Regardless of the math used, eventually you have to transform the math into something, a public key, a h160, whatever type collision/match you are looking for.
Everything you listed is some math implementation.
But let us say it's pure math, do the "math" for how long it takes a current CPU to do straight additions, just using numbers. And use a higher end CPU with say 5.0 mghz capability.
IMO, you have to eventually transform the pure math into what you are searching for, or have a precomputed list of something...so to me, it can never be, just math.
You're failing on the assumption that nobody, nowhere, will ever advance the math itself. Or contrarily on the assumption that somebody will prove one day that you do need "precomputed tables" - this hasn't happened yet as well. The concept of a logarithm was invented just a few centuries ago and immediately changed engineering as we know it. Until that point, math without logs was the peak of advancements in human knowledge. So I beg you pardon - it is foremost, before of anything else, the math, not the count of transistors jumbling around in logic gates in your CPU, GPU, ASIC, or whatever. Those are just tools, not the fundaments.
I can give you a public key in a small bit range, and just using math, you would never solve/know if a match was found. Understand?
Arrogance much? What does "never" mean? Or is time only relevant when you zoom and peek into a nanosecond, a day, a trillion year? Maybe a single unit of Planck time?
Here's a hint: I start from 1 up to your N modulus, and I have a 100% probability that at some point I will break your key, or that at the end I can tell you a simple truth - that your key isn't in the finite cycle. Understand?