Enhancing Security: Combining Asymmetric Encryption with Error Correction 🔐

An analysis of modern research in the field of asymmetric cryptosystems is conducted, demonstrating the importance of developing algorithms capable of ensuring a high level of data protection in the context of emerging threats. Approaches to optimizing cryptographic systems have been explored, particularly the application and integration of error correction methods. A combined encryption algorithm is proposed, which integrates the RSA algorithm with the construction of Hamming codes in finite fields, enhancing the reliability of encryption and data protection. The computational complexity of the proposed algorithm is assessed, demonstrating that the encoding process does not increase overall complexity since the RSA decryption operation remains dominant. This confirms the approach's practical applicability in real systems. It also provides cryptographic resilience, effective error correction during data transmission, and enhances the ciphertext's resistance to cryptanalysis.