According to this Wired article, Ray Ozzie may have a solution to the crypto backdoor problem. No, he hasn't. He's only solving the part we already know how to solve. He's deliberately ignoring the stuff we don't know how to solve. We know how to make backdoors, we just don't know how to secure them.
The vault doesn't scale
Yes, Apple has a vault where they've successfully protected important keys. No, it doesn't mean this vault scales. The more people and the more often you have to touch the vault, the less secure it becomes. We are talking thousands of requests per day from 100,000 different law enforcement agencies around the world. We are unlikely to protect this against incompetence and mistakes. We are definitely unable to secure this against deliberate attack.
A good analogy to Ozzie's solution is LetsEncrypt for getting SSL certificates for your website, which is fairly scalable, using a private key locked in a vault for signing hundreds of thousands of certificates. That this scales seems to validate Ozzie's proposal.
But at the same time, LetsEncrypt is easily subverted. LetsEncrypt uses DNS to verify your identity. But spoofing DNS is easy, as was recently shown in the recent BGP attack against a cryptocurrency. Attackers can create fraudulent SSL certificates with enough effort. We've got other protections against this, such as discovering and revoking the SSL bad certificate, so while damaging, it's not catastrophic.
But with Ozzie's scheme, equivalent attacks would be catastrophic, as it would lead to unlocking the phone and stealing all of somebody's secrets.
In particular, consider what would happen if LetsEncrypt's certificate was stolen (as Matthew Green points out). The consequence is that this would be detected and mass revocations would occur. If Ozzie's master key were stolen, nothing would happen. Nobody would know, and evildoers would be able to freely decrypt phones. Ozzie claims his scheme can work because SSL works -- but then his scheme includes none of the many protections necessary to make SSL work.
What I'm trying to show here is that in a lab, it all looks nice and pretty, but when attacked at scale, things break down -- quickly. We have so much experience with failure at scale that we can judge Ozzie's scheme as woefully incomplete. It's not even up to the standard of SSL, and we have a long list of SSL problems.
Cryptography is about people more than math
We have a mathematically pure encryption algorithm called the "One Time Pad". It can't ever be broken, provably so with mathematics.
It's also perfectly useless, as it's not something humans can use. That's why we use AES, which is vastly less secure (anything you encrypt today can probably be decrypted in 100 years). AES can be used by humans whereas One Time Pads cannot be. (I learned the fallacy of One Time Pad's on my grandfather's knee -- he was a WW II codebreaker who broke German messages trying to futz with One Time Pads).
The same is true with Ozzie's scheme. It focuses on the mathematical model but ignores the human element. We already know how to solve the mathematical problem in a hundred different ways. The part we don't know how to secure is the human element.
How do we know the law enforcement person is who they say they are? How do we know the "trusted Apple employee" can't be bribed? How can the law enforcement agent communicate securely with the Apple employee?
You think these things are theoretical, but they aren't. Consider financial transactions. It used to be common that you could just email your bank/broker to wire funds into an account for such things as buying a house. Hackers have subverted that, intercepting messages, changing account numbers, and stealing millions. Most banks/brokers require additional verification before doing such transfers.
Let me repeat: Ozzie has only solved the part we already know how to solve. He hasn't addressed these issues that confound us.
We still can't secure security, much less secure backdoors
We already know how to decrypt iPhones: just wait a year or two for somebody to discover a vulnerability. FBI claims it's "going dark", but that's only for timely decryption of phones. If they are willing to wait a year or two a vulnerability will eventually be found that allows decryption.
That's what's happened with the "GrayKey" device that's been all over the news lately. Apple is fixing it so that it won't work on new phones, but it works on old phones.
Ozzie's solution is based on the assumption that iPhones are already secure against things like GrayKey. Like his assumption "if Apple already has a vault for private keys, then we have such vaults for backdoor keys", Ozzie is saying "if Apple already had secure hardware/software to secure the phone, then we can use the same stuff to secure the backdoors". But we don't really have secure vaults and we don't really have secure hardware/software to secure the phone.
Again, to stress this point, Ozzie is solving the part we already know how to solve, but ignoring the stuff we don't know how to solve. His solution is insecure for the same reason phones are already insecure.
Locked phones aren't the problem
Phones are general purpose computers. That means anybody can install an encryption app on the phone regardless of whatever other security the phone might provide. The police are powerless to stop this. Even if they make such encryption crime, then criminals will still use encryption.
That leads to a strange situation that the only data the FBI will be able to decrypt is that of people who believe they are innocent. Those who know they are guilty will install encryption apps like Signal that have no backdoors.
In the past this was rare, as people found learning new apps a barrier. These days, apps like Signal are so easy even drug dealers can figure out how to use them.
We know how to get Apple to give us a backdoor, just pass a law forcing them to. It may look like Ozzie's scheme, it may be something more secure designed by Apple's engineers. Sure, it will weaken security on the phone for everyone, but those who truly care will just install Signal. But again we are back to the problem that Ozzie's solving the problem we know how to solve while ignoring the much larger problem, that of preventing people from installing their own encryption.
The FBI isn't necessarily the problem
Ozzie phrases his solution in terms of U.S. law enforcement. Well, what about Europe? What about Russia? What about China? What about North Korea?
Technology is borderless. A solution in the United States that allows "legitimate" law enforcement requests will inevitably be used by repressive states for what we believe would be "illegitimate" law enforcement requests.
Ozzie sees himself as the hero helping law enforcement protect 300 million American citizens. He doesn't see himself what he really is, the villain helping oppress 1.4 billion Chinese, 144 million Russians, and another couple billion living in oppressive governments around the world.
Ozzie pretends the problem is political, that he's created a solution that appeases both sides. He hasn't. He's solved the problem we already know how to solve. He's ignored all the problems we struggle with, the problems we claim make secure backdoors essentially impossible. I've listed some in this post, but there are many more. Any famous person can create a solution that convinces fawning editors at Wired Magazine, but if Ozzie wants to move forward he's going to have to work harder to appease doubting cryptographers.