Arithmetic Progressions on Edwards Curves
Computer Security Division
National Institute of Standards and Technology (NIST)
100 Bureau Drive
Gaithersburg, MD 20899-8930
We look at arithmetic progressions on elliptic curves known as Edwards
curves. By an arithmetic progression on an elliptic curve, we mean
that the x-coordinates of a sequence of rational points on the curve
form an arithmetic progression. Previous work has found arithmetic
progressions on Weierstrass curves, quartic curves, and genus 2
curves. We find an infinite number of Edwards curves with an
arithmetic progression of length 9.
Full version: pdf,
Received December 13 2010;
revised version received January 25 2011.
Published in Journal of Integer Sequences, February 8 2011.
Journal of Integer Sequences home page