College of Arts and Sciences
Computer Science; Mathematics
Cryptography, Algebra, Fields, McEliece, Quantum, Post-Quantum
Algebra | Applied Mathematics | Computer Sciences | Mathematics | Quantum Physics
Hanna, Isaac, "The McEliece Cryptosystem as a Solution to the Post-Quantum Cryptographic Problem" (2023). Senior Honors Theses. 1342.
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.