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How Do I Prove I Know The Answer to x²-x-42, Without Giving You The Answer?

We give away too much of our data. Why should we give away our password every single time that we log into a system? Why can’t we just prove that we still know it? Thus Victor (the verifier) can prompt Peggy (the prover) with a puzzle, and where she can show that she can solve it. This is the method that zero-knowledge proof (ZKP) uses to prove things. In this…