Factoring Algorithms for Exponential Speed | Tips & Advice

[paradigmjump]

Is anyone aware of any factoring algorithms that factor in exponential speed?
Working on improving mine and need a comparison.

Have not had much luck finding such.
Thanks

 

[mfb]

Isn't trial division exponential? For a number of length n, you need at most $\left(\sqrt{2}\right)^n$ attempts to find a factor and there is at most one really time-consuming step, so all other factors can be neglected. Assuming base 2, base 10 just changes this to $\left(\sqrt{10}\right)^n$.
Good algorithms are much better, so I don't see why you want a comparison with exponential algorithms.

 

[paradigmjump]

My reference is to reducing beyond the root exponentially. For very large numbers this greatly reduces time and makes factoring of large numbers possible within a useful period of time.
Thanks,

 

[mfb]

Which reference, and what do you mean with "reducing beyond the root exponentially"?

For very large numbers this greatly reduces time and makes factoring of large numbers possible within a useful period of time.

Better than existing algorithms? Those are way below exponential time...