This dissertation emphasizes the security aspects of real-time media. The problems of existing real-time media protections are identified in this research, and viable solutions are proposed. First, the security of real-time media depends on the Secure Real-time Transport Protocol (SRTP) mechanism. We identified drawbacks of the existing SRTP Systems, which use symmetric key encryption schemes, which can be exploited by attackers. Elliptic Curve Cryptography (ECC), an asymmetric key cryptography scheme, is proposed to resolve these problems. Second, the ECC encryption scheme is based on elliptic curves. This dissertation explores the weaknesses of a widely used elliptic curve in terms of security and describes a more secure elliptic curve suitable for real-time media protection. Eighteen elliptic curves had been tested in a real-time video transmission system, and fifteen elliptic curves had been tested in a real-time audio transmission system. Based on the performance, X9.62 standard 256-bit prime curve, NIST-recommended 256-bit prime curves, and Brainpool 256-bit prime curves were found to be suitable for real-time audio encryption. Again, X9.62 standard 256-bit prime and 272-bit binary curves, and NIST-recommended 256-bit prime curves were found to be suitable for real-time video encryption.The weaknesses of NIST-recommended elliptic curves are discussed and a more secure new …

This dissertation presents spatial partitioning algorithms to solve location-allocation problems. Location-allocations problems pertain to both the selection of facilities to serve demand at demand points and the assignment of demand points to the selected or known facilities. In the first part of this dissertation, we focus on the well known and well-researched location-allocation problem, the "p-median problem", which is a distance-based location-allocation problem that involves selection and allocation of p facilities for n demand points. We evaluate the performance of existing p-median heuristic algorithms and investigate the impact of the scale of the problem, and the spatial distribution of demand points on the performance of these algorithms. Based on the results from this comparative study, we present guidelines for location analysts to aid them in selecting the best heuristic and corresponding parameters depending on the problem at hand. Additionally, we found that existing heuristic algorithms are not suitable for solving large-scale p-median problems in a reasonable amount of time. We present a density-based decomposition methodology to solve large-scale p-median problems efficiently. This algorithm identifies dense clusters in the region and uses a MapReduce procedure to select facilities in the clustered regions independently and combine the solutions from the subproblems. Lastly, …