Publication Date
2023
School
College of Arts and Sciences
Major
Computer Science; Mathematics
Keywords
Cryptography, Algebra, Fields, McEliece, Quantum, Post-Quantum
Disciplines
Algebra | Applied Mathematics | Computer Sciences | Mathematics | Quantum Physics
Recommended Citation
Hanna, Isaac, "The McEliece Cryptosystem as a Solution to the Post-Quantum Cryptographic Problem" (2023). Senior Honors Theses. 1342.
https://digitalcommons.liberty.edu/honors/1342
Abstract
The ability to communicate securely across the internet is owing to the security of the RSA cryptosystem, among others. This cryptosystem relies on the difficulty of integer factorization to provide secure communication. Peter Shor’s quantum integer factorization algorithm threatens to upend this. A special case of the hidden subgroup problem, the algorithm provides an exponential speedup in the integer factorization problem, destroying RSA’s security. Robert McEliece’s cryptosystem has been proposed as an alternative. Based upon binary Goppa codes instead of integer factorization, his cryptosystem uses code scrambling and error introduction to hinder decrypting a message without the private key. This cryptosystem cannot be reduced to the hidden subgroup problem and stands as a viable post-quantum alternative to RSA encryption.
Included in
Algebra Commons, Applied Mathematics Commons, Computer Sciences Commons, Quantum Physics Commons
