[ninkendo]

No I don't think the paper is talking about breaking hashing here, they're talking about breaking the 256-bit elliptic curve encryption of keys in the Bitcoin network.

Hashing isn't really the same thing... you're not "encrypting" data when you hash it, you're putting it through a one-way function that produces a consistent fixed-size output, such that if you provide the same input again, you get the same output.

Hashes aren't "reversible" in any reasonable sense of the word. Sure, you can keep guessing inputs until you produce one that has the same hash, but it's misleading to say that you're "decrypting" it. I'd instead say you're finding collisions.

To me, "decryption" implies that there's some secret you have which can take the hash and turn it back into its original input in constant or linear time. Using the word "decryption" to describe "finding a hash collision" isn't really correct.