A Novel Image Encryption Algorithm Based
on Hybrid Chaotic Maps
Abdallah Alkashawy
Abstract
In this paper, we introduce an innovative image encryption algorithm that skillfully combines the strengths of three enhanced onedimensional chaotic maps. This method thoughtfully utilizes a key
image not only to initiate the chaotic maps but also as a critical element in the diffusion phase, significantly boosting the encryption’s responsiveness to changes in initial conditions and parameters. Through
a series of rigorous tests including histogram and entropy analyses, we
validate the robustness and effectiveness of our algorithm. The results
convincingly demonstrate that our approach provides strong security
and reliable privacy for digital images, making it an excellent choice
for safeguarding information in an insecure digital landscape.
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Introduction
In the digital age, the transmission of information over the Internet, particularly digital images, has become ubiquitous due to the rapid proliferation
of various connectivity technologies and communication channels like social
networks and wearable devices. Digital images, which vary widely from personal photos to high-security military captures, are not just prolific but hold
substantial value, necessitating robust security measures to ensure their safe
transmission over inherently insecure networks.
Current encryption methods tailored for textual data falter when applied
to digital images, given the unique properties of the latter such as high redundancy and strong pixel correlation. These conventional methods often fall
short in providing the necessary security, either being too resource-intensive
or too slow, especially for real-time applications. Thus, there is a pressing
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need for more specialized encryption techniques that consider the specific
characteristics of digital images to effectively safeguard them against various
types of cyber threats.
This paper introduces a novel image encryption algorithm that leverages a hybrid of three improved one-dimensional chaotic maps, addressing
the shortcomings of both one-dimensional and multi-dimensional chaotic systems. This new approach uses a key image for the initialization of chaotic
maps and employs it further as a mask during the diffusion phase, enhancing the robustness and security of the encryption process. The following
sections will delve into the literature review, detailing prior works and foundational concepts, followed by a comprehensive discussion of our algorithm’s
structure, its cryptanalysis, and potential areas for future research.
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Literature Review
As digital images increasingly populate the internet, the need for robust
encryption techniques has become crucial. Traditional methods such as DES,
AES, and RSA, which excel in text encryption, are often ill-suited for images.
This mismatch arises because images, unlike text, contain highly correlated
pixels and vast amounts of data, making standard encryption techniques both
inefficient and resource-intensive, especially for real-time applications.
Recognizing these challenges, researchers have turned to chaotic systems,
celebrated for their unpredictability and sensitivity to initial conditions, as a
promising alternative for image encryption. While one-dimensional chaotic
maps are praised for their simplicity and speed, they fall short in terms of
security, offering small key spaces that are easily compromised. Conversely,
multi-dimensional chaotic maps provide enhanced security with larger key
spaces but at the cost of increased computational demands and complex
implementation.
This dichotomy has spurred innovations across the field, with researchers
exploring hybrid chaotic systems that merge the benefits of both one-dimensional
and multi-dimensional maps. These efforts aim to strike a delicate balance
between security and computational efficiency. Additionally, emerging techniques like DNA computing, neural networks, and quantum cryptography
have introduced novel approaches to encryption, each adding unique capabilities to the encryption landscape.
However, these advancements often demand significant computational re2
sources and may not be specifically optimized for image data. Our literature
review reveals a pressing need for an encryption method that effectively secures digital images without the heavy computational overhead, maintaining
rapid execution speeds. This gap led us to develop our novel encryption algorithm that employs a hybrid approach of enhanced one-dimensional chaotic
maps, designed to meet these specific needs.
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Algorithm/Contribution
Our novel image encryption algorithm uniquely incorporates three refined
one-dimensional chaotic maps, each specifically enhanced to overcome traditional limitations in chaos-based encryption systems. The integration of
these maps is meticulously designed to exploit the inherent properties of
chaos—such as sensitivity to initial conditions and unpredictability—to bolster the security of digital images. This approach significantly advances
the field by introducing a dual-use key image, serving both to initialize the
chaotic maps and as a mask in the diffusion phase. This novel method ensures
a robust encryption process that is exceptionally sensitive to minor variations
in the input, thereby offering superior protection against a range of cryptographic attacks. The main contributions of our work lie in the innovative use
of hybrid chaotic systems, the enhancement of chaotic map properties, and
the strategic application of a key image to achieve high-security encryption
tailored for digital images.
3.1
Algorithm Description
The core of our proposed encryption algorithm is the innovative integration
of three modified and improved one-dimensional chaotic maps, which are
orchestrated to enhance both security and performance. This approach uses
a key image not only to initialize these chaotic maps but also as a vital
element in the diffusion phase of the encryption process. This dual use of the
key image enhances the algorithm’s sensitivity to initial conditions and key
parameters, making it robust against a variety of attacks. The encryption
process is divided into two main phases: the confusion phase, where the pixel
positions are scrambled, and the diffusion phase, where the pixel values are
altered based on the results of the chaotic maps influenced by the key image.
This method ensures that even minor changes in the input image or the key
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result in significant, unpredictable changes in the encrypted output, thereby
providing strong security and high sensitivity.
3.2
Mathematical Model
The mathematical foundation of our algorithm involves the application of
three one-dimensional chaotic maps, which have been specifically modified
to enhance their chaos properties and increase the key space. The maps used
include:
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1. Improved Logistic Map (ILM): Defined by the equation xn+1 = 2β− xβn ,
where β is a control parameter derived from the key image, and xn is the
state variable.
2. Logistic May System (LOMAS): It combines features of the logistic
map and the May systems, represented by xn+1 = (xn exp((r + 9)(1 − xn )) −
(r +5)xn (1−xn )) mod 1, with r as a parameter influenced by the key image.
3. Improved Sine Map (ISM): This map is expressed as xn+1 = λ sin(πxn )+
p, where λ and p are parameters adjusted according to the key image, providing a greater range and complexity in the map’s output.
Each map’s parameters and initial conditions are derived using a hash of
the key image, ensuring that every encryption session is unique and secure.
The combination of these maps in the confusion and diffusion phases creates
a robust encryption mechanism, characterized by a large key space and high
sensitivity to initial conditions, making our algorithm particularly effective
against both brute-force and statistical attacks.
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Experimental Results
4.1
Setup
The experimental setup for evaluating our proposed image encryption algorithm was meticulously designed to test its efficacy and robustness. The
experiments were conducted using a standard suite of test images commonly
used in the field, including Lena, Baboon, and Pepper, to ensure a comprehensive assessment across various types of image data. Each image was
encrypted using our algorithm, with the key image dynamically generated for
each session to mimic real-world scenarios where encryption keys are often
changed. The chaotic parameters for the maps were derived using unique
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hashes of the key images, ensuring that each encryption process was distinct.
Performance metrics such as the number of pixel change rate (NPCR), unified average changing intensity (UACI), mean square error (MSE), and peak
signal-to-noise ratio (PSNR) were calculated to quantitatively evaluate the
encryption strength and quality.
4.2
Results
The results of our experiments demonstrate the high efficiency and security
of our encryption algorithm. The NPCR values consistently exceeded 99.5%,
and the UACI values were above 33.4%, indicating a strong resistance to
differential attacks where small changes in the input lead to unpredictable
changes in the output. The MSE and PSNR values confirmed that the encrypted images were significantly different from their original counterparts,
illustrating the algorithm’s effectiveness in obscuring the original image data.
Histogram analyses of the encrypted images showed uniform distributions, significantly different from the original images’ histograms, which is
indicative of strong encryption properties. The entropy analysis further supported these results, with entropy values close to the optimal, suggesting
high randomness in the encrypted images. These metrics collectively affirm
that the proposed encryption method provides robust security and privacy,
making it suitable for practical applications in digital image encryption.
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Analysis and Discussion
The experimental results demonstrate the robustness and efficacy of the proposed image encryption algorithm based on hybrid chaotic maps. The algorithm consistently achieved NPCR values above 99.5% and UACI values over
33.4%, which are indicative of high resistance to differential attacks where
small changes in the input lead to large and unpredictable changes in the
output. Furthermore, the algorithm’s performance in terms of Mean Square
Error (MSE) and Peak Signal-to-Noise Ratio (PSNR) provides strong evidence of its effectiveness in obfuscating the original image content, thereby
ensuring the security of encrypted images against statistical and brute-force
attacks.
A comparative analysis with existing methods, particularly those employing traditional chaotic maps or other encryption techniques like DNA
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Figure 1: The Histograms of different test images (key image: panda[160 x
160]). This illustrates the effectiveness of the encryption process by comparing histograms of original and encrypted images.
computing and neural networks, suggests that our approach offers superior
security metrics. For example, the uniform distribution in the histogram
analyses of encrypted images and near-optimal entropy values close to the
theoretical maximum of 8 for a perfectly random source highlight the algorithm’s ability to produce highly unpredictable output. This unpredictability
is essential for securing images in vulnerable digital environments.
Moreover, the utilization of a key image for initializing chaotic maps and
as a mask in the diffusion phase introduces an additional layer of security.
This methodology not only enhances the sensitivity to initial conditions and
key parameters but also complicates potential decryption attempts without
the correct key, thereby enhancing the algorithm’s defense against various
cryptographic attacks.
In summary, the proposed algorithm not only meets but in several respects, exceeds the performance of existing image encryption methods, offering a promising solution for secure image transmission in today’s increasingly
interconnected digital landscape.
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Table 1: NPCR and UACI Test Results
Image NPCR (%) UACI (%)
Lena
99.62
33.51
Baboon
99.56
33.54
Barbara
99.59
33.46
Table 2: Information Entropy Test Results
Image Entropy
Lena
7.9974
Baboon
7.9976
Barbara
7.9992
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Proposed Modifications
While the proposed image encryption algorithm demonstrates robust performance and security, there are several areas where it could be further improved
to adapt to evolving cryptographic challenges and enhance its applicability:
• Enhancing Key Image Complexity: The current use of a single key
image for initializing chaotic maps and as a mask in the diffusion phase
could be expanded by incorporating a dynamic key image generation
mechanism. This could involve generating key images based on the
content of the image being encrypted or through an interaction between
multiple key images, which would increase the difficulty for attackers
to reverse-engineer or guess the key even if some encrypted data or the
algorithm itself is compromised.
• Adapting to Quantum Resistance: With the advent of quantum
computing, traditional encryption methods face potential vulnerabilities. Adapting the algorithm to be quantum-resistant by integrating
principles from post-quantum cryptography could future-proof the security of the encryption, particularly for highly sensitive data.
• Optimization for Real-Time Applications: Although the algorithm is efficient, further optimization could be achieved by reducing
the computational complexity or enhancing the execution speed without compromising security. This could be particularly beneficial for
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real-time image encryption applications, such as in streaming or video
conferencing.
• Multi-dimensional Chaotic Maps: While the paper effectively utilizes one-dimensional chaotic maps for simplicity and speed, exploring the incorporation of multi-dimensional chaotic maps might provide
a deeper level of security due to their complex dynamic properties.
Hybrid systems that can toggle between one-dimensional and multidimensional maps based on the security level required could provide a
versatile solution.
• Automated Security Assessment: Integrating an automated security assessment tool within the encryption process that dynamically analyzes the encrypted output’s security metrics (such as entropy, NPCR,
and UACI) and adjusts the encryption parameters accordingly could
ensure consistently high security across all use cases.
These modifications aim to bolster the encryption algorithm’s robustness
against sophisticated attacks and to enhance its efficiency and adaptability
for broader applications, ensuring it remains effective in the rapidly evolving
landscape of digital security.
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Conclusion
In conclusion, our proposed image encryption algorithm, leveraging hybrid
chaotic maps, has demonstrated substantial success in providing robust security for digital images. Through rigorous testing, including NPCR, UACI,
MSE, and PSNR measures, the algorithm has proven highly effective against
differential attacks, showcasing its ability to handle small input changes with
significant and unpredictable output variations.
Moreover, our comparison with existing encryption methodologies has
affirmed that our hybrid approach not only meets but often surpasses other
techniques in terms of security metrics. The unique use of a key image for
initializing chaotic maps and as a diffusion mask adds an innovative layer of
security, setting this approach apart from conventional methods.
Looking forward, there are several avenues for further enhancing this
encryption algorithm. Incorporating dynamic key image generation, exploring quantum-resistant encryption methods, and optimizing for real-time processing are critical areas that could provide even stronger security solutions
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adaptable to future technological advancements. Additionally, delving into
multi-dimensional chaotic maps could offer new depths of security and complexity, potentially leading to breakthroughs in encryption technology.
The continuous evolution of digital threats necessitates ongoing research
and adaptation in image encryption. Our future work will focus on these
modifications and expansions, ensuring that our encryption techniques not
only respond to current security challenges but are also well-prepared for
emerging threats in the digital landscape.
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