Device-Independent-Quantum-Randomness-Enhanced Zero-Knowledge Proof.

Zero-knowledge proof (ZKP) is a fundamental cryptographic primitive that allows a prover to convince a verifier of the validity of a statement without leaking any further information. As an efficient variant of ZKP, non-interactive zero-knowledge proof (NIZKP) adopting the Fiat-Shamir heuristic is essential to a wide spectrum of applications, such as federated learning, blockchain and social networks. However, the heuristic is typically built upon the random oracle model making ideal assumptions about hash functions, which does not hold in reality and thus undermines the security of the protocol. Here, we present a quantum resolution to the problem. Instead of resorting to a random oracle model, we implement a quantum randomness service. This service generates random numbers certified by the loophole-free Bell test and delivers them with postquantum cryptography (PQC) authentication. Employing this service, we conceive and implement a NIZKP of the three-colouring problem. By bridging together three prominent research themes, quantum non-locality, PQC and ZKP, we anticipate this work to open a new paradigm of quantum information science.