SNARKs
Research
SNARKs
Vector Commitment soundness says that for an (adversarily chosen) C, a malicious prover can't open any index to conflicting values
Vector Commitment completeness says that if C is the commitment to a vector A (where vector a is known to the prover) the prover can produce a proof opening at every point in A that will be accepted by the verifier (for sure, with probability 1)
Vector commitment schemes must satisfy both correctness and soundness
Naive vector commitment: for a collision-resistant function H, commit to x as H(x). To open this commitment, reveal x.
There's often a link between the structure of a statement and the structure of its proof.