Depends on how deeply you want to understand how it works... could be anything between why sometimes factors pop out any why large B1,B2 values have a higher chance of finding a given factor, to details of elliptic curve arithmetic and curve parameterisation.

A starting point is the

http://www.mersennewiki.org/index.ph...c_Curve_Method page. A must-read for anyone who wants to implement ECM is Peter Montgomery's thesis, "An FFT extension of the Elliptic Curve Method of Factorization" (

ftp://ftp.cwi.nl/pub/pmontgom/ucladissertation.psl.gz).

Alex