ZKP Protocol Examples

Cryptography · Axiom Academy

Step-by-step walkthrough of Schnorr protocol and graph 3-coloring with concrete values Excellent work! You've completed the ZKP protocol examples. Here's what we learned: Schnorr Protocol Mechanics: The three-move protocol (commitment, challenge, response) allows proving knowledge of discrete log without revealing it. Each step has a specific mathematical purpose. Graph 3-Coloring as ZKP: By permuting colors and revealing only challenged edges, the prover demonstrates valid coloring without exposing the actual solution. This shows ZKPs work for NP-complete problems. Soundness Probability: A cheating prover succeeds with probability 1/2 per round in graph coloring, and exponentially small probability after multiple rounds. In Schnorr, a cheater would need to solve discrete log. Zero-Knowledge Property: The verifier learns nothing beyond validity: in Schnorr, the transcript can be simulated; in graph coloring, seeing two different colors on an edge reveals no global coloring information. These protocols demonstrate the power of interactive proofs: proving complex statements with minimal information leakage!

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