[MatteoFrigo]

This is, of course, very technical, but here is how it works at a high level.

In the non-ZKP presentation, the "holder" (phone) sends the credential to the relying party (website), and the RP executes some verification algorithm. In the ZK presentation, the holder executes the verification algorithm and sends to the RP a proof that the algorithm was executed correctly.

The "proof" has this magical property that it reveals nothing other than the check passed. (You will have to take on faith that such proofs exist.) In particular, if the check was the predicate "I have a signature by ISSUER on HASH, and SHA256(DOCUMENT)==HASH, and DOCUMENT["age_gt_18"]=TRUE", anybody looking at the proof cannot infer ISSUER, HASH, DOCUMENT, or HASH, or nothing else really. "Cannot infer" means that the proof is some random object and all HASH, DOCUMENT, ISSUER, etc. that satisfy the predicate are equally likely, assuming that the randomness used in the proof is private to the holder. Moreover, a generating a proof uses fresh randomness each time, so given two proofs of the same statement, you still cannot tell whether they come from the same ISSUER, HASH, DOCUMENT, ...

[parineum]

If it's not linked to an identity, why can't a kid use a parent's key?

[MatteoFrigo]

Excellent question. More generally, what prevents me from copying the credential and giving it to somebody else?

The currently favored approach works like this. The DOCUMENT contains a device public key DPK. The corresponding secret key is stored in some secure hardware on the phone, designed so that I (or malware or whatever) cannot extract the secret key from the secure hardware. Think of it as a yubikey or something, but embedded in the phone. Every presentation flow will demand that the secure element produce a signature of a random challenge from the RP under the secret key of the secure hardware. In the ZKP presentation, the ZKP prover produces a proof that this signature verifies correctly, without disclosing the secret key of the secure hardware.

In your example, the parent could give the phone to the kid. However, in current incarnations, the secure hardware refuses to generate a signature unless unlocked by some kind of biometric identification, e.g. fingerprint. The fingerprint never leaves the secure hardware.

How does the issuer (e.g. the republic of France) know that DOCUMENT is bound to a given fingerprint? This is still under discussion, but as a first bid, a French citizen goes to city hall with his phone and obtains DOCUMENT after producing a fingerprint on the citizen's phone (as opposed to a device belonging to the republic of France). You can imagine other mechanisms based on physical tokens (yubikeys or embedded chips in credit cards, or whatever). Other proposals involve taking pictures compared against a picture stored in DOCUMENT. As always, one needs to be clear about the threat model.

In all these proposals the biometric identification unlocks the secure hardware into signing a nonce. The biometrics themselves are not part of the proof and are not sent to the relying party or to the issuer.

[jolmg]

I think a parent should be able to give their kid access if they deem their kid mature enough. If the kid can handle social media without it becoming an addiction or a self-esteem issue or similar, then it would generally be a net positive. For example, social media may include YouTube which has a lot of educational content. Why hold the kid back?

[pksebben]

the more I think about it, the more I feel like I need someone with deep knowledge to explain ZKPs to me.

So like, we've got this algorithm that gets sent our way and we run it and that provides kind of a cryptographic hash or whatever. But if we're running the algorithm ourselves what's to stop us from lying? Where does the 'proof' come from? What's the check that it's running and why do we inherently trust the source it's checking?

[kahnclusions]

I’m not exactly sure about ZKPs but for age verification the “proof” can come from the government but in such a way that the web service doesn’t know anything more than whether an assertion is true, and the government doesn’t know anything more than you wanted to verify some assertion.

This is a simplified method for age verification:

I want to buy alcohol from my phone and need to prove I’m over 18. SickBooze.com asks me for proof by generating a request to assert “age >= 18”.

My phone signs this request with my own private key, and forwards it to the government server.

The government verifies my signature against a public key I previously submitted to them, checks my age data in their own register of residents, and finally signs the request with one of their private keys.

My phone receives the signed response and forwards it back to SickBooze.com, which can verify the government’s signature offline against a cached list of public keys. Now they can sell me alcohol.

- the “request” itself is anonymous and doesn’t contain any identifying information unless that is what you intended to verify

- the government doesn’t know what service I used, nor why I used it, they only know that I needed to verify an assertion about my age

- the web service I used doesn’t know my identity, they don’t even know my exact age, they just know that an assertion about being >= 18 is true.

[MatteoFrigo]

I am someone with "deep knowledge", but HN is not the proper place for this discussion. See https://people.cs.georgetown.edu/jthaler/ProofsArgsAndZK.htm... for the gory details.

Here is a hopefully simple example of how this ZKP thing may even be possible. Imagine that you give me a Sudoku puzzle. I solve it, and then I want to prove to you that I have solved it without telling you the solution. It sounds impossible, but here is one way to do it. I compute the solution. I randomly scramble the digits 1-9 and I put the scrambled solution in a 9x9 array of lock boxes on a table. I have the keys to the 81 locks but I am not giving you the key yet. You randomly ask me to open either 1) one random row chosen by you; 2) one random column chosen by you; 3) one random 3x3 block chosen by you; or 4) the cells corresponding to the original puzzle you posed to me. In total you have 28 possibilities, and assume that you choose them with equal probability. You tell me what you want and I open the corresponding lockboxes. You verify that the opened lock boxes are consistent with me knowing a solution, e.g. all numbers in a row are distinct, the 3x3 block consists of distinct numbers, etc. If I am cheating, then at least one of your 28 choices will be inconsistent, and you catch me with probability 1/28, so if we repeat this game 1000 times, and I don't know the solution, you will catch me with probability at least 1-(1/28)^1000 which is effectively 1. However, every time we repeat the game, I pick a different random scrambling of the integers 1-9, so you don't learn anything about the solution.

All of ZKP is a fancy way to 1) encode arbitrary computations in this sort of protocol, and 2) amplify the probability of success via clever error-correction tricks.

The other thing you need to know is that the protocol I described requires interaction (I lock the boxes and you tell me which ones to open), but there is a way to remove the interaction. Observe that in the Sudoku game above, all you are doing is flipping random coins and sending them to me. Of course you cannot let me pick the random coins, but if we agree that the random coins are just the SHA256 hash of what I told you, or something else similarly unpredictable, then you will be convinced of the proof even if the "coins" are something that I compute myself by using SHA256. This is called the "Fiat-Shamir transformation".

How do we implement the lock boxes? I tell you SHA256(NONCE, VALUE) where the NONCE is chosen by me. Given the hash you cannot compute VALUE. To open the lock box, I tell you NONCE and VALUE, which you believe under the assumption that I cannot find a collision in SHA256.