The Fractal Spectral Wave Filter: A Quantum-Resilient Cryptographic Primitive Harnessing the Aliasing Collisions

This preprint presents the Fractal Spectral Wave Filter, a cryptographic framework that combines Morton Z-order spatial mapping, chaotic key generation, and Number Theoretic Transform (NTT)-based spectral processing over modular arithmetic. The proposed approach intentionally omits conventional zero-padding during spectral processing to investigate the use of aliasing collisions as a data-diffusion mechanism. The framework is evaluated for grayscale and RGB image data using computational complexity, Shannon entropy, correlation coefficient, Mean Squared Error (MSE), NPCR, and UACI. The study reports an asymptotic computational complexity of O(N log N) for the transform-based processing pipeline and evaluates the resulting encrypted image characteristics. The work explores the relationship between spectral-domain transformations, chaotic data scrambling, and post-quantum-cryptography-aligned mathematical operations. The results and limitations presented in this preprint are intended to provide a basis for further investigation and experimental validation.