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Zero-Knowledge Argument for Polynomial Evaluation with Applications to Blacklists

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.: A A A A A A A A A A A A A. P olynomial.

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Zero-Knowledge Argument for Polynomial Evaluation with Applications to Blacklists

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  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 Statement: such that SoundnessStatement is true Zero-knowledgeNothing else revealed remains secret Witness  Prover Verifier

  4. Membership and non-membership proofs • List and • Define • If then • Prove where committed trivially • If then • Prove where and prove

  5. Zero-knowledge argument for correct polynomial evaluation Statement: such that Special honest-verifier zero-knowledgeGiven any challenge possible to simulate the argument Argument of knowledgeCan extract such that Witness 3-move argument Public coinVerifier picks challenge Easy to convert to full zero-knowledge Prover Verifier

  6. Commitment properties • Additively homomorphic • SHVZK argument for multiplicative relationship • Examples • Pedersen commitments • ElGamal-style commitments

  7. Simple SHVZK argument for correct polynomial evaluation Horner’s rule gives us Commit to the intermediate values and prove correct )

  8. Efficiency – using Pedersen commitments

  9. Rewriting the polynomial Prover wants to demonstrate Without loss of generality Write in binary to get

  10. Commit to powers of … … commitments and arguments

  11. Zero-knowledge argument of knowledge of power of KnowledgeAnswers to 2 challenges would reveal Zero-knowledge is uniformly random regardless of Statement: Witness Accept if opens to

  12. Masked powers of …

  13. Completeness If prover ok SoundnessIf prover fails A helpful polynomial … commitments

  14. SHVZK argument for point on polynomial Statement: such that … Accept if is inside Soundness …

  15. SHVZK argument for polynomial evaluation Statement: such that • 3-move public coin argument • Simple setup with commitment key • Perfect completeness • Comp. soundness based on discrete log. problem • Perfect special honest verifier zero-knowledge

  16. Efficiency – using Pedersen commitments 256-bit subgroup modulo 1536-bit prime on MacBook, 2.54 GHz

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