# Elliptic Curve Over Finite Field ## Metadata **Status**:: #x **Zettel**:: #zettel/literature **Created**:: [[2024-03-29]] **Topic**:: [[♯ Cryptography]], [[♯ Math]] **Parent**:: [[Elliptic Curve]], [[Finite Field]] ## Synopsis Elliptic Curve over Finite Field is a set of points on the curve which coordinates are from the Finite Field. Elliptic curve over the finite field with an order p is written as: $y^2 = x^3 + ax + b \pmod{p}$ The elliptic curve over finite field plus the point at infinity is closed under the [[Elliptic Curve Addition]]. When $p$ is a prime number, the division is also closed in the finite field, so the formulas in [[Elliptic Curve Addition]] can be used for elliptic curve over finite field as well. See [[Modular Multiplicative Inverse#Modular Division]] on computing the division. ## References - [[RareSkills Authors - Elliptic Curves Over Finite Field (Highlights)]]