1. 21.11.2016 IP, (NON)ISOGRAPH and Zero Knowledge Protocol COSC 6111 Advanced Algorithm Design and Analysis Daniel Stübig

2. Presentation IP: What is it? Example of IP: ISOGRAPH & NONISOGRAPH Zero Knowledge Protocol: What is it and how does it work (Example)

3. Interactive proof system Prover Generates certificate unlimited computational resources Verifier Verify certificate bounded computation power Interaction.....

4. NP ProverVerifier Interaction Computates a wittness Validates the wittness witness

5. Definition (Graphisomorphism) G and H are isomorph if there exists a permutation π so that H = π(G)

6. ISOGRAPH ProverVerifier Interaction Computates a wittness Validates the wittness witness

7. Example of IP - NONISOGRAPH Graph VerifierProver permutation b‘ = b

8. Probability

9. Zero Knowledge A zero-knowledge proof must satisfy three properties: Completeness: if the statement is true, the honest verifier will be convinced of this fact by an honest prover. Soundness: if the statement is false, no cheating prover can convince the honest verifier that it is true (except with some small probability) Zero-knowledge: if the statement is true, no cheating verifier learns anything other than this fact. Important to cryptography application

10. Zero-knowledge protocol - Example … T he cave is shaped like a circle, with the entrance in one side and the magic door blocking the opposite side. Victor says he'll pay her for the secret, but not until he's sure that she really knows it. Peggy says she'll tell him the secret, but not until she receives the money. They devise a scheme by which Peggy can prove that she knows the word without telling it to Victor….

11. Example of Zero Knowlegde - ISOGRAPH Graph VerifierProver Π is the secret, b = a, a = 1 and b = 0, a = 0 and b = 1 G 0, G 1 are public We are done!

12. Questions