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MIT IAP 2023 Modern Zero Knowledge Cryptography课程笔记

Lecture 5: Commitment 2 (Ying Tong Lai)

  • Polynomial Commitment

    • f(x) = a 0 a_0 a0​ + a 1 x a_1x a1​x + a 2 x 2 a_2x^2 a2​x2 + … \dots … + a n x n a_nx^n an​xn

    • a i a_i ai​ is secret

    • commit(f,z,y) = C

    • The commitment proved that

      • f(z) = y
      • C is the commitment of f

    • KZG commitment scheme. It is used in protocols like Sonic, Marlin, and PlonK. (Marlin and PlonK improve on Sonic by constructing a different polynomial IOP.)

    • How to generate τ \tau τ (trusted setup)

      • Multiple-party computation
        • Each party generate a random beacon
        • Aggregate all beacons as τ \tau τ
        • No one knows τ \tau τ exceplt compeletly collusion

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