An Enhanced 3D Haar Wavelet Approach for Parabolic Equations Involving Coupled Nonlinear Source Terms

Nadwah Najm  Hamzah

doi:10.17605/cajmns.v6i3.2824

Nadwah Najm Hamzah Department of Mathematics Numerical Analysis, Islamic Azad University, Isfahan (Khorasgan)Branch, International Faculty

DOI: https://doi.org/10.17605/cajmns.v6i3.2824

Keywords: 3D Haar wavelets, Parabolic equations, Coupled nonlinear sources, Iterative coupling algorithms, Adaptive wavelet methods

Abstract

The paper presents a new hybrid cryptographic system for image encryption algorithm combining the lightweight Ascon-AEAD with neural networks and chaotic systems. The CNAIE system uses Mish activation functions for neural diffusion and employs Q-learning-based reinforcement learning for the adaptability of key scheduling. Our solution caters to the current pressing demand of lightweight secure encryption methods with minimum computational overhead for IoT embedded systems. Results of encryption on some test images show the system testing near-optimal encryption entropy (≈7.99) and negligible adjacent pixel correlation (<0.01) compared to that of plaintext images (>0.90). The uniform histogram distribution and lack of meaningful pixel relations within encrypted images bear witness to the system's strength against statistical attacks. Furthermore, patch analysis establishes that the algorithm is quite sensitive to minor changes in key bits and cavity output variations caused by changes in even a single bit of the key. Performance evaluation establishes the system as feasible with security as per NIST for resource-constrained environments of the IoT.

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