Cryptographic Algorithms and Computational Complexity: A Mathematical Approach to Securing IT Networks

Abstract

Cryptographic algorithms are at the core of IT network protection through data confidentiality, integrity, and authentication. This study explores the computational efficiency and complexity of four cryptographic algorithms: Advanced Encryption Standard (AES), Rivest-Shamir-Adleman (RSA), Lattice-Based Cryptography (LBC), and Hyperelliptic Curve Cryptography (HECC). The investigation compares these algorithms using encryption time, decryption time, key generation time, and security strength. Experiment outcome shows that AES has the optimal encryption time of 2.3 ms for real-time applicability and that RSA has the maximum encryption time of 15.7 ms, emphasizing computational overhead. LBC, which is a promising post-quantum cryptographic method, offers strong security with an average encryption time of 8.9 ms, while HECC offers balance between security and efficiency with an encryption time of 5.4 ms. A comparative analysis shows that lattice-based encryption is most fitting for future quantum-resistant security use and that AES is best used for high-speed encryption. The research emphasizes the need for choosing proper cryptographic algorithms in accordance with security needs and computational efficiency. Research in the future should also be aimed at hybrid cryptographic models and AI-based encryption methods to improve security in the future IT infrastructure.