A bit of advice: Bitcoin and PoW crypto-currencies like it are unique because to understand them you can't just understand crypto, you also need to understand a bit of economics, game theory, and even politics. Equally, it's very common that ideas that seem technically sound fall flat when analyzed from an economic/social/political point of view; it's easy to make ideas that only work if all the participants are "honest" in some way, which just isn't good enough here.
The key problem is that in a PoW consensus system the defenders only have a linear advantage over the attackers, where in basically all other cryptography they have an exponential advantage. It's why the latter can say things like:
These numbers have nothing to do with the technology of the devices; they are the maximums that thermodynamics will allow. And they strongly imply that brute-force attacks against 256-bit keys will be infeasible until computers are built from something other than matter and occupy something other than space.
-
https://www.schneier.com/blog/archives/2009/09/the_doghouse_cr.htmlwhile with Bitcoin we're worried that economics incentives won't be enough to ward off attacks.