  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.
