This article gives an elementary computational proof of the group law for Edwards elliptic curves. The associative law is expressed as a polynomial identity over the integers that is directly checked by polynomial division. Unlike other proofs, no preliminaries such as intersection numbers, B́ezout’s theorem, projective geometry, divisors, or Riemann Roch are required.
- Hales, T., & Raya, R. (2020). Formal Proof of the Group Law for Edwards Elliptic Curves. Lecture Notes in Computer Science, 254–269. https://doi.org/10.1007/978-3-030-51054-1_15