UCLA computer grad constructs “crown jewel of cryptography”

Same reason. Money.

I mean, the same argument has been applied to other cryptographic tools. Why encrypt your messages, unless you're sending something sketchy? Why obfuscate programs, unless you're hiding something?

Yet I think the utility of encryption is well-demonstrated, and not just theoretical. It can be used by good people to defend against adversarial intent. And it may well be that obfuscation (in its most direct application) has the same effect. (e.g. companies sharing proprietary algorithms for you to run at home, without revealing the secret sauce; or me delegating computation to AWS without revealing secrets)

Note that this is not why indistinguishability obfuscation (iO) is a crown jewel, here. Practically, iO is nowhere close to obfuscating anything larger than a tiny circuit. But it can still be useful to do things like obfuscate secret keys when designing cryptographic protocols. Theoretically, iO allows us to derive essentially every cryptographic primitive, which is why this paper is interesting, and why iO is called a crown jewel. And now, we can build iO for the first time from well-studied hardness assumptions.

Because figuring out what a worm does doesn't help if it has already done it, and for that matter they're supposed to remain undetected. Furthermore people already cannot tell whether code has backdoors, or what ML classifiers do for that matter.

Unfortunately, the biggest industrial use case is making wi-fi routers that are absolutely impossible to install OpenWRT on, etc...

DRM implementations already use code obfuscation heavily. Can someone with knowledge of the math clarify why this is a big deal? Why would it matter that there is mathematical proof that someone cannot figure out what the code is doing? How does it apply to crypto?

The code obfuscation that DRM implementations use is not provably secure. I don't think anyone would (or should) hide a bitcoin secret key inside of an obfuscated program. There's no formal guarantee of security.

This work, on the other hand, shows a provably secure construction for obfuscation (assuming that some assumptions about the hardness of various well-studied mathematical problems are true). In other words, extracting a bitcoin secret key from an obfuscated algorithm is as hard as insert math problem here. (This is how all cryptography works; e.g. breaking RSA encryption is as hard as factoring large products of primes.) This paper is special because, for the first time, the hard math problem they use (to build the obfuscation) is "reasonable": they've been studied for decades, and no one knows how to break them. (Indeed, a lot of cryptography is built on top of the same assumptions/problems.)

Thus, we would be surprised if someone extracted our bitcoin secret key from our obfuscated program, because it means they solved some "thought-to-be-unsolvable" mathematical problem. This is a much nicer guarantee than the alternative, e.g. with current obfuscation, where we say "oh, it looks pretty random, let's stick my key in" and then trusting that no one will break it. (That's a lot of trust, when you might have a 100,000 Bitcoin at stake.)

Of course, none of this is really feasible; at best, we can securely obfuscate tiny circuits (in the present time). So the main utility is probably to hide keys and the such, not to obfuscate entire programs. This might enable better secure MPC schemes, NIZKs, etc. So I guess, per your question, it's also targeted towards a different use case.

Now, as to why theoretical cryptographers care about obfuscation in general: it's not so much about the direct application of obfuscating programs. (It's not obvious why obfuscation is more interesting than encryption, etc, from an applied point of view.) Instead, from a theoretical point of view, if we can build indistinguishability obfuscation, we can directly build public key encryption, non-interactive zero knowledge proofs, Multiparty computation, etc. etc. (assuming one-way functions). So really, this is a primitive that somehow connects all of the other primitives, which is why theoreticians think it is a big deal.