Implementasi Kode Goppa dalam Kriptosistem McEliece untuk Keamanan Data Terhadap Serangan Kuantum

Abstract

The importance of data security in the digital era is growing, particularly in the face of quantum computing threats against classical cryptographic algorithms. One of the main candidates for post-quantum cryptography is the McEliece cryptosystem, which employs error-correcting codes to enhance encryption strength. This study implements Goppa codes within the McEliece cryptosystem to increase resistance against quantum attacks. A degree-two polynomial over a finite field with sixteen elements was used, resulting in code parameters with a length of twelve, a dimension of four, and the ability to correct two errors. Encryption is carried out by multiplying the binary message with the public key and adding a random error vector, while decryption utilizes the private key to correct errors through syndrome calculation. The results demonstrate that employing Goppa codes enhances system security by complicating the ciphertext structure, thereby strengthening resilience against quantum-based attacks. This implementation confirms that classical coding techniques remain relevant and effective in supporting modern cryptography.