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Arithmetic Progressions on Edwards Curves

Published

Author(s)

Dustin Moody

Abstract

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.
Citation
Journal of Integer Sequences
Volume
14

Keywords

elliptic curves, arithmetic progressions, Edwards curves

Citation

Moody, D. (2011), Arithmetic Progressions on Edwards Curves, Journal of Integer Sequences, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=907596 (Accessed May 27, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created February 8, 2011, Updated February 19, 2017