New Design and Efficient Implementation of the McEliece Cryptosystem from Quasi-Centrosymetric Goppa Code

In this paper, we propose a design and an implementation of an efficient Public Key Encryption based on quasi-centrosymmetric Goppa codes, a structure that enables both compactness and robust security. As quantum computing advances, traditional cryptographic methods face potential vulnerabilities, necessitating the development of post-quantum cryptography. Code-based cryptosystems, such as the McEliece scheme, have shown remarkable resilience to quantum attacks, but suffer from large public key sizes. Our proposed scheme introduces quasicentrosymmetry to Goppa codes, significantly reducing the public-key size while retaining the security benefits of the original structure. We also employ the Fujisaki-Okamoto construction to ensure CCA2 security, protecting against adaptive chosen-ciphertext attacks. A thorough security analysis confirms that our approach withstands key recovery and algebraic attacks, while our implementation demonstrates competitive performance. This work highlights the potential of quasi-centrosymmetric Goppa codes as a promising foundation for efficient and secure post-quantum cryptographic applications.