2012/08/31 by Andrew V. Sutherland
Computer Science · Mathematics · #Algebra over a field #Algorithm #Coding theory and cryptography #Computer science #Computer security #Cryptographic Implementations and Security #Cryptography #Cryptography and Residue Arithmetic #Discrete mathematics #Elliptic curve #Elliptic curve cryptography #Encryption #Field (mathematics) #Isogeny #Mathematics #Public-key cryptography #Pure mathematics #cs.CR #math.NT #msc:11G07 #msc:11G15 #msc:11G20 #msc:11Y16
paper · pdf · doi:10.2140/obs.2013.1.507
published as ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium, 2012, 507-530 · Invited ANTS X paper, minor edits, 18 pages
arxiv created 2013/05/07 · openalex publication_date 2013/11/14 · arxiv updated 2014/06/20 · openalex created_date 2020/07/02 · openalex updated_date 2026/08/06
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.