Assume the role of a cryptographer. Design a detailed Zero-Knowledge Proof (ZKP) protocol for user authentication on a decentralized network. Specify the mathematical primitives used (e.g., elliptic curve discrete log problem). Define the Prover, Verifier, and the Challenge-Response mechanism. Explain how this protocol prevents replay attacks, man-in-the-middle attacks, and ensures both completeness and soundness. Additionally, provide a pseudo-code implementation of the verification function and a security analysis discussing potential side-channel attacks. Avoid specific libraries; focus on the logic and mathematical structure.