Protocol-level description and self-contained security proof of decoy-state BB84 QKD protocol

In this paper, we present a flowchart-based description of the decoy-state BB84 quantum key distribution (QKD) protocol and provide a step-by-step, self-contained information-theoretic security proof for this protocol within the universal composable security framework. As a result, our proof yields a key rate consistent with previous findings. Importantly, unlike all the prior security proofs, our approach offers a fully rigorous and mathematical justification for achieving the key rate with the claimed correctness and secrecy parameters, thereby representing a significant step toward the formal certification of QKD systems.