ZKP Mathematical Building Blocks 1

2023-12-20 16:54:47

MIT IAP 2023 Modern Zero Knowledge Cryptography课程笔记

Lecture 3: Mathematical Building Blocks (Yufei Zhao)

  • Example: I (Prover) want to convince you (Verifier) that I can distinguish two colors that you see as identical
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    • A Similar Example: How to prove two colors are different to a blind verifier
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    • What is a proof?

      • A proof is something that could convince someone else
      • Properties: completeness, soundness, zero-knowledge

    • What is the prover and the verifier (based on blockchain)

      • Prover: run on the regular computer (much more powerful than the verifier)
      • Verifier: run on the smart contract

  • Example: Hamilton cycle [Blum '87]

    • Hamilton cycle: a cycle can go through every vertex of the graph exactly once and return to the start
    • Everybody knows a graph
    • P knows a Hamilton cycle in the graph without revealing any additional information
    • Protocol
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  • ZKP Properties

    • Completeness: If everyone behaves then protocol accepts
    • Soundness: If there is no Ham cycle, then no matter what P does, V rejects with the probability of ≥ 1 2 \geq \frac{1}{2} ≥21?
      • There is a stronger requirement called knowledge soundness which says that even if the graph has a Ham Cycle , the prover doesn’t know it, the protocol will still fail. The precise definition involves an extractor with rewinding abilities.
    • Zero-knowledge: If V accepts then it learns no addl into from the interaction because V could have simulated the entire dialog by itself.

文章来源:https://blog.csdn.net/weixin_45347752/article/details/135108650
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