Journal article
ECM using Edwards curves
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.
Language: | English |
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Publisher: | American Mathematical Society |
Year: | 2013 |
Pages: | 1139-1179 |
ISSN: | 10886842 and 00255718 |
Types: | Journal article |
DOI: | 10.1090/S0025-5718-2012-02633-0 |