ECM using Edwards curves

Daniel J.  Bernstein; Peter Birkner; Tanja Lange; Christiane Peters

Paper 2008/016

ECM using Edwards curves

Daniel J. Bernstein, Peter Birkner, Tanja Lange, and Christiane Peters

Abstract

This paper introduces EECM-MPFQ, a fast implementation of the elliptic-curve method of factoring integers. EECM-MPFQ uses fewer modular multiplications than the well-known GMP-ECM software, takes less time than GMP-ECM, and finds more primes than GMP-ECM. The main improvements above the modular-arithmetic level are as follows: (1) use Edwards curves instead of Montgomery curves; (2) use extended Edwards coordinates; (3) use signed-sliding-window addition-subtraction chains; (4) batch primes to increase the window size; (5) choose curves with small parameters and base points; (6) choose curves with large torsion.

Note: Updated paper with more constructions.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Factorization ECM elliptic-curve method curve selection Edwards coordinates extended Edwards coordinates
Contact author(s): tanja @ hyperelliptic org
History: 2011-10-08: last of 9 revisions; 2008-01-14: received; See all versions
Short URL: https://ia.cr/2008/016
License: CC BY

BibTeX

@misc{cryptoeprint:2008/016,
      author = {Daniel J.  Bernstein and Peter Birkner and Tanja Lange and Christiane Peters},
      title = {{ECM} using Edwards curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/016},
      year = {2008},
      url = {https://eprint.iacr.org/2008/016}
}