Implementation of A New Quasi-Cyclic Goppa Code in McEliece Cryptography

Cryptography is fundamental in ensuring data privacy and security in the digital age. It provides the necessary tools and techniques for building trust and maintaining the confidentiality, integrity, and authenticity of data. The advancement of information technology could both act as catalyst for improvements as well as new threats to cryptography. For example, quantum computers have the potential to break public key algorithms whose hardness are based on integer factorization or discrete logarithm problems, like the ubiquitous RSA and ECC. NIST has been conducting a standardization process for Post-Quantum Cryptography, which are cryptographic algorithms proven secure against attacks by quantum computers. One of the candidates in the ongoing fourth round is Classic McEliece, that uses error-correcting code in its encryption and decryption process. It has a fast encryption and decryption algorithms, but a relatively large key size. One of the attempts to reduce the size is by choosing separable quasi-cyclic Goppa codes. This research implemented a new subclass of Goppa codes having separable polynomial, quasi-cyclic property, and improved lower bounds for its dimension and minimum distance. Two error vectors were chosen for the implementation in McEliece with different weight to see if the improved minimum distance leads to more bits in the error vectors that could be corrected.