Factorizing with MSIEVE, GGNFS & Factmsieve.py

[Romuald]

Ah, sympa, je me sens moins dépaysé à présent... Mais je sais pas si tout le monde ici maîtrise suffisamment le français pour que je puisse y poster des demandes d'aide, questions ou autres.

[Romuald]

Bon, je reprends l'anglais maintenant...

I just saw this page, about most adapted factorization algorithms depending on the integer's size:

The method will work, but will be slow. "How big are your numbers?" determines the method to use:

• Less than 2^16 or so: Lookup table.
• Less than 2^70 or so: Richard Brent's modification of Pollard's rho algorithm.
• Less than 10^50: Lenstra elliptic curve factorization
• Less than 10^100: Quadratic Sieve
• More than 10^100: General Number Field Sieve

[Dubslow]

Originally Posted by Romuald

Bon, je reprends l'anglais maintenant...

I just saw this page, about most adapted factorization algorithms depending on the integer's size:

The method will work, but will be slow. "How big are your numbers?" determines the method to use:

• Less than 2^16 or so: Lookup table.
• Less than 2^70 or so: Richard Brent's modification of Pollard's rho algorithm.
• Less than 10^50: Lenstra elliptic curve factorization
• Less than 10^100: Quadratic Sieve
• More than 10^100: General Number Field Sieve

Yeah... there's only two or three, and I'm not one of them

That is more or less correct. If you do manage to install YAFU, you can watch how it tries to factor arbitrary numbers -- first trial factoring (which is basically a lookup against the first ~100K primes), Pollard's rho is indeed run, Fermat's method, before resorting to P-1 and ECM, and should those also fail, QS and NFS as appropriate. On most computers, the crossover between Yafu's QS and ggnfs/msieve NFS is aroung 95-96 digits, well in like with the 100 digit rule of thumb you mention.