One thing you're missing: cryptography is secured by say, the difficulty of factoring large numbers, but cryptocurrencies are secured by no one being able to take over more than 51% of the network's processing (in proof-of-work currencies, like Bitcoin). They're kind of the same technology, but cryptocurrencies are relying on a second-order effect.
Put another way: this "hardness" isn't a fundamental computational limit, but more of an enforced limitation because other parties want to verify your computation.
Also, one hole in your idea: the actual mac...