Isogeny volcanoes
Copyright policy )Isogeny volcanoes
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.
Invited ANTS X paper, minor edits, 18 pages
- Massachusetts Institute of Technology United States
FOS: Computer and information sciences, Computer Science - Cryptography and Security, 11G07, 11Y16 (Primary) 11G15, 11G20 (Secondary), Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT), Cryptography and Security (cs.CR)
FOS: Computer and information sciences, Computer Science - Cryptography and Security, 11G07, 11Y16 (Primary) 11G15, 11G20 (Secondary), Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT), Cryptography and Security (cs.CR)
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