  Coherent-one-way (COW) quantum key distribution (QKD) is a significant
communication protocol that has been implemented experimentally and deployed in
practical products due to its simple equipment requirements. However, existing
security analyses of COW-QKD either provide a short transmission distance or
lack immunity against coherent attacks in the finite-key regime. In this paper,
we present a tight finite-key security analysis within the universally
composable framework for a variant of COW-QKD, which has been proven to extend
the secure transmission distance in the asymptotic case. We combine the quantum
leftover hash lemma and entropic uncertainty relation to derive the key rate
formula. When estimating statistical parameters, we use the recently proposed
Kato's inequality to ensure security against coherent attacks and achieve a
higher key rate. Our paper confirms the security and feasibility of COW-QKD for
practical application and lays the foundation for further theoretical study and
experimental implementation.
