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Full-Text Articles in Algebra
Building An Algebraic Representation Of The Aes In Sage, Thomas Gagne
Building An Algebraic Representation Of The Aes In Sage, Thomas Gagne
Summer Research
First developed in 2001, the Advanced Encryption Standard (AES) cipher is now one of the most commonly used encryption algorithms worldwide. However, the algebraically simple description of the AES leads some cryptographers to question whether an algebraic weakness in the cipher exists, which would be fatal to the security of the AES. This summer, I studied the algebraic properties of the AES with the goal of designing a computational tool for researchers and algebraic cryptanalysts of the AES which would allow more rigorous study of the algebraic qualities of the AES. I accomplished this by implementing an algebraic representation of …
Finitely Presented Groups For The Undergraduate Algebra Student, Davis Shurbert
Finitely Presented Groups For The Undergraduate Algebra Student, Davis Shurbert
Summer Research
The concept of a finitely presented group is a topic which students do not normally see until graduate school. Through contributions to the open source computer algebra system Sage, I was able to accomplish my goal of making finitely presented groups more accessible to undergraduate students. Implementing this goal required a series of smaller tasks, all building together to expand the original framework regarding this type of group representation. I began my research by creating a catalogue of named groups easily accessible to the user as finitely presented group objects, along with a method to convert from a permutation group …