What is zk-snark?
- Zero-knowledge: A verifier can validate the integrity of a statement without knowing anything else about the statement. The only knowledge the verifier has of the statement is whether it is true or false.
- Succinct: The zero-knowledge proof is smaller than the witness and can be verified quickly.
- Non-interactive: The proof is ‘non-interactive’ because the prover and verifier only interact once, unlike interactive proofs that require multiple rounds of communication.
- Argument: The proof satisfies the ‘soundness’ requirement, so cheating is extremely unlikely.
- (Of) Knowledge: The zero-knowledge proof cannot be constructed without access to the secret information (witness). It is difficult, if not impossible, for a prover who doesn’t have the witness to compute a valid zero-knowledge proof.
State-of-art
Proof and verifier time are sublinear to the circuit size
ZKP MOOC Lecture 2: Overview of Modern SNARK Constructions (youtube.com)

ZK Terminology