Fine-Grained Verifier NIZK and Its Applications

In this paper, we propose a new type of non-interactive zero-knowledge (NIZK), called Fine-grained Verifier NIZK (FV-NIZK), which provides more flexible and more fine-grained verifiability of proofs than standard NIZK that supports public verifiability and designated-verifier NIZK (DV-NIZK) that supports private verifiability. FV-NIZK has two statistically equivalent verification approaches: We require unbounded simulation soundness (USS) of FV-NIZK to hold, even if an adversary obtains derived secret keys $$sk_d$$ with d of its choices, and define proof pseudorandomness which stipulates the pseudorandomness of proofs for adversaries that are not given any secret key. We present two instantiations of FV-NIZK for linear subspace languages, based on the matrix decisional Diffie-Hellman (MDDH) assumption. One of the FV-NIZK instantiations is pairing-free and achieves almost tight USS and proof pseudorandomness. We illustrate the usefulness of FV-NIZK by showing two applications and obtain the following pairing-free schemes: