My question is brief, is there an algorithm or method to calculate the consecutive X coordinates on an elliptic curve to find out if the distance between is constant?
The reason for the question is as follows: 1. Base Generator Point is given. 2. Embedding degree is given. 3. The total number of points is given (N). 4. For the curve, 1 - (N-1) are the multipliers for the points on the curve. 5. The curve is half the full curve for X-Coordinates meaning 1 and N-1 are the same X coordinate but the inverse on the Y coordinate.
Thanks.
Not sure if this is helpful, but there are a number of papers that discuss $x$-coordinates on elliptic curves that lie in arithmetic progression. Here's one paper:
A. Bremner, N. Tzanakis, J.H. Silverman, Integral points in arithmetic progression on $y^2=x(x^2-n^2)$, Journal of Number Theory 80 (2000), 187-208.