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This seems to be what "double-blind" verification is doing:

> The report highlights emerging approaches, such as “double-blind” verification systems used in France, where websites receive only confirmation that a user meets age requirements without learning the user's identity, while the verification provider does not see which websites the user visits.

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It's a question of blind trust in your government to respect this, when they themselves control the age verification apps, at least in the EU who wants to impose its own system and not rely on an autonomous third party.
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It is cryptography. Just like you don't have to blindly trust Signal with end-to-end encryption (their client app is open source), it could be implemented in a way that you don't need to blindly trust your government.
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From a tech perspective it has been a solved problem since about a decade ago, via DID (decentralised identities) and their Verifiable Proofs.

The EU digital wallet framework is built around those, and your suggested scenario is a first class citizen.

It is now moving from the academic/research world, to the political field, and feedback/pressure from both commercial groups and political agendas is muddling the field.

Here are some links to canonical docs, you can easily find high quality videos that explain this is shorter/simpler terms to get a grasp of it.

https://www.w3.org/TR/did-1.0/

https://www.w3.org/TR/vc-data-model-2.0/

A note: it’s one of the healthy byproducts of the blockchain age, don’t get sidetracked by some hyped videos from crypto bros.

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It's a "solved problem" that didn't ever need solving in the first place.
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You are right, it is possible to do age verification in a privacy-preserving manner. Feels like most people being very vocal against the idea don't know about that.

At least most complaints I see here are assuming that age verification means tracking.

Too bad, there could be interesting discussions about privacy-preserving age verification, if people just bothered getting informed before complaining.

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We already have privacy preserving age verification: the website asks for your age (or just whether you're over 18), and lets you through.

There's no issuing party to collude with to deanonymize users, no hard requirement on owning a Google- or Apple-vetted smartphone, and generally no way to identify me besides my choice of random numbers.

You move past that, and people rightfully tell you that your scheme outright breaks privacy, or that it makes too many assumptions or is too complex to easily verify it actually preserves privacy.

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