Linear-map Vector Commitments and their Practical Applications.

Vector commitments (VC) are a cryptographic primitive that allows one to commit to a vector and then "open" some of its positions efficiently. Vector commitments are increasingly recognized as a central tool to scale highly decentralized networks of large size and whose content is dynamic. In this work, we examine the demands on the properties that a vector commitment should satisfy in the light of the emerging plethora of practical applications and propose new constructions that improve the state-of-the-art in several dimensions and offer new tradeoffs. We also propose a unifying framework that captures several constructions and we show how to generically achieve some properties from more basic ones. On the practical side, we focus on building efficient schemes that do not require a new trusted setup (we can reuse existing ceremonies for other pairing-based schemes, such as "powers of tau" run by real-world systems such as Zcash or Filecoin).