kate polynomial commitment scheme (pronounced kah-tay)
tl; dr
- it allows a prover to compute a commitment to a polynomial, with the properties that this commitment can later be opened at any position.
- the prover shows that the value of the polynomial at a certan position is equal to a claimed value.
- once a commitment (an elliptic curve point) is sent to the verifier, the prover cannot change the polynomial they are working with.
- a merkle tree is a "vector commitment": using a merkle tree of depth, you can compute a commitment to a list of elements of fixed length. using merkle proofs, you can provide a proof that an element is a member of this vector at position using hashes.
- in the kate commitment scheme, the element is the commitment to the polynomial: could the prover (without knowing) find another polynomial that has the same commitment.x
