Are there any clever (fast) methods for adding the basepoint (generator) to an arbitrary point on elliptic curve, finally ending in affine coordinates?
G is the generator for a group on the curve (e.g. 25519) and
P is an arbitrary point, is there a faster-than-naive way to find
P + G in affine coordinates?
I'm interested in quickly enumerating the points on a curve, starting with
3G, etc, with final values in affine coordinates.
My current solution starts with
P in Edwards coordinates and then converts
G + P to affine coordinates (which is slow). But I figure there might be some magic that 1) takes advantage of
G being known or 2) uses the work previously done when computing the sequence
EDIT: To be clear, I'm not interested in scalar multiplication of an elliptic curve point by a number (I don't want to compute
nG for arbitrary
n). Instead I want to "increment" a point
P by adding it with the generator