3. Notation

3. Notation

Throughout this document, the following notation is used:

p
Denotes the prime number defining the underlying field.

GF(p)
The finite field with p elements.

A
An element in the finite field GF(p), not equal to -2 or 2.

d
A non-zero element in the finite field GF(p), not equal to 1, in the case of an Edwards curve, or not equal to -1, in the case of a twisted Edwards curve.

order
The order of the prime-order subgroup.

P
A generator point defined over GF(p) of prime order.

U(P)
The u-coordinate of the elliptic curve point P on a Montgomery curve.

V(P)
The v-coordinate of the elliptic curve point P on a Montgomery curve.

X(P)
The x-coordinate of the elliptic curve point P on a (twisted) Edwards curve.

Y(P)
The y-coordinate of the elliptic curve point P on a (twisted) Edwards curve.

u, v
Coordinates on a Montgomery curve.

x, y
Coordinates on a (twisted) Edwards curve.