Kilian ZK Argument

Prover gives to verifier the root (and height) of Merkle tree and all children (and siblings) leading to desired leaf.

Goldreich Micali Wigderson

All of NP $\in$ computational ZK

3SAT NP Completeness

Albert Mayer (discovered by Larry Stokmayer)

Prover claims some graph is 3 colorable

Prover takes some permutation of the colors

Prover commits to every color and sends the commitment to the verifier

Verifier picks edge of G at random

Prover decommits two of the colors

Verifier can see that they’re different

Repeat this process starting with permutation