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With the rapid development of cognitive radios, spectrum efficiency in cognitive radio networks (CRN) has increased by secondary users (SU) accessing the licensed spectrum dynamically and opportunistically without creating harmful interference to primary users. However, the performance and security of CRN is considerably constrained by its limited power, memory and computational capacity. Fortunately, the advent of cloud computing has the potential to mitigate these constraints due its vast storage and computational capacity. In this paper, we propose secure radio resource management algorithm for CRN where cloud computing unit stores the spectrum occupancy information of heterogeneous wireless networks in CRN and facilitates the access of spectrum opportunities for secondary users. The proposed algorithm leverages the geolocation of secondary user and idle licensed bands to facilitate the secure allocation of radio resources to SU. Furthermore, the secondary users who provide high benefit are admitted while satisfying the quality of service (QoS) requirement of secondary users in terms of data rate and service time. We also present the design to implement the proposed algorithm on Cloud computing platform, and propose a scalable mapping method under the Storm, real time processing model to dynamically partition the geographical area according to the SU density. Simulation results are presented to demonstrate the performance of the proposed secure radio resource management algorithm.