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Full-Text Articles in Other Mathematics
Codes, Cryptography, And The Mceliece Cryptosystem, Bethany Matsick
Codes, Cryptography, And The Mceliece Cryptosystem, Bethany Matsick
Senior Honors Theses
Over the past several decades, technology has continued to develop at an incredible rate, and the importance of properly securing information has increased significantly. While a variety of encryption schemes currently exist for this purpose, a number of them rely on problems, such as integer factorization, that are not resistant to quantum algorithms. With the reality of quantum computers approaching, it is critical that a quantum-resistant method of protecting information is found. After developing the proper background, we evaluate the potential of the McEliece cryptosystem for use in the post-quantum era by examining families of algebraic geometry codes that allow …
Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, Richard M. Shumate
Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, Richard M. Shumate
Senior Honors Theses
Differential equations have bearing on practically every scientific field. Though they are prevalent in nature, they can be challenging to solve. Most of the work done in differential equations is dependent on the use of many methods to solve particular types of equations. Sophus Lie proposed a modern method of solving ordinary differential equations in the 19th century along with a coordinate free variation of finding the infinitesimal generator by combining the influential work of Élie Cartan among others in the field of differential geometry. The driving idea behind using symmetries to solve differential equations is that there exists a …