Isogeny volcanoes

Andrew Sutherland
2013 The Open Book Series  
The remarkable structure and computationally explicit form of isogeny graphs of elliptic curves over a finite field has made them an important tool for computational number theorists and practitioners of elliptic curve cryptography. This expository paper recounts the theory behind these graphs and examines several recently developed algorithms that realize substantial (often dramatic) performance gains by exploiting this theory.
doi:10.2140/obs.2013.1.507 fatcat:k75vmyytwvafdk67punumfhbha