Black-Box Non-Interactive Zero Knowledge from Vector Trapdoor Hash.

We present a new approach for constructing non-interactive zero-knowledge (NIZK) proof systems from vector trapdoor hashing (VTDH) – a generalization of trapdoor hashing [Döttling et al., Crypto’19]. Unlike prior applications of trapdoor hash to NIZKs, we use VTDH to realize the hidden bits model [Feige-Lapidot-Shamir, FOCS’90] leading to black-box constructions of NIZKs. This approach gives us the following new results: The above constructions are black-box and satisfy single-theorem zero-knowledge property. Building on the works of Feige et al.(FOCS’90) and Fischlin and Rohrback (PKC’21), we upgrade these constructions (under the same assumptions) to satisfy multi-theorem zero-knowledge property at the expense of making non-black-box use of cryptography.