ECM using Edwards curves

Abstract

This paper introduces GMP-EECM, a fast implementation of the elliptic-curve method of factoring integers. GMP-EECM is based on, but faster and more effective than, the well-known GMP-ECM soft-ware. The main changes are as follows: (1) use Edwards curves instead of Montgomery curves; (2) use twisted inverted Edwards coordinates; (3) use signed-sliding-window addition chains; (4) batch primes to increase the window size; (5) choose curves with small parameters a, d, X1, Y1, Z1; (6) choose curves with larger torsion.