Foundational Algorithms for Modern Cybersecurity: A Unified Review on Defensive Computation in Adversarial Environments

Cyber defense has evolved into an algorithmically intensive discipline where mathematical rigor and adaptive computation underpin the robustness and continuity of digital infrastructures. This review consolidates the algorithmic spectrum that supports modern cyber defense, from cryptographic primitives that ensure confidentiality and integrity to behavioral intelligence algorithms that provide predictive security. Classical symmetric and asymmetric schemes such as AES, ChaCha20, RSA, and ECC define the computational backbone of confidentiality and authentication in current systems. Intrusion and anomaly detection mechanisms range from deterministic pattern matchers exemplified by Aho-Corasick and Boyer-Moore to probabilistic inference models such as Markov Chains and HMMs, as well as deep architectures such as CNNs, RNNs, and Autoencoders. Malware forensics combines graph theory, entropy metrics, and symbolic reasoning into a unified diagnostic framework, while network defense employs graph-theoretic algorithms for routing, flow control, and intrusion propagation. Behavioral paradigms such as reinforcement learning, evolutionary computation, and swarm intelligence transform cyber defense from reactive automation to adaptive cognition. Hybrid architectures now merge deterministic computation with distributed learning and explainable inference to create systems that act, reason, and adapt. This review identifies and contextualizes over 50 foundational algorithms, ranging from AES and RSA to LSTMs, graph-based models, and post-quantum cryptography, and redefines them not as passive utilities, but as the cognitive genome of cyber defense: entities that shape, sustain, and evolve resilience within adversarial environments.