Zero-knowledge proofs (ZKPs) are widely applied in digital economies, such as cryptocurrencies and smart contracts, for establishing trust and ensuring privacy between untrusted parties. However, almost all ZKPs rely on unproven computational assumptions or are vulnerable to quantum adversaries. We propose and experimentally implement an unconditionally secure ZKP for the graph three-coloring problem by combining subset relativistic bit commitments with quantum nonlocality game. Our protocol achieves a linear relationship between interactive rounds and the number of edges, reducing round complexity and storage requirements by thirteen orders of magnitude, thereby significantly enhancing practical feasibility. Our work illustrates the powerful potential of integrating special relativity with quantum theory in trustless cryptography, paving the way for robust applications against quantum attacks in distrustful internet environments.

翻译：零知识证明（ZKPs）在数字经济（如加密货币和智能合约）中被广泛应用，用于在不可信方之间建立信任并确保隐私。然而，几乎所有ZKPs都依赖于未经证明的计算假设，或易受量子对手攻击。我们提出并通过实验实现了一种针对图三着色问题的无条件安全ZKP，其方法是将子集相对论比特承诺与量子非局域性博弈相结合。我们的协议实现了交互轮数与边数之间的线性关系，将轮复杂度和存储需求降低了十三个数量级，从而显著提升了实际可行性。我们的工作展示了将狭义相对论与量子理论结合在无信任密码学中的巨大潜力，为在不可信的互联网环境中抵御量子攻击的鲁棒应用铺平了道路。