Enhancing Image Security Through Memelements Based Chaotic and Hyperchaotic Systems

Abstract

In today’s digitally interconnected world, the volume and sensitivity of visual data continue to grow rapidly, highlighting the critical importance of secure image transmission, particularly in cloud computing, surveillance, healthcare, and military systems. Conventional encryption algorithms often fail to account for the high correlation between image pixels and the large size of image data, making them vulnerable to modern attacks. To overcome these limitations, this study presents several novel image encryption frameworks that incorporate hyperchaotic systems with memristive, memcapacitive, and meminductive devices, DNA-based encoding, and intelligent optimization techniques. First, a new encryption approach integrates DNA coding with a logistic map and a hyperchaotic memcapacitor-based model, achieving high NPCR values (99.587% 99.634%) and UACI values (27.474%–33.935%), as well as entropy values close to 8, indicating strong randomness and statistical resistance. The key space of 2⁵³¹ surpasses brute-force threshold threshold of 2100. Recognizing the limitations of traditional Particle Swarm Optimization (PSO), the study introduces Chaotic PSO (CPSO) to fine-tune parameters of a four-dimensional memristor-based hyperchaotic system. This method, combined with DNA coding and a Logistic Sine Adjusted Integrated Map (LSAIM), achieves enhanced image encryption performance, including a key space of 2¹¹¹⁶, MSE of 10676.01, and PSNR of 7.85 dB. To address noise interference in transmission, an integrated encryption-denoising scheme is proposed using an Online Sequential Extreme Learning Machine (OSELM) autoencoder paired with a two memristor-based hyperchaotic system, a 2D sine map and DNA coding. This approach shows resilience against multiple noise types (Gaussian, salt-and-pepper, quantization, speckle, etc.), achieving PSNR between 23.63 and 37.45 dB for denoised images, and maintaining strong security metrics (NPCR up to 99.64%, UACI ~33.92%, entropy ≈ 8, key space ≈ 2⁷⁹⁷). Finally, a dual-stage architecture is proposed for image compression and encryption. It combines MobileNetV2-based CNN compression with a memelement-driven fractional-order hyperchaotic encryption scheme enhanced by a Logistic-Sine-Cubic Iterative Map (LSCIM), DNA coding, and dynamic diffusion. This method maintains near-lossless compression quality (PSNR > 55 dB, SSIM ≈ 0.9999, MSE ≈ 0.2) while achieving a key space of 2¹²⁷⁶, ensuring high robustness against brute-force and statistical attacks. Together, these contributions form a comprehensive solution for secure, efficient, and noise-resilient image processing, making them highly applicable in sensitive domains such as medicine, defense, astronomy, and biological imaging.