Wasp: Succinct Non-Interactive Zero-Knowledge Proofs from VOLE

Zero-knowledge proofs (ZKPs) based on vector oblivious linear evaluation (VOLE) excel in prover efficiency but typically require linear communication and verification. Antman (Weng et al., CCS '22) introduced information-theoretic polynomial authentication codes (IT-PACs) to achieve sublinear communication: $O(B + C)$ for SIMD (single-instruction-multiple-data) circuits and $O(B^3 + C)$ for general circuits, where $N=B \cdot C$ is the total circuit size and $B,C$ are batch size and subcircuit size, respectively. Antman++ (Bui et al., J. Cryptol. '25) further reduced the general-case communication to $O(B + C)$. However, these protocols remain interactive and cannot be made non-interactive via traditional techniques like Fiat-Shamir, due to limited functionalities of IT-PACs; also, the verifier of Antman++ is not succinct for processing $N\times N$ public matrices.

In this work, we present a succinct non-interactive ZKP system $\mathsf{Wasp}$. Specifically, (1) we enhance the IT-PAC primitive to a fully functional polynomial commitment scheme (PCS) with the support of generic evaluation openings. With this PCS, we construct $\mathsf{Wasp^S}$, a non-interactive ZKP for SIMD circuits based on Antman; also, we build $\mathsf{Wasp^G}$, a general zkSNARK with constant verifier time and proof size based on the Plonkish constraint system. (2) We optimize the SIMD-to-general compiler from Antman++ by exploiting sparse representation of matrices and extending preprocessing techniques to the SIMD setting, and achieve a sublinear verifier. All our protocols achieve non-interactivity in the VOLE-hybrid model (i.e., given preprocessed VOLE correlations). Experiments show the non-interactive verifier of our SIMD zkSNARK $\mathsf{Wasp^S}$ is $1\sim 2$ orders of magnitude faster than the interactive one of Antman; when compiled with our compiler, the general-case verifier is $2\sim 3$ orders of magnitude faster than the one in Antman++. Our general zkSNARK $\mathsf{Wasp^G}$ has a $1\sim 2$ orders of magnitude faster prover than pairing-based, coding-based and lattice-based zkSNARKs, with less than 1 ms verifier time and 122 KB proof size; compared to the non-succinct VOLE-based ZKP, $\mathsf{Wasp^G}$ is $3\sim22\times$ slower in proving but can be 4 orders of magnitude faster in verification with $3$ orders of magnitude smaller proof size.