Lean Together 2025: David Kurniadi Angdinata, Division polynomials of elliptic curves
Автор: leanprover community
Загружено: 2025-01-18
Просмотров: 250
Elliptic curves are one of the simplest non-trivial objects in algebraic geometry and are pervasive in modern number theory such as in Wiles's proof of Fermat's last theorem. Their points form an abelian group under a geometric addition law given by explicit rational functions. In particular, there is an explicit formula for the multiplication of a point by $ n $ in terms of certain inductively-defined division polynomials, which are crucial in point counting algorithms and public key cryptography. In this talk, I will explain our formalisation of division polynomials and the multiplication-by-$ n $ formula, whose proof turned out to be quite elusive. This is joint work with Junyan Xu.
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