ECM using Edwards curves

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

Research output: Contribution to journalJournal articleResearchpeer-review


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.
Original languageEnglish
JournalMathematics of Computation
Issue number282
Pages (from-to)1139-1179
Publication statusPublished - 2013


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