McEliece Cryptosystem with Hidden Goppa Codes
Exploration of the original McEliece public-key cryptosystem, including a from-scratch implementation in SageMath. Studied the role of binary Goppa codes as a candidate for post-quantum security.
Sep 2023 - May 2024 • 8 months
Tech Stack
SageMathCoding TheoryPost-Quantum Cryptography
Summary
The McEliece cryptosystem (1978) is one of the oldest public-key schemes still considered secure against quantum adversaries. Its security rests on the hardness of decoding general linear codes — specifically, the indistinguishability of disguised Goppa codes from random ones.
This project covers:
- The mathematical structure of binary Goppa codes
- McEliece key generation, encryption, and decryption
- A SageMath implementation suitable for pedagogical study
- A reading of the security argument and known structural attacks
Presented as an abstract titled “Analysis of Goppa Code Scheme on Post-Quantum Cryptography” at ICT-CEEL 2023.