<p>This manuscript presents a novel quantum image encryption scheme that integrates two independent two-dimensional (2D) Arnold cat maps—one for spatial permutation and one for intensity permutation—with a robust chaotic diffusion process. This unified dual-permutation framework–applying independent permutations to spatial and intensity data–distinguishes itself from prior dual-map approaches and, to our knowledge, has not been previously explored in QIE. The algorithm features dual permutation, where independent cat maps are applied to coordinate and nibble-split pixel data, followed by quantum diffusion implemented through bit-plane cyclic shifts, chaotic key-based modular addition, and intra-qubit XOR operations. Critically, we provide the explicit formulation of the mathematical operators governing these quantum state transformations, addressing a key limitation of prior works. Moreover, since the proposed encryption transformations are formulated in terms of unitary quantum operators, the scheme is scalable, ensuring that our mathematical framework remains valid for future fault-tolerant quantum computers. This approach ensures that both spatial and intensity information are thoroughly scrambled, resulting in cipher images with near-uniform histograms, near-zero correlation coefficients, and extreme key sensitivity. The quantum implementation offers a theoretical exponential speedup in circuit depth compared to classical <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$O(R \cdot N^2)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo>·</mo> <msup> <mi>N</mi> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> time complexity counterparts while resisting statistical, differential, and brute-force attacks through chaotic parameterization. Comprehensive experimental validation confirms the cryptographic superiority of our scheme: it achieves information entropy values exceeding 7.999, Number of Pixel Change Rate (NPCR) > 99.6%, and Unified Average Changing Intensity (UACI) <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\sim $</EquationSource> <EquationSource Format="MATHML"><math> <mo>∼</mo> </math></EquationSource> </InlineEquation>33.46% on standard test images, outperforming recent state-of-the-art algorithms.</p>

Quantum inspired image encryption using dual chaotic maps

期刊论文
发表日期：

2025年11月24日

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Farhan Musanna

摘要

This manuscript presents a novel quantum image encryption scheme that integrates two independent two-dimensional (2D) Arnold cat maps—one for spatial permutation and one for intensity permutation—with a robust chaotic diffusion process. This unified dual-permutation framework–applying independent permutations to spatial and intensity data–distinguishes itself from prior dual-map approaches and, to our knowledge, has not been previously explored in QIE. The algorithm features dual permutation, where independent cat maps are applied to coordinate and nibble-split pixel data, followed by quantum diffusion implemented through bit-plane cyclic shifts, chaotic key-based modular addition, and intra-qubit XOR operations. Critically, we provide the explicit formulation of the mathematical operators governing these quantum state transformations, addressing a key limitation of prior works. Moreover, since the proposed encryption transformations are formulated in terms of unitary quantum operators, the scheme is scalable, ensuring that our mathematical framework remains valid for future fault-tolerant quantum computers. This approach ensures that both spatial and intensity information are thoroughly scrambled, resulting in cipher images with near-uniform histograms, near-zero correlation coefficients, and extreme key sensitivity. The quantum implementation offers a theoretical exponential speedup in circuit depth compared to classical $O(R \cdot N^2)$ $O (R \cdot N^{2})$ time complexity counterparts while resisting statistical, differential, and brute-force attacks through chaotic parameterization. Comprehensive experimental validation confirms the cryptographic superiority of our scheme: it achieves information entropy values exceeding 7.999, Number of Pixel Change Rate (NPCR) > 99.6%, and Unified Average Changing Intensity (UACI) $\sim $ $\sim$ 33.46% on standard test images, outperforming recent state-of-the-art algorithms.