Concise Vector Commitments and their Applications to Zero-Knowledge Elementary Databases

Zero knowledge sets (ZKS) [18] allow a party to commit to a secret set S and then to, non interactively, produce proofs for statements such as x ∈ S or x /∈ S. As recognized in [10], the key ingredient of ZKS is a primitive called (trapdoor) mercurial commitment. This primitive was later generalized by Catalano, Fiore and Messina [9] who proposed the notion of (trapdoor) q-Mercurial Commitment (q-TMC for short) which allows to (mercurially) commit to vectors of q messages, rather than to single messages. This property is interesting as openings of specific vector positions can be made short and independent from q. Moreover, Catalano et al. show that one can get Compact Zero Knowledge Sets (i.e. ZKS with very short proofs) when combining q-TMC with a Merkle tree of branching degree q. The first construction of q-TMC with constant size openings, however, was proposed only very recently, by Libert and Yung in [16]. Their solution relies on the q-Diffie-Hellman Exponent assumption ov...

• Type: Journal
• Year: 2011
• Where: IACR
• Authors: Dario Catalano, Dario Fiore
• Keywords: Cdh, IACR 2011, Knowledge Sets, Zero Knowledge