Or what would happen if improved cryptography comes along, how would the protocol deal with this? Would a layer on top of the current protocol be enough to patch it up or will Bitcoin die?
That's quite a tall order.
What would happen if the force of gravity suddenly reversed? How would we deal with this? Would modifications to our current way of living be enough to save us, or will we all die?
Yes, I realize that my hyperbole is a bit excessive, but it points out some of the issues in what you are asking.
First you are taking something that is extremely unlikely to happen (a sudden and secret complete break of multiple dissimilar cryptographic functions) and asking "what if it happens?"
Next, you are essentially asking if we can "patch up" something that relies entirely on trust in the cryptography in order to have any value. While "patching it up" may be technically possible, isn't likely to restore the trust necessary for it to continue to be useful. If you take away one of the very things that are necessary for existence, then modifications aren't likely to be enough to restore useful existence.
Note that when cryptography is "broken" it generally starts out by being weakened. Then after months or years it is weakened more. And so on until it is no longer trusted at all. Since bitcoin uses multiple layers of cryptographic functions, there should be time to adopt replacements for any layer that begins to be weakened, while maintaining the security of everyone's funds in the interim.
To steal any of my bitcoins through broken cryptography, you'd first have to completely reverse the RIPEMD-160 hash function to determine what SHA-256 result was used as its input. Then you'd have to completely reverse the SHA-256 function to determine what public key was used as its input. Then you'd have to solve the discrete logarithm problem for ECDSA with the Secp256k1 curve to find the private key. Even if one of those 3 functions were weakened so much that you could calculate its input in a matter of years (or days, or hours), I'd be protected by the remaining 2 functions. Once it's discovered that one of those functions has such a weakness, the code would be updated to replace it with a secure (as far as cryptography can determine at that time) replacement.
So, "the cryptography of Bitcoin gets cracked" isn't really a likely scenario. Far more likely is the slow replacement of various cryptographic functions within Bitcoin over the course of multiple decades.
Fantastic explanation, thanks Danny. I was concerned about Bitcoin eventually being "cracked wide open", but you did a great job of explaining how secure it really is.
