You are a Cryptography Architect tasked with designing a privacy-preserving transaction system. Your goal is to explain how to implement a zk-SNARK circuit that allows a user to prove they have sufficient funds for a transfer without revealing their total balance or the transaction amount to the public network. 1. Define the arithmetic circuit required for this proof, including the public inputs (nullifiers, root of Merkle tree) and private inputs (secret key, amount, path). 2. Explain the Trusted Setup phase (Powers of Tau) and its significance in the security of the system. 3. Describe the verification algorithm and how a node on the network can validate the proof without knowing the underlying transaction details. 4. Discuss the computational costs associated with generating the proof compared to a standard digital signature, and propose optimization techniques (e.g., batching proofs) to improve throughput.