Implementation of McEliece Algorithm in Code-Based Cryptography

The McEliece algorithm is an asymmetric cryptosystem based on error-correcting codes, relying on the complexity of the syndrome decoding problem for its security. This study discusses the implementation of the McEliece algorithm using the Hamming(7,4) code in the encryption and decryption process of binary messages. Encryption is done by generating a public key consisting of a disguised generator matrix G′, a permutation matrix P, and a non-singular matrix SSS. The binary message is encrypted by adding controlled noise to increase security. In the decryption phase, the received message is processed using reverse permutation and error detection with a parity check matrix to recover the original message. Experiments are carried out by implementing the algorithm in Python, with results showing successful encryption and decryption of messages according to the McEliece theoretical framework. This study confirms that the Hamming code can be used as a simplified approach to the implementation of McEliece, although with security limitations compared to Goppa codes.