These are my notes and are not written in an article form

• Interactive protocol
• Fiat Shamir transform to convert IP to SNARK

Prove that -

1. I know pre image of hash function
2. My encrypted transaction is a well formed transaction

SNARK

Key terms

1. Arithmetic circuit, C

2. Public statement, x

3. Secret witness, w

4. Pre- processing setup, S(C) → pp, vp, Reads the circuit and acts as a sort of Summary of Circuit C for verifier

5. pp - Prover public parameter

6. vp - Verifier public parameter

7. Prover inputs (pp, x, w)

8. Prover will generate proof $\pi$, Prover is proving that they know some witness, such that C(x,w) = 0

   1. Proof should be logarithmic (Or constant) in the size of circuit, C and it should also be sublinear to the size of w. Cannot send w and have a trivial proof

   2. Proof should be fast to verify, time is logarithmic to the size of circuit C and linear in the size of public statement x

      

9. Verifier gets (vp, x, $\pi$) to decide to accept to reject the proof

10. Random oracle - all these have access to Random oracle

Explain what is a Random Oracle