Only in theory, and only if you blindly trust a third party. The implementations in practice are still massive privacy violations.

what third party do you need? The program can be opensource. The verification can be done onchain

Is there any production ready implementation out there?

ZKP is integrated in Google Wallet and has been running in production for a few months. We (Google) released the ZKP library as open source last year (this is the library used in production).

Announcement: https://blog.google/innovation-and-ai/technology/safety-secu...

Library: https://github.com/google/longfellow-zk

Paper: https://eprint.iacr.org/2024/2010

Afterwards, folks from ISRG produced an independent implementation https://github.com/abetterinternet/zk-cred-longfellow with our blessing and occasional help. I don't know if the authors would call it "production ready" yet, but it is at least code complete, fast enough, and interoperable with ours.

Thanks. I'll have a look.