[vabmit]

I think you're confusing complexity with difficulty. It may be 10^12 times more complex. But, if you're making your own FGPAs or chips and you can just use different word sizes or massively add more gates or processing cores. Or, even more specialized custom built super computers. The capabilities of what they're able to fabricate I think mitigate most of the protection provided by using 2048bit over 1024bit. It seems you need to be talking on the scale of at least 4096bit before the problem becomes intractable due to the limits of technology and the processing improvements that can be provided by custom hardware.

To put it in simple terms, doing operations with a 32bit numbers and a 64bit numbers have a calculable complexity gap. But, that gap means very different things in terms of difficulty on a 8bit microprocessor vrs a 32bit microprocessor vrs a 64bit microprocessor.