1. Zero-Knowledge Argument for Polynomial Evaluation with Applications to Blacklists Stephanie Bayer Jens Groth University College London TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAA

2. Polynomial

3. Zero-knowledge argument for correct polynomial evaluation ProverVerifier 

4. Membership and non-membership proofs

5. Zero-knowledge argument for correct polynomial evaluation ProverVerifier 3-move argument Easy to convert to full zero-knowledge

6. Commitment properties

7. Simple SHVZK argument for correct polynomial evaluation

8. Efficiency – using Pedersen commitments Degree D polynomialRoundsProverVerifierComm. Chaum and Ped. 19923 Brands et al. 20073 Degree D polynomialRoundsProverVerifierComm. This work3

9. Rewriting the polynomial

10. … …

11. Statement:

12. …

13. A helpful polynomial …

14. SHVZK argument for point on polynomial Accept if is inside … …

15. SHVZK argument for polynomial evaluation

16. Efficiency – using Pedersen commitments Degree D polynomialRoundsProverVerifierComm. This work3 Degree DRoundsProverVerifierComm. 10313 ms17 ms8 KB 100324 ms30 ms15 KB 1000341 ms45 ms21 KB 100003182 ms81 ms29 KB 10000031,420 ms217 ms35 KB 1000000315,512 ms1,315 ms41 KB 256-bit subgroup modulo 1536-bit prime on MacBook, 2.54 GHz