We present position-hiding linkability for vector commitment schemes: one can prove in zero knowledge that one or m values that comprise commitment cm all belong to the vector of size N committed to in C.

Vector commitments (VC) are a cryptographic primitive that allow 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.

We revisit the notion of Witness Authenticated Key Exchange (WAKE) where a party can be authenticated through a generic witness to an NP statement. We point out shortcomings of previous definitions, protocols and security proofs in Ngo et al.