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.

Zero-knowledge SNARKs (zk-SNARKs) are non-interactive proof systems with short and efficiently verifiable proofs. zk-SNARKs are widely used in decentralised systems to address privacy and scalability concerns. One of the main applications is the blockchain, were SNARKs are used to prove computations with private inputs and reduce on-chain footprint verification and transaction sizes.