Topics in cryptography

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Cryptography is an essential component in secure systems. Applications include securing many types of networks, including various types of ad-hoc and wireless networks. Developing secure cryptographic protocols and algorithms in many diverse settings is an ongoing challenge as computers and networks become ever more prevalent and ubiquitous. I have had a long-term interest in the general topic of "unconditionally secure schemes'' in cryptography. These are schemes that can be proven secure without any computational assumptions. Unconditional security has a long history, dating back to the pioneering work of Shannon, and unconditionally secure schemes will likely play an increasingly important role in the future due to their built-in immunity from computational attacks by both quantum and conventional computers. Cryptographic research topics that are investigated in the setting of unconditional security include secret sharing schemes, key distribution schemes, broadcast encryption, and private information retrieval. I have interests in all these areas. This research proposal will investigate topics such as key predistribution in sensor networks, protocols for private information retrieval, secret sharing schemes, hash functions, and various problems in network security and efficiency.