Quote:
Originally Posted by gbvalor
But what I meant, sorry if I not explained well, is try to use this form in the modular exponentiation we have to do with the few candidates we still have after sieve work, when the size is over 64 bits .

Ah, I see now.
When the candidate factor F is over 64 bits, you want to use the method described in your first post to break it into several operations of < 64 bits.
I think the question you want is:
Is your method faster than [sp] karisuba multiplication (or other), plus a size*2 bit mod.
You'll want to compare your method for factor sizes of 64, <128, <192 bits, ... to see if it beats the others at that size range.
If you could code a function gbv(m, f) that uses your method to calculate 2^m  1 (mod f), and someone codes it using several other big number methods, then we could run a time trial and see.
Any takers?
Bruce