  A commitment scheme is a cryptographic tool that allows one to commit to a
hidden value, with the option to open it later at requested places without
revealing the secret itself. Commitment schemes have important applications in
zero-knowledge proofs and secure multi-party computation, just to name a few.
This survey introduces a few multivariate polynomial commitment schemes that
are built from a variety of mathematical structures. We study how Orion is
constructed using hash functions; Dory, Bulletproofs, and Vampire using the
inner-product argument; Signatures of Correct Computation using polynomial
factoring; DARK and Dew using groups of unknown order; and Orion+ using a
CP-SNARK. For each protocol, we prove its completeness and state its security
assumptions.
