Publication Date
2020
School
College of Arts and Sciences
Major
Mathematics
Keywords
cryptography, coding theory, post-quantum, cryptosystem
Disciplines
Algebra | Algebraic Geometry | Number Theory | Other Mathematics
Recommended Citation
Matsick, Bethany, "Codes, Cryptography, and the McEliece Cryptosystem" (2020). Senior Honors Theses. 973.
https://digitalcommons.liberty.edu/honors/973
Abstract
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.
Included in
Algebra Commons, Algebraic Geometry Commons, Number Theory Commons, Other Mathematics Commons
