Paper 2026/683

VEIL: Lightweight Zero-Knowledge for Hash-Based Multilinear Proof Systems

Abstract

As efficient proof systems mature rapidly, more practical use cases that require zero-knowledge (ZK) guarantees are arising. Adding ZK typically requires either composing the non-zk base system with an expensive zk one that proves correctness of the cryptographic hashes performed by the base verifier, or alternatively making tightly coupled modifications to every component of the base protocol. We introduce VEIL, a lightweight and non-intrusive compiler for hash-based multilinear proof systems. VEIL achieves ZK without these drawbacks. Our approach decouples the protocol's algebraic interactions from the cryptographic hashing and applies a ZK wrapper solely to the algebraic components. This results in a simple, plausibly post-quantum, protocol that achieves a minimal prover overhead of $(1+o(1))$, while maintaining the architectural integrity of the base proof system. Our proof-of-concept implementation demonstrates that, over a $31$-bit base prime field, for a trace of $2^{29}$ field elements, compared to the non-zk proof system, VEIL has a prover overhead of about $3\%$, verifier overhead of $22\%$ and proof-size overhead of $12\%$.

Note: minor technical fixes: clarification in zk-code examples, fix in circuit-eval scheme to make it fully zk instead of statistically zk