Chaotic-Lattice Hybrid Key Encapsulation: Harnessing Modular Chaos for Quantum-Safe Security

While Hooshmand (2024) reduces key sizes using LDLCs, and Gode et al. (2025) demonstrate chaotic properties in modular arithmetic, neither cross-pollinates these domains. This idea proposes a KEM where lattice coefficients are generated via chaotic modular recurrence functions (e.g., prime-based sequences with Lyapunov exponents >0.8). The chaos introduces sensitivity to initial conditions, making secret keys unpredictable even if lattice parameters are compromised. Unlike Hooshmand’s static LDLCs, this dynamic approach could thwart attacks exploiting structural weaknesses. The chaos-lattice hybrid could be validated against Craps et al.’s (2022) quantum complexity bounds to ensure quantum resistance while using Gode’s chaos metrics (bifurcation analysis, Hausdorff dimensions) to quantify security margins. Impact: A new paradigm where chaos theory fortifies lattice cryptography, potentially reducing key sizes further while enhancing resilience.

References:

1. A Key Encapsulation Mechanism from Low Density Lattice Codes. Reza Hooshmand (2024). arXiv.org.
2. Bounds on quantum evolution complexity via lattice cryptography. B. Craps, Marine De Clerck, O. Evnin, Philip Hacker, M. Pavlov (2022). SciPost Physics.
3. Nonlinear Dynamics In Number Theory: Exploring Iterative Functions And Chaos. R. Gode, Dr. C. Balarama Krishna, Jasmeet Kaur (2025). International Journal of Environmental Science.