Succinct Hash-Based Arbitrary-Range Proofs

Zero-knowledge range proof (ZKRP) asserts that a committed integer V lies in a given range like $[{0, 2^{n}-1}]$ without other leakages of V. 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 in n, 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 to n, 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 $ .