139
United States