Zero-knowledge and succinctness are two important properties that arise in the study of non-interactive arguments. Previously, Kitagawa et al. (TCC 2020) showed how to obtain a non-interactive zero-knowledge (NIZK)
argument for NP from a succinct non-interactive argument (SNARG) for NP. In particular, their work demonstrates
how to leverage the succinctness property from an argument system and transform it into a zero-knowledge property.
In this work, we study a similar question of leveraging succinctness for zero-knowledge. Our starting point
is a batch argument for NP, a primitive that allows a prover to convince a verier of 𝑇 NP statements 𝑥1
𝑥𝑇
with a proof whose size scales sublinearly with 𝑇 . Unlike SNARGs for NP, batch arguments for NP can be built from
group-based assumptions in both pairing and pairing-free groups and from lattice-based assumptions. The challenge
with batch arguments is that the proof size is only amortized over the number of instances, but can still encode full
information about the witness to a small number of instances.
We show how to combine a batch argument for NP with a local pseudorandom generator (i.e., a pseudorandom
generator where each output bit only depends on a small number of input bits) and a dual-mode commitment scheme
to obtain a NIZK for NP. Our work provides a new generic approach of realizing zero-knowledge from succinctness
and highlights a new connection between succinctness and zero-knowledge.
