The primary objective of this work is to develop an algorithm for detecting the secret round key used in encryption by analyzing a collection of plaintexts and ciphertexts encrypted with the three-round Kuznyechik algorithm. In addition, the fundamentals of using the integral cryptanalysis method for the Substitution-permutation (SP) network-based Kuznyechik encryption have been investigated. It has been found that the Kuznyechik three-round encryption algorithm is useful for creating a balanced set before the third round and an unbalanced set at the end of the round, using a set in which the first byte is active, and the remaining bytes are passive. Based on the findings above, an efficient algorithm to determine the key of the final round for the 3-round Kuznyechik algorithm is proposed utilizing the method of integral cryptanalysis. According to simulation results, the proposed approach offers approximately 90% improvement compared to baseline algorithms in terms of time complexity, data, and memory overhead.

Modern network infrastructures are under attack from increasingly sophisticated attacks that static, rule-based defenses cannot adequately mitigate. We introduce a multilayer anomaly detection and mitigation framework for Software-Defined Networking (SDN) environments consisting of four integrated subsystems: (i) a Micro-segmentation Integrated Management and Defense System (MIMDS), (ii) an Adaptive CNN-LSTM-Attention Deep Packet Inspection (MCLA-DPI) module, (iii) a Hybrid Adaptive Cyberattack Prediction (KBGM) framework, and (iv) an AI-driven log analysis pipeline. Detection, prediction and containment operate in parallel (as opposed to conventional approaches) and correlate results through a common risk-scoring mechanism to coordinate policy enforcement via OpenFlow and P4-compatible data planes. The experimental evaluation shows promising performance. MIMDS achieves 94.3%. detection accuracy with full traffic isolation in 10.1 s. MCLA-DPI achieves 98.9% classification accuracy with 14 ms inference latency, outperforming baseline models SVM and LSTM on encrypted traffic. KBGM achieves 98.4% detection accuracy with 7.2 ms mean response time on the CICIDS2017 dataset. All modules are trained in federated learning to preserve data locality with continuous improvements of the global model. The results collectively demonstrate quantifiable improvements over single-paradigm approaches in detection fidelity, response latency, resource efficiency, and privacy compliance. An ablation study isolates the contribution of integration itself. Removing the coordination layer while retaining all four detectors reduces accuracy from 0.892 to 0.634 and raises the false-positive rate from 0.031 to 0.436, while peak rule installation rises from 22.3 to 98.4 rules per second and oscillation events increase by two orders of magnitude; the integrated framework also exceeds its strongest individual subsystem, which reaches 0.831 accuracy at a false-positive rate of 0.117. These figures are obtained from the released reference implementation over a synthetic campaign and are reported separately from the component measurements.

This paper studies structural properties of semiprimes $N=pq$ in computational number theory, focusing on cases where the prime factors are close. We analyze the relationship between $\sqrt{N}$ and $\sqrt{\phi \left(N\right)}$ and show that, under a bounded prime gap condition, these quantities exhibit strong proximity. Specifically, assuming $|p-q|\le 2^{l/4}$ for an l-bit semiprime, we prove that the Euler totient function admits the exact representation $\phi \left(N\right)=N-1-2\lfloor \sqrt{N}\rfloor$. Based on this result, we develop an interval-based method for reconstructing $\phi \left(N\right)$ within a narrow neighborhood derived from square-root bounds, followed by a discriminant-based refinement step for recovering the prime factors. Experimental evaluation on large semiprimes, including RSA-type moduli of 4095 and 4096 bits, shows that the method operates efficiently under the stated structural condition using only elementary integer arithmetic. These results provide a theoretical characterization of semiprimes with small prime gaps and offer a framework for identifying structurally weak RSA moduli. This method, given its high efficiency when the prime factors are close to each other, can be regarded as an alternative to Fermat’s factorization method. In particular, for semiprime integers with a small prime gap (i.e., $|p-q|$ is small), the proposed approach exploits structural properties based on the proximity of square roots, thereby significantly accelerating the factorization process. Consequently, it not only aligns with the theoretical foundation of Fermat’s method but, under certain conditions, may also achieve comparable or even superior practical performance.