# Different Orders in Elliptic Curve ## Metadata **Status**:: #x **Zettel**:: #zettel/fleeting **Created**:: [[2024-03-25]] **Parent**:: [[Elliptic Curve]] ## Synopsis - [[Elliptic Curve Order]] n - [[Elliptic Curve Base Field]] order q - [[Elliptic Curve Scalar Field]] order r Curve order n represents number of points in the curve over the finite field. Base field is the field over which the curve is defined. Its order $q$ is used as the modulus for x, y, a, and b in the fomula. $ y^2 = x^3 + ax + b \pmod q $ The order of a point G is used as the modulus for the scalar number $z$ in $zG$. ## References - [[Mike Rosing - Elliptic Curve Cryptography - Basic Math (Highlights)#^697670872]] - [[Mike Rosing - Elliptic Curve Cryptography - Key Exchange and Signatures (Highlights)#^697680437]]