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The core of this program is mathematics at its purest, encompassing abstract algebra, linear algebra, and discrete mathematics with cryptology as a bridge to applied mathematics. It is through cryptology, which has in recent years become deeply embedded in many aspects of society, that the most abstract mathematical ideas find a fruitful reflection in real-life applications where security remains an imperative. Continued advances in cryptology are required to expand robust security measures for data storage, transmission, and verification. Indeed, as digital technologies advance and become more widespread the data they collect, create, process, and store the demand for security is increasing dramatically. The novelty of this research program is its approach to advancing the state of the art in cryptology research and while embedding new advances in connected fields by leveraging IoT, blockchain, and discrete mathematics.