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Succinct Hash-Based Arbitrary-Range Proofs
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DOI：10.1109/TIFS.2024.3497806.png)
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Abstract
En 中文
-Zero-knowledge range proof (ZKRP) asserts that a committed integer V lies in a given range like [0, 2n - 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 10x 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 10x.
Keywords:
Lattices
Security
Sustainable development
Zero-knowledge range proof
post-quantum
inner product argument
hash-based proofs
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