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Constructing a zk-SNARK Circuit

#cryptography #blockchain #zero-knowledge

Design the logic for a zero-knowledge proof circuit.

Explain the process of constructing an arithmetic circuit for a zk-SNARK that proves knowledge of a discrete logarithm without revealing it. Specifically, detail how to convert the statement 'I know x such that y = g^x' into Rank-1 Constraint System (R1CS) constraints, including the definition of the witness vector and the matrices A, B, and C.