College of Arts and Sciences
cryptography, coding theory, post-quantum, cryptosystem
Algebra | Algebraic Geometry | Number Theory | Other Mathematics
Matsick, Bethany, "Codes, Cryptography, and the McEliece Cryptosystem" (2020). Senior Honors Theses. 973.
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 for increased security. Finally, we develop a family of twisted Hermitian codes that meets the criteria set forth for security.
Algebra Commons, Algebraic Geometry Commons, Number Theory Commons, Other Mathematics Commons