Byzantine Fault-Tolerant Post-Quantum Distributed Quorum Signatures

Threshold, aggregate, and multi-signatures -- which we collectively call quorum signatures -- certify that a quorum of nodes endorsed a statement, with a certificate as small as a single signature. No constant-size post-quantum quorum signature is known: all candidates grow with the number of signers and are slow to aggregate, making quorum signatures the hardest obstacle to migrating byzantine fault-tolerant systems to post-quantum security. In this paper, we sidestep this open cryptographic problem by changing how the protocol communicates. We introduce a primitive we call Distributed Quorum Signature (DQS), built solely from ordinary digital signatures and a Bracha-style approval broadcast. DQS turns certificates from network messages into local events. Two event types divide the roles certificates play: weak certificates capture safety, strong certificates capture liveness. In DQS every message is constant size, fitting a single datagram regardless of the number of nodes. The total communication is quadratic, and no security assumptions change. In a large distributed system, the overhead of post-quantum DQS is competitive with the canonical pre-quantum BLS scheme.