Code-Based Cryptography and Chaotic Maps as Pseudo-Random Bit Generator
Received: 29 July 2025 | Revised: 27 August 2025 and 8 September 2025 | Accepted: 11 September 2025 | Online: 8 December 2025
Corresponding author: Tayseer Karam Alshekly
Abstract
Random number generation is a fundamental requirement in cryptography, as the security of secret keys depends on their unpredictability. Yet, many existing Pseudo-Random Number Generators (PRNGs) face challenges such as limited key space, weak statistical performance, high computational cost, and vulnerability to post-quantum attacks. These limitations restrict their use in applications such as the Internet of Things (IoT), where both efficiency and strong security are needed. To address this problem, this paper presents a new PRNG that combines Code-based Cryptography (CBC) with a 3D logistic chaotic map. Chaotic maps provide sensitivity to initial conditions and a large key space, whereas code-based encryption offers resistance to quantum adversaries. The proposed scheme is based on the Cipher Feedback (CFB) mode, where chaotic outputs are converted into binary sequences and applied as key arrays. Due to its lightweight design, the generator is suitable for resource-constrained devices, such as IoT nodes. Experimental results show that the generated sequences pass the National Institute of Standards and Technology (NIST) statistical test suite with p-values between 0.98056 and 0.99944. Additional tests confirm low inter-sequence correlation (Pearson Correlation Coefficient (PCC) within -0.16591–0.14187), balanced Hamming distances (0.429–0.583), and favorable Sum of Absolute Differences (SAD ) results (0.3173–0.3849). Overall, the proposed PRNG achieves efficiency, scalability, and post-quantum security, making it a strong candidate for future cryptographic systems.
Keywords:
Code-based Cryptography (CBC), 3D logistic map, Pseudo-Random Number Generator (PRNG), National Institute of Standards and Technology (NIST) testDownloads
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