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<p>Secure and efficient image encryption is essential for protecting sensitive visual data in modern communication systems. This article presents a multi-image encryption scheme that integrates a Rubik’s cube model, a memristive coupled neural network (MCNN), a Gauss Circle Map, and Josephus scrambling to enhance security and performance. Unlike conventional single-image methods, the proposed approach supports simultaneous encryption of multiple images, improving throughput and scalability for high-performance and distributed environments. In particular, the simultaneous mode amortizes initialization, improves memory locality, and increases cross-image diffusion, yielding higher throughput and stronger resistance to chosen-plaintext patterns than single-image baselines. Keys are generated from a memristive system and a Mersenne Twister PRNG. Inputs are transformed into one-dimensional bit streams and mapped onto a virtual <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(4\times 4\)</EquationSource> </InlineEquation> Rubik’s cube that is dynamically shuffled, then deconstructed and further diffused using the Gauss Circle Map and an auxiliary PRNG, followed by Josephus permutation for final scrambling. Experiments show robustness with PSNR 8.3 dB, entropy 7.999, NPCR <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(99.62\%\)</EquationSource> </InlineEquation>, UACI <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(31.16\%\)</EquationSource> </InlineEquation>, and a key space of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(2^{7175}\)</EquationSource> </InlineEquation>. The algorithm has complexity <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(O(M \times N)\)</EquationSource> </InlineEquation> and encrypts each image in 0.72 s on average. These results confirm strong cryptographic security, high randomness, and efficient multi-image processing suitable for cluster-based and cloud–edge deployments.</p>

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Multiple image encryption employing rubik’s cube, a memristive coupled neural network system and Josephus scrambling

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月29日

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  • Yousef Korayem,
  • Youstina Megalli,
  • Wassim Alexan

摘要

Secure and efficient image encryption is essential for protecting sensitive visual data in modern communication systems. This article presents a multi-image encryption scheme that integrates a Rubik’s cube model, a memristive coupled neural network (MCNN), a Gauss Circle Map, and Josephus scrambling to enhance security and performance. Unlike conventional single-image methods, the proposed approach supports simultaneous encryption of multiple images, improving throughput and scalability for high-performance and distributed environments. In particular, the simultaneous mode amortizes initialization, improves memory locality, and increases cross-image diffusion, yielding higher throughput and stronger resistance to chosen-plaintext patterns than single-image baselines. Keys are generated from a memristive system and a Mersenne Twister PRNG. Inputs are transformed into one-dimensional bit streams and mapped onto a virtual \(4\times 4\) Rubik’s cube that is dynamically shuffled, then deconstructed and further diffused using the Gauss Circle Map and an auxiliary PRNG, followed by Josephus permutation for final scrambling. Experiments show robustness with PSNR 8.3 dB, entropy 7.999, NPCR \(99.62\%\) , UACI \(31.16\%\) , and a key space of \(2^{7175}\) . The algorithm has complexity \(O(M \times N)\) and encrypts each image in 0.72 s on average. These results confirm strong cryptographic security, high randomness, and efficient multi-image processing suitable for cluster-based and cloud–edge deployments.