Complexity-Bounded Post-Quantum Security: A New Metric from Quantum Evolution

NIST PQC standardization focuses on classical attack complexity, ignoring quantum-specific metrics. Craps et al. (2022) link CVP (used in lattice attacks) to quantum evolution complexity, providing an algorithmic bridge between quantum chaos theory and cryptography. This research proposes: 1. Benchmarking PQC schemes (e.g., Kyber, LDLC-KEM) using their upper complexity bounds (integrable vs. chaotic system classifications). 2. Designing lattices that maximize quantum evolution complexity (e.g., by enforcing chaotic coefficient distributions via Gode et al.’s (2025) methods). Unlike Wang et al.’s (2021) qualitative QSC overview, this introduces a quantifiable, physics-based security dimension. It could resolve conflicts in security assessments (e.g., when lattice reduction attacks outperform theoretical estimates). Impact: Pioneers a quantum-native security taxonomy, future-proofing PQC against emerging quantum algorithms.

References:

1. Bounds on quantum evolution complexity via lattice cryptography. B. Craps, Marine De Clerck, O. Evnin, Philip Hacker, M. Pavlov (2022). SciPost Physics.
2. Quantum-safe cryptography: crossroads of coding theory and cryptography. Jiabo Wang, Ling Liu, Shanxiang Lyu, Zheng Wang, Mengfan Zheng, Fuchun Lin, Zhao Chen, L. Yin, Xiaofu Wu, Cong Ling (2021). Science China Information Sciences.
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.