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If a trusted entity is required to attest to a user's data accuracy, what is the value-add of ZKP's?

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I think I understand the value of using ZKP's for proving things about data in isolated systems, like for privacy and computation roll-ups in blockchains L2's.

But I hear a lot about real-world use-cases, a classic example is proving your age is above a certain number, or proving your income to a mortgage lender, without revealing exact figures. While this sounds fantastic, in both these scenarios you need a trusted third party (government and bank respectively) to attest to the accuracy of the data you're trying to prove. Otherwise I could just make up an age and income.

Given this is the case, what is the value-add of ZKP here over just asking the trusted entity for a yes/no answer?

Is it that the trusted entity only has to provide a one-time signed data bundle which the user can prove things about "offline" without real-time reliance on a third party?

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