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<p>Chaotic maps play a crucial role in applications that require high unpredictability and complexity, such as cryptography and secure communications. However, many existing low-dimensional chaotic maps suffer from limited chaotic parameter ranges, which restrict their randomness and weaken their suitability for high-security applications. To address this limitation, this paper introduces an enhanced Simple Quadratic Map (SQM) that exhibits highly dynamic chaotic behavior and supports an infinite control-parameter range. The chaotic properties of the enhanced SQM map were rigorously evaluated using several chaos evaluation tests, including the Lyapunov exponent, bifurcation diagram, 2D and 3D phase plots, time sensitivity, approximate and sample entropies, cobweb plots, and the 0–1 test. Moreover, the enhanced SQM map has been incorporated into the design of a pseudorandom bit generator (PRBG). The designed PRBG has been analyzed for resource efficiency, speed, and randomness through rigorous evaluation with fifteen NIST tests. The performance analysis reveals that the proposed PRBG requires a minimal number of operations per bit, achieving high throughput by generating multiple bits per iteration. Furthermore, the results of the NIST test suite validate the high statistical randomness of the generated bit sequences. Additionally, the paper introduces a novel lightweight encryption scheme tailored for securing image data in IoT applications. The proposed scheme employs the proposed map combined with lightweight techniques, such as region of interest selection, lossy FFT compression, adaptive key generation, and a Feistel-based confusion and diffusion encryption method. The scheme has been comprehensively evaluated across various metrics, including compression ratio, compression, encryption, decryption times, SSIM, NPCR, UACI, MSE, PSNR, histogram and correlation analysis, histogram variance, and entropy. Additionally, the resilience against median filtering, histogram equalization, low-pass filtering, noise, and cropping attacks has been assessed. The results illustrate that the scheme achieves enhanced security while maintaining low computational complexity. In addition, it outperforms state-of-the-art encryption methods in execution speeds, thus affirming its viability for safeguarding time-critical Internet of Things environments. Thus, the overall findings highlight the efficacy of the enhanced SQM map, proposed PRBG, and lightweight image encryption schemes as less resource-intensive yet highly secure options for safeguarding IoT applications and other domains requiring robust security measures.</p>

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Enhanced simple quadratic map for lightweight PRBG and IoT image encryption

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Mir Nazish,
  • Mehreen Farooq,
  • M. Tariq Banday

摘要

Chaotic maps play a crucial role in applications that require high unpredictability and complexity, such as cryptography and secure communications. However, many existing low-dimensional chaotic maps suffer from limited chaotic parameter ranges, which restrict their randomness and weaken their suitability for high-security applications. To address this limitation, this paper introduces an enhanced Simple Quadratic Map (SQM) that exhibits highly dynamic chaotic behavior and supports an infinite control-parameter range. The chaotic properties of the enhanced SQM map were rigorously evaluated using several chaos evaluation tests, including the Lyapunov exponent, bifurcation diagram, 2D and 3D phase plots, time sensitivity, approximate and sample entropies, cobweb plots, and the 0–1 test. Moreover, the enhanced SQM map has been incorporated into the design of a pseudorandom bit generator (PRBG). The designed PRBG has been analyzed for resource efficiency, speed, and randomness through rigorous evaluation with fifteen NIST tests. The performance analysis reveals that the proposed PRBG requires a minimal number of operations per bit, achieving high throughput by generating multiple bits per iteration. Furthermore, the results of the NIST test suite validate the high statistical randomness of the generated bit sequences. Additionally, the paper introduces a novel lightweight encryption scheme tailored for securing image data in IoT applications. The proposed scheme employs the proposed map combined with lightweight techniques, such as region of interest selection, lossy FFT compression, adaptive key generation, and a Feistel-based confusion and diffusion encryption method. The scheme has been comprehensively evaluated across various metrics, including compression ratio, compression, encryption, decryption times, SSIM, NPCR, UACI, MSE, PSNR, histogram and correlation analysis, histogram variance, and entropy. Additionally, the resilience against median filtering, histogram equalization, low-pass filtering, noise, and cropping attacks has been assessed. The results illustrate that the scheme achieves enhanced security while maintaining low computational complexity. In addition, it outperforms state-of-the-art encryption methods in execution speeds, thus affirming its viability for safeguarding time-critical Internet of Things environments. Thus, the overall findings highlight the efficacy of the enhanced SQM map, proposed PRBG, and lightweight image encryption schemes as less resource-intensive yet highly secure options for safeguarding IoT applications and other domains requiring robust security measures.