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Here is quote from gnark documenation.

Note that careful consideration must be given to this step in production environment. groth16.Setup uses some randomness to precompute the Proving and Verifying keys. If the process or machine leaks this randomness, an attacker could break the ZKP protocol.

It sounds like there is some randomness in setup process. I would share Verifying key. So it is more like PublicKey. But do I have to keep Proving key in secret and desctoy it later?

PS Are Prover and Verifier keys are something that is called "public paramters" ?

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Yes. Prover key can be public.

https://consensys.net/blog/developers/introduction-to-zk-snarks/

The key generator G takes a secret parameter lambda and a program C, and generates two publicly available keys, a proving key pk, and a verification key vk.

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