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ZKP学习笔记

ZK-Learning MOOC课程笔记

Lecture 8: FRI-based Polynomial Commitments and Fiat-Shamir (Justin Thaler)

8.2 FRI (Univariate) Polynomial Commitment

  • Recall: Univariate Polynomial Commitments

  • Initial Attempt from Lecture 4 (Merkle Tree)

  • Fixing the first problem (Want P time linear in degree, not field size)

  • Biger blowup factor -> more prover time, less verifier time, shorter proofs
  • The key subset: roots of unity

  • Example

  • Fixing the second problem

    • Merkle tree does not tell you any structure of the vertor at all

    • The (interactive) low-degree test: Folding Phase

      • Example

    • The (interactive) low-degree test: Query Phase

  • Back to the folding phase: more details

    • The (interactive) low-degree test: Folding Phase

  • Example

  • The (interactive) low-degree test: Folding Phase

  • Compare to Lecture 7

本文标签： FRIUnivariatecommitmentPolynomial

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