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

Kevin Song, Noorullah Imran, Jake Y. Chen, Allan C. Dobbins

TL;DR

CryptoChaos proposes a post-quantum secure symmetric framework by combining chaotic maps with standard cryptographic primitives to harden key material against quantum adversaries. It builds a hybrid entropy pool from four discrete maps (Logistic, Chebyshev, Tent, Hénon) whose outputs are fused and hashed with $SHA3-256$, then augmented with an ephemeral X25519 Diffie–Hellman shared secret compressed with Blake3 and processed via HKDF to yield an AES-GCM key. Benchmark results show near-maximal entropy of about $8$ bits per byte, minimal adjacent-byte correlation, and strong NIST SP 800-22 statistics, along with robust visual diffusion metrics. Quantum-resilience analysis indicates a Grover-based key-recovery cost of about $2.1 imes 10^9$ $T$ gates, substantially elevating the barrier compared to conventional ciphers, even when accounting for the $2^{128}$ effective search space. The approach is modular and hardware-friendly, offering a practical path toward post-quantum encryption standards for TLS/IPsec, IoT, and high-assurance domains.

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.

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

TL;DR

CryptoChaos proposes a post-quantum secure symmetric framework by combining chaotic maps with standard cryptographic primitives to harden key material against quantum adversaries. It builds a hybrid entropy pool from four discrete maps (Logistic, Chebyshev, Tent, Hénon) whose outputs are fused and hashed with , then augmented with an ephemeral X25519 Diffie–Hellman shared secret compressed with Blake3 and processed via HKDF to yield an AES-GCM key. Benchmark results show near-maximal entropy of about bits per byte, minimal adjacent-byte correlation, and strong NIST SP 800-22 statistics, along with robust visual diffusion metrics. Quantum-resilience analysis indicates a Grover-based key-recovery cost of about gates, substantially elevating the barrier compared to conventional ciphers, even when accounting for the effective search space. The approach is modular and hardware-friendly, offering a practical path toward post-quantum encryption standards for TLS/IPsec, IoT, and high-assurance domains.

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.

Paper Structure

This paper contains 5 sections, 16 equations, 1 figure, 5 tables.

Table of Contents

  1. Logistic Map
  2. Chebyshev Map
  3. Tent Map
  4. Hénon Map
  5. Hybrid Key Derivation

Figures (1)

  • Figure 1: Illustration of image encryption examples using chaotic systems. Each chaotic system generates unique key sequences that are combined for enhanced unpredictability and security. For CryptoChaos, the resulting key stream drives the encryption of plaintext using SHA3-512 and AES-GCM, ensuring confidentiality, integrity, and resistance to quantum attacks.