Succinct Hash-Based Arbitrary-Range Proofs

Abstract

Zero-knowledge range proof (ZKRP) asserts that a committed integerVlies in a given range like$[{0, 2^{n}-1}]$without other leakages ofV. It is vital in various privacy-preserving systems. Moving forward, the quest for post-quantum security is still in its infancy; the proof size of state-of-the-art lattice-based ZKRP (Lyubashevsky et al., CCS 20 and Couteau et al., Eurocrypt 21) remains linear inn, directly impacting the long-term sustainability in applications such as immutable ledgers. Confronting this unresolved impasse, we propose SHARP-PQ,i.e., succinct hash-based arbitrary-range proof with post-quantum security. SHARP-PQ offers proof size poly-logarithmic ton, optimized batch proofs, and versatile (new) capabilities. Its success stems from the improved inner product argument and exploitation of homomorphism. Empirically, SHARP-PQ features at least$10\times $smaller proof size for multiple ranges over lattice-based ZKRPs while maintaining competitive prover and verifier times. SHARP-PQ also outperforms ZKRPs directly constructed from hash-based generic zero-knowledge proofs at most$10 \times $.