Arithmetic of the Group of Elliptic Curve
Points
This section describes the Intel IPP functions that implement
arithmetic operations with points of elliptic curves [EC].
The elliptic curve is defined by the following equation:
y
2
=
x
3
+
A
⋅
x
+
B
where
- AandBare the parameters of the curve
- xandyare the coordinates of a point on the curve
This document considers elliptic curves constructed over the finite
field GF(
p
) (prime or its extension), therefore the
arithmetic of elliptic curves is based on the arithmetic of the underlying
finite field. In the equation above,
A, B, x,
and
y
belong to the underlying field
GF(p
).