<p>With the rapid growth of digital image data across cloud computing, healthcare and Internet of Things (IoT) applications, secure transmission and storage of image content has become a pressing challenge. Conventional encryption algorithms, typically optimized for textual data often struggle to accommodate the unique properties of images such as high redundancy and strong spatial correlation. To overcome these limitations, this study presents a Novel Color Image Encryption Scheme (NCIES) that synergistically integrates chaotic systems, mathematical transformations and modern cryptographic mechanisms to ensure high levels of security, robustness and computational efficiency. The NCIES architecture is built upon several core innovations: a newly designed one-dimensional Chaotic Map (DCM) that generates five high-entropy, key-sensitive chaotic sequences; secure key generation and exchange via Elliptic Curve Cryptography (ECC); Fibonacci-based permutation and Tribonacci-based block transformations to enhance spatial diffusion and a layered hybrid encryption mechanism combining modular arithmetic, XOR-based diffusion and digital signature authentication for integrity verification. This multi-tiered structure successfully unifies the principles of confusion, diffusion and sensitivity to initial conditions. Extensive experiments validate the cryptographic strength of NCIES. It achieves near ideal information entropy (7.9994), high NPCR <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:\left(99.61\%\right),\)</EquationSource> </InlineEquation> UACI <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\:\left(32.98\%\right)\)</EquationSource> </InlineEquation> and negligible correlation coefficients <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\:(-0.0029,\:-0.0019,\:0.0021),\)</EquationSource> </InlineEquation> affirming its effectiveness in breaking spatial correlations. The NCIES also boasts a formidable key space of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\:2^{512},\)</EquationSource> </InlineEquation> offering strong resistance against brute-force attacks. Noise robustness tests show significant MSE increases under both salt-and-pepper noises, highlighting its resilience during transmission. Furthermore, comparative evaluations against several state-of-the-art encryption algorithms demonstrate that NCIES not only achieves high cryptographic strength but also offers decent computational efficiency across different image resolutions with encryption times suitable for real-world applications. These characteristics position NCIES as a promising candidate for high-security environments, including cloud-based storage, medical image protection and secure IoT infrastructures.</p>

Enhancing color image encryption scheme with a chaotic map and Fibonacci transform

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发表日期：

2025年10月9日

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Shalini Gupta,
Anand Nayyar,
Nitish

摘要

With the rapid growth of digital image data across cloud computing, healthcare and Internet of Things (IoT) applications, secure transmission and storage of image content has become a pressing challenge. Conventional encryption algorithms, typically optimized for textual data often struggle to accommodate the unique properties of images such as high redundancy and strong spatial correlation. To overcome these limitations, this study presents a Novel Color Image Encryption Scheme (NCIES) that synergistically integrates chaotic systems, mathematical transformations and modern cryptographic mechanisms to ensure high levels of security, robustness and computational efficiency. The NCIES architecture is built upon several core innovations: a newly designed one-dimensional Chaotic Map (DCM) that generates five high-entropy, key-sensitive chaotic sequences; secure key generation and exchange via Elliptic Curve Cryptography (ECC); Fibonacci-based permutation and Tribonacci-based block transformations to enhance spatial diffusion and a layered hybrid encryption mechanism combining modular arithmetic, XOR-based diffusion and digital signature authentication for integrity verification. This multi-tiered structure successfully unifies the principles of confusion, diffusion and sensitivity to initial conditions. Extensive experiments validate the cryptographic strength of NCIES. It achieves near ideal information entropy (7.9994), high NPCR \(\:\left(99.61\%\right),\) UACI \(\:\left(32.98\%\right)\) and negligible correlation coefficients \(\:(-0.0029,\:-0.0019,\:0.0021),\) affirming its effectiveness in breaking spatial correlations. The NCIES also boasts a formidable key space of \(\:2^{512},\) offering strong resistance against brute-force attacks. Noise robustness tests show significant MSE increases under both salt-and-pepper noises, highlighting its resilience during transmission. Furthermore, comparative evaluations against several state-of-the-art encryption algorithms demonstrate that NCIES not only achieves high cryptographic strength but also offers decent computational efficiency across different image resolutions with encryption times suitable for real-world applications. These characteristics position NCIES as a promising candidate for high-security environments, including cloud-based storage, medical image protection and secure IoT infrastructures.