3GPP 33.246 proposes Key Management Mechanism (KMM) to distribute security keys for Universal Mobile Telecommunications System (UMTS) Multimedia Broadcast and Multicast Service (MBMS). KMM introduces extra communication overhead to UMTS. The previous study, Key-Tree Scheme (KTS), resolves this issue for the IP multicast network. However, this scheme may not be so efficient while applied in UMTS MBMS due to lots of storage space and heavy multicast traffic introduced, which may decrease the QoS of UMTS MBMS. In this paper, we propose a more efficient scheme, Hash Function Scheme (HFS), to release both storage and communication overhead for KMM in UMTS MBMS. We first modify the KTS applied in the UMTS MBMS and then detail the execution of HFS, which is proven to be correct. We conduct an analytical model and simulation experiments to compare the performance between the UMTS KMM with KTS and with HFS. Our study shows that the proposed HFS can reduce both communication and storage overhead...