Cryptology ePrint Archive: Report 2008/016

ECM using Edwards curves

Daniel J. Bernstein and Peter Birkner and 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.

Category / Keywords: Factorization, ECM, elliptic-curve method, curve selection, Edwards coordinates, extended Edwards coordinates

Date: received 9 Jan 2008, last revised 8 Oct 2011

Contact author: tanja at hyperelliptic org

Available format(s): PDF | BibTeX Citation

Note: Updated paper with more constructions.

Version: 20111008:180328 (All versions of this report)

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