A Hybrid Chaos-Based Cryptographic Framework for Post-Quantum Secure Communications

Abstract: We present CryptoChaos, a novel hybrid cryptographic framework that synergizes deterministic chaos theory with cutting-edge cryptographic primitives to achieve robust, post-quantum resilient encryption. CryptoChaos harnesses the intrinsic unpredictability of four discrete chaotic maps (Logistic, Chebyshev, Tent, and Henon) to generate a high-entropy, multidimensional key from a unified entropy pool. This key is derived through a layered process that combines SHA3-256 hashing with an ephemeral X25519 Diffie-Hellman key exchange and is refined using an HMAC-based key derivation function (HKDF). The resulting encryption key powers AES-GCM, providing both confidentiality and integrity. Comprehensive benchmarking against established symmetric ciphers confirms that CryptoChaos attains near-maximal Shannon entropy (approximately 8 bits per byte) and exhibits negligible adjacent-byte correlations, while robust performance on the NIST SP 800-22 test suite underscores its statistical rigor. Moreover, quantum simulations demonstrate that the additional complexity inherent in chaotic key generation dramatically elevates the resource requirements for Grover-based quantum attacks, with an estimated T gate count of approximately 2.1 x 10^9. The modular and interoperable design of CryptoChaos positions it as a promising candidate for high-assurance applications, ranging from secure communications and financial transactions to IoT systems, paving the way for next-generation post-quantum encryption standards.