# 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]]