The assumption that it ends with ASICs is based on several assumptions.
#1 Silicon will always be dominant. I think that one day quantum computers will blow silicon away. There may be other tech we have yet to consider that lays between here and there or after there. Any or all of which would blow an asic away. There could also be algorithmic short cuts that could be implemented in current silicon.
#2 The keysign algo is mathematically intractable.
We've seen lately a lot of ingenious attacks against previously hardened crypto. My guess is that the algo we use for key signing will eventually fall. While we could always switch, the fact that the algo fell would undermine confidence in the currency and render it worthless.
In fact if someone just took a large enough set of public keys and ran a brute force random attack against them on a large enough botnet, they could fairly easily show "control" of enough bitcoins to undermine the entire economy.
There are ALOT of bitcoins tied to keys that have long since been lost, these haven't been moved at all in years. I know I had a hardrive with some 1,500 bitcoins years ago that died but back then they might have been worth a total of $1.50
I would guess that the next mining innovation beyond what we see now, will be bots built to do ummm let's calling it private key mining.
It's trivial to do. People have developed programs that just generate absolutely huge numbers of bitcoin addresses using your GPU.
Why don't you build a powerful network and just run these for a few months, checking each created address to see if it has any bitcoins in it, and let me know how many bitcoins you steal.
..because with this, you would make many million times less bitcoins than with simple mining.
I can't reproduce the exact numbers nor have the thread available, but with comparing the mining difficulty with the 256 bit private key, you, well, get some pretty large numbers ;-)
In fact with such large numbers all that stuff is simply not imaginable. Like "more cpus needed than grains of sand on a beach" and the like.
I'm sure someone will produce real numbers here!
Ente