Due to their widespread applications in decentralized and privacy preserving technologies, commitment schemes have become increasingly important cryptographic primitives. With a wide variety of applications, many new constructions have been proposed, each enjoying different features and security guarantees. In this article, we systematize the designs, features, properties, and applications of vector commitments (VCs). We define vector, polynomial, and functional commitments and we discuss the relationships shared between these types of commitment schemes. We first provide an overview of the definitions of the commitment schemes we will consider, as well as their security notions and various properties they can have. We proceed to compare popular constructions, taking into account the properties each one enjoys, their proof/update information sizes, and their proof/commitment complexities. We also consider their effectiveness in various decentralized and privacy preserving applications. Finally, we conclude by discussing some potential directions for future work.
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