Notes from Lecture 4 of ZKP MOOC.

Interactive Proofs:

  • complete
  • statistical soundness: prover is computationally unbounded

arguments vs proofs: in arguments, as in SNARKs, prover is computationally bounded, specifically polynomial time while in proofs, prover is unbounded.

Another comparison in circuit satisfiability problem is difference between soundness and knowledge soundness. where, soundness means, prover is trying to prove existence of a valid which satisfies the circuit whereas in knowledge soundness, prover knows . There can be cases where one make sense over the other. For example: soundness is needed when sends along with input to check whether input satisfies. Knowledge soundness is needed when Prover has a secret along with computation, like proving knowledge of private key to a wallet.

Creating SNARK from Interactive proof:

  • simply sending the input to the verifier with circuit C to check the computation, not a SNARK as proof size too large and verification time too much.
  • sending to , and sending an IP to verify satisfies . Proof size might still be too big.


Sumcheck Protocol