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Efficient Hash Family Creation and Implementation

The goal of this research project is to create the largest Perfect Hash Families (PHF) possible in the most efficient manner while simultaneously maximizing the efficiency of the system in which they are being implemented. A PHF is an array in which any selection of t-columns, the degree of separation, will always contain at least

Randomized Construction of Homogeneous Scattering Hash Families

The goal of this research is to explore the homogeneous property of scattering hash families, which is very useful for creating broadcast encryption schemes, and other areas of computer security. This research is looking at the construction of homogenous scattering hash families and methods for improving the probability that an array is both homogeneous and

Efficient Algorithms for the Construction of Low-Density Parity-Check Codes

Low-density parity-check (LDPC) codes are a form of high performance error-correcting codes with a substantial number of theories developed for their uses in classical and quantum systems. However, practical applications have been limited by the difficulty of finding good LDPC codes for specific parameters. The objective of this research is to devise efficient algorithmic methods