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Publication Citation: Arithmetic Progressions on Edwards Curves

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Author(s): Dustin Moody;
Title: Arithmetic Progressions on Edwards Curves
Published: February 08, 2011
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
Pages: 4 pp.
Keywords: elliptic curves, arithmetic progressions, Edwards curves
Research Areas: Math, Computer Security
PDF version: PDF Document Click here to retrieve PDF version of paper (74KB)