Penerapan Kriptosistem Niederreiter Menggunakan Kode Goppa Biner untuk Mendukung Keamanan Data dalam Sistem Kriptografi Modern

Abstract

The advancement of modern cryptography presents new challenges posed by quantum computers, necessitating the development of stronger encryption processes. One of the post-quantum cryptographic methods capable of providing protection against such threats is the Niederreiter cryptosystem based on binary Goppa codes. In this study, binary Goppa codes are utilized in the formation of public and private keys, as well as in the decoding process. The implementation employs a specific polynomial over a finite field of order sixteen, resulting in code parameters with a length of 12, a dimension of 4, and the capability to correct up to two errors. Goppa codes are applied in the error correction process through syndrome calculation, enabling the detection and correction of erroneous bits and accurate recovery of the original message. The results demonstrate that binary Goppa codes are effective in detecting and correcting errors, thereby ensuring message integrity. This research is expected to contribute to the development of more robust cryptosystems for maintaining information confidentiality in the rapidly evolving digital era.