[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.

[parineum]

So adults are required to own a phone to prove their age?

Can I log into an age gated service at a library without a phone?

[MatteoFrigo]

Another excellent question. The current answer in the EU seems to be "you need a phone". My preferred answer (despite being one of the Google guys who designed the ZKP mechanism) would be that the government sends you some sort of plastic card with a chip that does not tie you to a phone. Still fighting that battle.

[fsflover]

I guess owning some computer should be fine as a requirement? It just should not be tied to the US megacorps. A web app perhaps?

[MatteoFrigo]

Yes. However, at some point there needs to be some unforgeable piece of hardware that prevents copying the document. I am a big fan of yubikeys and I wish everybody used them, but the reality is that people lose them way more often than they lose their phone.

[parineum]

Thanks for answering, I appreciate it.

[donmcronald]

> 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).

Are you saying that someone goes to city hall, shows ID, and gets a DOCUMENT that certifies age, but doesn't link back to the person's identity? And it's married to a fingerprint in front of the person checking ID?

Is there a limit on how many times someone can get a DOCUMENT? If not, it'll become a new variation of fake id and eventually there's going to be an effort to crack down on misuse. If yes, what happens if I get unlucky and lose / break my phone limit + 1 times? Do I get locked out of the world? The only way I can imagine limiting abuse and collateral damage at the same time is to link an identity to a DOCUMENT somehow which makes the whole ZKP thing moot.

I'd be more worried about the politics though. There's no way any government on the planet is going to keep a system like that limited to simple age verification. Eventually there's going to be enough pretense to expand the system and block "non-compliant" sites. Why not use the same DOCUMENT to prove age to buy beer? Sanity for guns? Loyalty for food?

What happens if the proof gets flipped to run the other direction and a DOCUMENT is needed to prove you're a certified journalist? Any sources without certification can be blocked and the ZKP aspect doesn't matter at that point because getting the DOCUMENT will be risky if you're a dissenter. Maybe there's an interview. Maybe there's a background check. Has your phone ever shown up near a protest?

It's just like the Android announcement that developers need to identify themselves to distribute apps, even via side loading. The ultimate goal is to force anyone publishing content to identify themselves because then it's possible to use the government and legal system to crush dissenting views.

Big tech caused most of the problems and now they're going to provide the solution with more technology, more cost, and less freedom which is basically what they've been doing for the last 2 decades so it's not a surprise.

[cycomanic]

I somewhat understand your argument about how to prevent misuse, but I'd say one could do that by embedding the key in an ID card and someone will have to connect the ID card to the phone/computer (e.g. via NFC). So obviously you can pretend you lost your ID card and get a new one, but I would say that you can only do that so often until someone will get suspicious, just as if you would ask for a new passport every couple of months someone would start asking you some serious questions.

Regarding using the document to buy beer, that's already done, you need to provide ID. I also hope you being asked to provide ID for buying guns, but then again I'm not from the US, so I have quite a different opinion on gun ownership.

All that said though, we are currently watching some of the most significant civil rights abuses by authorities, all without any ID system and people are worried about age verification? If the government wants to abuse their power they don't need an ID system, they just look at your social media profile at the border.

[MatteoFrigo]

This post is restricted to the context of the European Union and is intended to be factual.

The EU age verification app is intended to be a pilot to the EU Digital Identity Wallet (EUDIW), which EU law requires to be deployed everywhere in Europe by the end of 2026. (Thus your "worry" is in fact the explicit plan of record.)

The EUDIW will store more attributes than age. Think of it as a digital form of a passport (with name, address, etc.). The exact set of attributes is determined by local laws.

Thus, the DOCUMENT that you obtain is tied to you, and of course the state knows what is in the DOCUMENT since the state creates the document in the first place.

The state does not generate proofs. The phone generates proofs. Given a proof (and only the proof), nobody can associate the proof to the phone or to you.

Now I switch to less factual statements, which are still approximately correct.

Why would you trust the wallet software not to phone home to the state or us (Google)? The EUDIW regulations require that the wallet software be open source. However, states will only issue DOCUMENT to their own certified wallet software---you cannot just take the open source and recompile it, since the state won't issue DOCUMENT to your uncertified wallet. (Maybe your gym will issue a gym membership to your raspberry pi wallet, since it's not a big deal.)

The reason for this strictness is that the EUDIW is intended for official or semi-official uses. For example, you can open a bank account with it, or use it as ID to get a mortgage. The bank must by law accept DOCUMENT, the state guarantees that DOCUMENT is correct, and you get better privacy than handling over a piece of plastic that is then photocopied by who knows whom. This is the tradeoff of the current EU law. It would be inappropriate for this kind of official, passport-like documents to store attributes such as your profession (journalist or whatever), and nobody is talking about it.

[donmcronald]

Thanks for replying to me. I'm having a tough time understanding how it's zero knowledge, but also tied to a person's identity. At some point I'm going to try to read the manuscript you linked to someone else, but I started skimming it and I'll be lucky if I understand a tiny fraction of it.

> The state does not generate proofs. The phone generates proofs. Given a proof (and only the proof), nobody can associate the proof to the phone or to you.

I get that part. I visit a website and it basically asks me to prove my DOCUMENT has an attestation for age and my phone generates the proof. The part I don't get yet is how it proves the issuer.

> However, states will only issue DOCUMENT to their own certified wallet software---you cannot just take the open source and recompile it, since the state won't issue DOCUMENT to your uncertified wallet.

I don't get why that would matter. I think of it in terms of proving you have a signed DOCUMENT (like a signed executable), but that concept doesn't work for a proof with a subset of data in the DOCUMENT. The wallet can't be trusted either, can it? What would stop me from running a proxy to tamper with the responses?

> Why would you trust the wallet software not to phone home to the state or us (Google)?

To be honest, I don't and I think calling certified wallets "tamper proof" is incorrect. They're tamper proof from the perspective of the users, but the designers, maintainers, policy makers can "tamper" at will.

> For example, you can open a bank account with it, or use it as ID to get a mortgage.

This starts to get into the biggest issue for me. As an average person, all I know is that I have this DOCUMENT with all my vital personal information on it and some of that information can be sent to a 3rd party that asks for it. Because it's such a complex technical system I have no way of understanding what's happening or verifying I'm only sending the information I expect them to be asking for. If it's a permission system like we have on phones, that's broken. People have been conditioned to think they need to click yes on everything or things won't work. I'd worry that suddenly people will be giving away vital information without even knowing.

> you get better privacy than handling over a piece of plastic that is then photocopied by who knows whom

On a technical level, that's right. On the level of an average person understanding what information they're handing over and how it's being used (or potentially misused), that's wrong. I understand perfectly what I'm handing over when I give someone my credit card or drivers license. A digital ID system is basically opaque to me.

We have to put 100% faith in a few companies; Google, Apple, etc.. We need to trust they're acting in good faith and getting the implementation perfect. The saying is trust but verify, but what happens when the system is so complex that not enough people can verify it does what it says, or, more importantly, that policy makers aren't giving classified orders that force the handful of certified wallets to change the way things work?

The technology is very cool. When I see documents like that manuscript you linked I'm envious. I wish I could understand the math well enough to conceptualize the whole system. I think there's a ton of value in leveraging technology to modernize identity. I also have no doubt the people working on the implementation are acting in good faith. Flat out though, I don't trust the institutions. There's always someone willing to act in bad faith for one reason or another.

I think it's important to understand there's a difference between analog verification systems and digital verification systems. If someone is checking my ID or comparing my face to pictures in a book of banned patrons, that has a natural limit on the scalability. Once things are digital, all bets are off. Think of the difference between a manager banning someone from a single store vs facial recognition being used to ban someone from every store in a chain. Digital IDs could very well be the next step up where people can be banned from participating in society.

Also think about the difference between fingerprint unlock for releasing a digital ID vs Face ID. With a fingerprint, you're creating a limit on what people will tolerate in terms of the number of times their ID is queried. With Face ID, people will tolerate a much larger volume. If the biometric ID is cached and allows multiple uses of a digital ID within X minutes, the number goes even higher. With a watch that's unlocked until you take it off your wrist, it's unlimited.

So, if you're working on these systems, consider there's more than just an algorithm and the implementation can leverage what the average person will tolerate to act as a bit of a check on the system. The fingerprint unlocking above is a good example where 1 fingerprint scan = 1 proof. People can understand that. Please don't build a system that allows for continuous identification.

Thanks for trying to explain some of the goals and how the system actually works. It's really hard to separate the politics from the technology, because they can't be separated, but I find it helps to have a better understanding of the technology as it helps when trying to focus on pragmatic concerns.

[Terr_]

> Eventually there's going to be enough pretense to expand the system and block "non-compliant" sites. Why not use the same DOCUMENT to prove age to buy beer? Sanity for guns? Loyalty for food?

You're not wrong to be concerned about those impulses, but I think this is getting into "perfect is the enemy of good" territory.

A really authoritarian government isn't going to make an effort to misuse the system that way: They'll tear it down entirely and go back to worse-alternatives which we already use, where they do know all parties involved and exactly when and what was being checked.

[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.

[hunter2_]

> the government [...] only know[s] that I needed to verify an assertion about my age

This is problematic if a majority of things needing age verification are looked down upon; for example, insurance companies would love to know what people don't do things needing age and therefore don't buy alcohol (at least not online).

[cycomanic]

The first question is how would the insurance find out that you are doing lots of things requiring age verification? The only body that could tell them is the government, while a distrust in the government can be healthy, I think this is the least thing to worry about, the government typically knows already much more damaging things than how often you ask for age verification.

Moreover, that would only work if there are relatively few things that require age verification and it needs more than just being looked down upon, i.e. while alcohol buying might be interesting information for insurances, watching porn is likely less interesting. Even worse, if the insurance can't distinguish between porn and alcohol (which they can't by design even if the government would give them the information about how often you ask for age verification).

[notpushkin]

I would throw in Privacy Pass [1], just in case the government and SickBooze.com can exchange info.

Sadly, it‘s still hard to explain how exactly it works, but conceptually simpler than arbitrary ZKPs.

[1]: https://privacypass.github.io/

[shermanyo]

Excellent, clear example.

[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.

[sdwr]

> 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.

That's the bit I was missing! The prover pre-registers the scrambled solution, so they can't cheat by making up values that fit the constraints.

[MatteoFrigo]

Yes. The whole trick is a delicate balance between 1) committing to enough information that uniquely pins down the solution, assuming that one can open all the lock boxes, and 2) not opening too many lock boxes so that the verifier does not learn the solution.