New trends and the effect of key factors influence the quality of the holes produced by ECM processes. Researchers developed a fuzzy logic controller by adding intelligence to the ECM process. Maintaining optimum ECM process conditions ensures higher machining efficiency and performance. This paper presents the development of a fuzzy logic controller to add intelligence to the ECM process. An e...

We present JKL-ECM, an implementation of the elliptic curve method of integer factorization which uses certain twisted Hessian curves in a family studied by Jeon, Kim and Lee. This implementation takes advantage of torsion subgroup injection for families of elliptic curves over a quartic number field, in addition to the ‘small parameter’ speedup. We produced thousands of curves with torsion Z/6...

This paper reports record-setting performance for the ellipticcurve method of integer factorization: for example, 604.99 curves/second for ECM stage 1 with B1 = 8192 for 280-bit integers on a single PC. The state-of-the-art GMP-ECM software handles 171.42 curves/second for ECM stage 1 with B1 = 8192 for 280-bit integers using all four cores of a 2.4GHz Core 2 Quad Q6600. The extra speed takes a...

18.1 Context of the ECM ...................................................... 461 18.1.1 ECM – What’s in a Name? ............................................. 462 18.1.2 Old and New ECMs ........................................................ 462 18.1.3 Biophysical Considerations ............................................. 462 18.1.4 Jelly Bombs ................................................

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 extende...