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:

y² = x³ + A ⋅ x + B

where

• A and B are the parameters of the curve
• x and y are 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).