The KDM CCA Security of the Kurosawa Desmedt Scheme

In this letter, we prove that the Kurosawa-Desmedt (KD) scheme, which belongs to the hybrid framework,is KDM-CCA secure w.r.t. an ensemble proposed by Qin et al. under the decisional Diffie-Hellman assumption. Since our proof does not rely on the random oracle model, we partially answer the question