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Novel image encryption scheme based on chaotic signals with finite -precision error

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Abstract

This paper presents a novel framework for generating new chaotic signals for image encryption that is based on the finite precision of computers. First, we select a system from a number of chaotic systems. Next, we obtain a trajectory of this system. Then, another trajectory is obtained by perturbing the initial values of the same chaotic system. Finally, we calculate the evolution error of two trajectories to obtain a new chaotic signal. Our method is successfully applied to simulate three new chaotic signals for image encryption. A novel image cryptography algorithm based on new chaotic signals and true random numbers is developed. These circular diffusion and local versus global scrambling methods are designed. The results show that the proposed method is effective and exhibits a higher level of security than other sophisticated methods.

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... As for the study of synchronization and control of chaotic systems, many researchers aim to understand the interactions between chaotic systems in complex networks and develop control strategies to achieve synchronization, including complete synchronization (CS) 8-10 , projective synchronization (PS) and modified projective synchronization (MPS) 11 , anti-synchronization (AS) 12 , lag synchronization (LS) 13 , modified projective phase synchronization (MPPS) 14 , complex function projective synchronization (CFPS) 15 , combination synchronization 16 , complex modified function projective synchronization 17,18 , etc. In the application of chaotic systems, researchers utilize these systems in various fields such as cryptography [19][20][21][22] , secure communications 23 , and optimization 24,25 . Mengxin Jin 26 introduced hyperchaotic systems and their importance in cryptography, communication and control, as well as research advancements in the generation, synchronization, and extreme multistability of complex chaotic systems. ...
... FIG. 14. The bifurcation diagram of 3D-SLS (19) With m = 3, the three-dimensional Sine-Logistic System(3D-SLS) is expressed as follows: ...
... The LEs are depicted in Fig.15. From the above figures, there are positive LE and the chaotic range of 3D-SLS gradually expands as the parameter a increases, which indicates the 3D-SLS (19) is chaotic. As for the fixed points of Eq. (19), we obtain ...
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The Sine-Cosine function, which is widely adopted in mathematics and physics, has attracted our attention due to its unique properties. By delving into the coupling effect of the Sine-Cosine function, we discover a previously unreported class of nonlinear systems, namely the Sine-Cosine Nonlinear System Family (SCNSF). This discovery is motivated by the need to expand the repertoire of nonlinear systems and understand the complex behaviors that can emerge from the combination of basic trigonometric functions. The SCNSF has both chaotic characteristics in the real number domain and fractal characteristics in the complex number domain. The classification and general mathematical description of SCNSF provide a solid theoretical foundation for further research. The proposal of three types of classic systems within SCNSF and the investigation of their chaotic properties and hardware implementation open up new avenues for practical applications. The large chaotic range exhibited by these systems implies their potential applications in various fields such as secure communication and chaotic circuit design. Moreover, the discovery of the chaos generation mechanism based on the coupling effect of the Sine-Cosine function deepens our understanding of the origin of chaos. In the complex number domain, the high parameter sensitivity and rich fractal patterns of SCNSF can be can be harnessed to develop more advanced encryption algorithms and more sensitive signal detection methods, thereby contributing to the advancement of information security and signal processing technologies. Overall, the chaotic and fractal properties of SCNSF make it a valuable asset in the pursuit of innovative solutions in multiple scientific and engineering disciplines.
... Recently, researchers have published some typical image encryption algorithms. Zhou et al. [1] proposed a novel image encryption scheme based on chaotic signals with finite-precision error. Zhou et al. [2] proposed a novel image encryption cryptosystem based on true random numbers and chaotic systems. ...
... r = 300, skip the transition form of chaotic mapping. Continue to iterate m × n times to obtain 6 chaos matrix codes {X1 }, {X 2 }, {X 3 }, {Y 1 }, {Y 2 }, {Y 3 }. Put {x 7 , a 2 , β 2 , θ 2 }, {x 8 , a 2 , β 2 , θ 2 }, {x9 , a 2 , β 2 , θ 2 }, {x 10 , a 2 , β 2 , θ 2 }, {x11 , a 2 , β 2 , θ 2 }, {x 12 , a 2 , β 2 , θ 2 } into Eq(14) and iterate r times, skip Transition form through chaotic mapping. ...
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Images are important information carriers in our lives, and images should be secure when transmitted and stored. Image encryption algorithms based on chaos theory emerge in endlessly. Based on previous various chaotic image fast encryption algorithms, this paper proposes a color image sector fast encryption algorithm based on one-dimensional composite sinusoidal chaotic mapping. The main purpose of this algorithm is to improve the encryption and decryption speed of color images and improve the efficiency of image encryption in the big data era. First, four basic chaos maps are combined in pairs and added with sine operations. Six one-dimensional composite sinusoidal chaos maps (CSCM) were obtained. Secondly, select the two best chaotic mappings LCS and SCS. The randomness of these two chaotic mappings was verified through Lyapunov index and NIST SP 800–22 randomness tests. Thirdly, the encryption process is carried out according to the shape of a traditional Chinese fan, and the diffusion and scrambling of each pixel of the image are performed in parallel. This greatly improves encryption speed. When diffusing, changing the value of one pixel can affect the values of multiple subsequent pixels. When scrambling, each pixel changes position with the three pixels before it according to the chaotic sequence. Finally, through many experiments, it is proved that the image encryption algorithm not only greatly improves the encryption and decryption speed, but also improves various indexes. The key space reached 2¹⁹², the average information entropy was 7.9994, the average NPCR was 99.6172, and the average UACI was 33.4646. The algorithm can also resist some common attacks and accidents, such as exhaustion attack, differential attack, noise attack, information loss and so on.
... The study in [24] described a collection of one-dimensional quadratic chaotic maps based on topological conjugate theory. In [25], a new framework utilising finite precision was introduced for generating chaotic signals to improve image encryption is presented. The encryption process was enhanced using S-BOX, an algorithm based on chaotic processes, which provided a high level of security and efficiency. ...
... Horizontal Vertical Diagonal [29] 0 -0.004 0.00030 [36] −0.001 −0.001 −0.00030 [37] 0.001 0.001 0.00051 [16] 0.0028 −0.001 0.0021 [25] 0.00070 0.00060 0.00031 [15] 0.001 0.001 0.001 [38] 0.002 0.001 0.00081 [39] 0.002 0.006 0.00051 [40] 0.00162 0.00027 0.00062 [41] 0.00006 0.00001 -0.00002 [42] 0.005 0.001 0.006 ...
Article
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Chaos' key qualities, such as initial state sensitivity and unpredictability, make it an ideal contender for cryptography applications. This study presents an encryption scheme for efficient and secure image encryption. The encryption scheme includes two ciphering stages and a substitution stage. In this work, an algorithm for key generation has been proposed. The design of a Pseudo-random number generator that used for key generation is based on chaotic algorithms. The chaotic map will be utilised in encryption systems due to its high security. To evaluate the proposed PRNG randomness, NIST tests are used for these sequences. In the following subsection, security analysis of the proposed image encryption technique has been made to know the efficiency of the proposed technique. The statistical analysis now reaffirms that the technique is secure and efficient for and encrypting simple or complex images, be it in shades of black and white or, colorful. By a comparison with past chaotic investigations, demonstrating that our algorithm is competitive with earlier work.
... The algorithms proposed by Alawida [7], Azam et al. [23], and Zhou et al. [24] were primarily designed for conventional images and standard computers. In contrast, the image encryption algorithm proposed by Feng et al. [12] is tailored for IoT devices with varying bit precisions. ...
... In contrast, the image encryption algorithm proposed by Feng et al. [12] is tailored for IoT devices with varying bit precisions. Azam et al. [23] focused on generating S-boxes using pseudorandom number generation in their image encryption scheme, while Alawida [7] and Zhou et al. [24] utilized chaotic maps with novel permutations and diffusion algorithms in their designs. ...
Article
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In the Industrial Internet of Things (IIoT), ensuring timely and secure data transmission between sensors and edge devices is paramount, particularly when dealing with sensitive information captured by high-resolution image sensors. However, existing methods often struggle to strike the delicate balance between security and efficiency, resulting in either vulnerable transmissions or significant processing delays. This article proposes a novel image encryption algorithm specifically designed for IIoT environments with constrained resources. The proposed algorithm leverages a new chaotic model that combines a cyclic construction with a 1-D perturbed logistic map. The proposed chaos model produces a single data sequence, subsequently utilized to generate three matrices mirroring the size of the image. Among these matrices, two contribute to crafting a permutation matrix for randomizing pixel positions, while the third matrix facilitates diffusion operations. The chaotic data sequence and generated matrices are preprocessed and can be used for encrypting multiple images under the same session key, enhancing efficiency. Encryption utilizes a single round that combines diffusion and permutation operations simultaneously, further reducing processing time. Experimental results demonstrate its effectiveness on an IoT camera sensor for encryption and a separate device for decryption. Statistical tests confirm the robustness of the encrypted images against various attacks, including correlation analysis, histogram analysis, differential attacks, and key and plaintext sensitivity. Furthermore, comparisons with existing image encryption techniques showcase the proposed algorithm's superior security and efficiency. Notably, it effectively encrypts images of varying sizes, making it suitable for deployment in IIoT environments.
... It can better solve the output discontinuity caused by the insufficient performance of PRNG. The traditional algorithms are divided into two steps [21][22][23][24][25][26][27], but this flow has been proven to be unsafe. Thus, this work proposes an encryption method based on jump diffusion. ...
... Ref. [8] Ref. [26] H [26] 99.610 33.402 ----Ref. [27] 99.600 33.420 ---- Content courtesy of Springer Nature, terms of use apply. Rights reserved. ...
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Due to the initial value sensitivity and high pseudo-randomness of the chaotic system. Chaotic systems are often applied as a Pseudo-Random Number Generator (PRNG) in related fields. Especially in cryptography based on chaos, the Pseudo-Random Numbers (PRNs) produced by PRNG are often used as an interference in the design of encryption algorithm. However, due to lower chaos performance of PRNG such as chaotic output is discontinuous and lower complexity, it may bring the negative impact to its application in related field. In this study, a novel model of 2D sine–cosine-logistic coupling (2D-SCLC) hyperchaotic map is proposed. In comparison with several existing chaos map, the proposed system has better chaotic performance. It can effectively improve the security performance of encryption algorithm, if the proposed chaos map is applied in the design of image encryption algorithm. Further, the PRNs generated by 2D-SCLC is applied to the new image encryption algorithms. By using the security test tools, we can obtain the values of NPCR and UACI have reach 99.61% and 33.44%, they are close to the ideal value. In particular, the information entropy is 7.9996. The security test shows that the algorithms has higher security. This research provides a theoretical guidance for related fields based on chaotic cryptography.
... The research in [24] delineated a series of one-dimensional quadratic chaotic maps grounded in topological conjugate theory. A novel approach employing finite accuracy for the generation of chaotic signals to enhance image encryption is provided in [25]. The encryption technique was improved through the utilization of S-BOX, an algorithm grounded in chaotic processes, which offered elevated security and efficiency. ...
Article
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The fundamental characteristics of chaos, including sensitivity to beginning conditions and unpredictability, render it a prime candidate for cryptographic applications. This research introduces an encryption methodology for effective and safe image encryption. The encryption system has two ciphering phases and a substitution phase. This study proposes a method for key creation. The design of a pseudo-random number generator utilized for key generation is founded on chaotic algorithms. The chaotic map will be employed in encryption systems owing to its superior security. NIST tests are employed to assess the randomness of the proposed PRNG sequences. The subsequent part presents a security study of the suggested picture encryption approach to evaluate its efficacy. The statistical analysis now confirms that the technique is secure and efficient for encrypting both basic and complicated images, whether in monochrome or color. Through a comparison with previous chaotic investigations, it is evident that our method is competitive with earlier efforts.
... Recently, Zhou et al. [2023] proposed a novel image encryption scheme based on new chaotic signals with finite-precision error. According to our analysis and experiments, their scheme has some limitations. ...
Article
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Recently, an image encryption scheme with new chaotic signals has been proposed. Some limitations of this scheme will be pointed out. It adopts a “diffusion–permutation” architecture. The diffusion encryption is linear and can be simplified. Bit-level permutation significantly decreases the encryption efficiency. To solve the above problems, an improved scheme is proposed. The new scheme employs a Feistel-like network with four rounds of encryption. The dynamic substitution box (S-box) generated by Fisher–Yates permutation increases the nonlinearity of encryption. The optimized diffusion process is applied to obtain the avalanche effect. The experimental results show that the improved scheme performs well. In addition, the resistance against various attacks is analyzed from the perspective of a cryptanalyst.
... with complex behaviors is meaningful [2]- [5]. Since Lorenz proposed the first chaotic system in 1963, new chaotic systems have been put forward continuously, such as Logistic, Hénon system, Rössler system, Chen system, etc. ...
Article
The chaotic system as a source of randomness is very important for chaos-based secure communication. Different from other chaotic maps, this work explores an n-dimensional (nD) non-degeneracy discrete hyperchaotic map with any desired Lyapunov exponents (LEs). First, theoretical analysis proves that the proposed map is chaotic. Based on this proof, it is designed for any desired LEs. To illustrate the effectiveness of the nD new map, we use some chaotic and non-chaotic maps as examples. The simulation results demonstrated that the proposed maps exhibit stronger chaotic properties and more complex dynamic behaviors compared to some previous results. Moreover, the chaotic signals generated by our maps passed NIST and TestU01 tests, which show our map has better randomness. Furthermore, a chaotic system with higher LEs do not necessarily have higher complexity degree. Next, the proposed map is implemented by hardware DSP platform, indicating the feasibility for industrial applications. More importantly, compared with other maps, the proposed map has simple structure with more complex behaviors and fewer parameters, and it is easy to set the desired LEs. Finally, we design a novel image encryption algorithm based on the proposed chaotic system and dynamic S-boxes. The experimental results show that the proposed chaotic system can be effectively applied in the field of data encryption.
... Chaotic systems are characterized by the phenomenon that tiny variations in initial conditions can lead to significant changes in system behavior. Exploiting this characteristic of chaotic systems [32], pseudo-random sequences can be generated as encryption keys for image encryption. Subsequently, the parameters for encryption techniques such as image diffusion and pixel permutation are generated using the encryption key, and based on these parameters, the image is encrypted. ...
Preprint
Vision is one of the essential sources through which humans acquire information. In this paper, we establish a novel framework for measuring image information content to evaluate the variation in information content during image transformations. Within this framework, we design a nonlinear function to calculate the neighboring information content of pixels at different distances, and then use this information to measure the overall information content of the image. Hence, we define a function to represent the variation in information content during image transformations. Additionally, we utilize this framework to prove the conclusion that swapping the positions of any two pixels reduces the image's information content. Furthermore, based on the aforementioned framework, we propose a novel image encryption algorithm called Random Vortex Transformation. This algorithm encrypts the image using random functions while preserving the neighboring information of the pixels. The encrypted images are difficult for the human eye to distinguish, yet they allow for direct training of the encrypted images using machine learning methods. Experimental verification demonstrates that training on the encrypted dataset using ResNet and Vision Transformers only results in a decrease in accuracy ranging from 0.3\% to 6.5\% compared to the original data, while ensuring the security of the data. Furthermore, there is a positive correlation between the rate of information loss in the images and the rate of accuracy loss, further supporting the validity of the proposed image information content measurement framework.
... Discrete chaotic systems are simpler to implement, easy to digitize, flexible and suitable for modern digital communication compared to continuous chaotic systems. In addition, the chaotic signals generated by chaotic systems are characterized by initial value sensitivity, non-periodicity, noise-like, unpredictability [4,5], which gives them a unique advantage in secure communications. ...
Article
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Chaotic systems are widely used in secure communication due to their sensitivity to initial values, unpredictability, and complex motion trajectories. In this paper, we study the encryption method of chaotic synchronization and introduce a scaling factor based on traditional feedback control synchronization to achieve more accurate projection synchronization. The effectiveness and robustness of the method in chaotic systems are verified through theoretical proofs and numerical simulations. A chaotic masked speech encryption system utilizing bit similarity is designed; the structural similarity index (SSIM) of the decrypted signal with the original signal is as high as 0.992866, while the SSIM value of the encrypted signal with the original signal is only 0.000030, proving the efficiency and security of the encryption process. Additionally, we analyzed the data transmission process of the encryption system. The fusion of the control signal and the encryption sequence into one transmission sequence in the channel not only saves hardware and software design resources but also reduces inter-channel interference and conflict, improving the reliability and stability of the transmission. Experimental results show that the system performs well in terms of data transmission security and anti-interference capability.
... Moreover, digital images are the main parts over the Internet. [1][2][3][4][5] To prevent information from being stolen, digital image encryption technology has become an important research field for many scholars and researchers. [6][7][8][9][10] In addition to digital image encryption, optical image encryption 11,12 can be another important aspect. ...
Article
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In view of the security problems of image encryption algorithms encoded by single DNA or RNA, to increase the randomness of the diffusion process and the uncertainty of the coding rules, we propose a combining dynamic RNA and DNA computing based chaotic image encryption algorithm, which has a more complicated encryption process for improving the security of the encryption algorithm and increases the difficulty of decoding. First, a new three-dimensional hyperchaotic map is proposed, which exhibits a rich set of dynamic behaviors. Second, the sequences generated by the proposed map are passed to NIST test with good randomness and implemented by digital signal processing hardware, which shows the feasibility of the proposed chaotic map for industrial applications. Second, the K-means algorithm is used to split the plaintext into two parts. Third, the chaotic sequence is used to displace and diffuse the two parts of the plaintext, respectively. Then, chaotic sequences were used to encode using dynamic DNA and RNA of these two parts, respectively. Then, the chaotic sequences were used to compute the dynamic DNA and RNA computing of these two parts, respectively. Finally, the cipher text is decoded accordingly. The experimental results show that compared with some related encryption algorithms, our method has higher security.
... While bringing convenience to us, it may also lead to the disclosure of personal private information, which will affect national security and even have more serious consequences [1,2]. Therefore, it is crucial to improve the security of image data [3][4][5]. Text encryption technology can effectively protect text information. ...
Article
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As the Internet of Things develops by leaps and bounds, digital image is more susceptible to attacks, thus images are encrypted to protect their security. Chaotic system is extensively wielded in image encryption owing to its characteristics, but it also has some defects, such as limited parameter range and vulnerability to attack. For obtaining a more secure encryption algorithm, this paper first proposed a new chaotic structure. The one-dimensional maps can be applied to this chaotic structure to generate the corresponding novel full chaotic maps. The chaotic performance analysis such as bifurcation diagram, Lyapunov exponent and sensitivity analysis verifies that the proposed novel full chaotic maps have excellent chaotic performance, large parameter space, strong sensitivity and high randomness. Then based on the novel full chaotic maps, the dynamic S-boxes generation scheme is designed. Finally, a new color image encryption scheme puts forward ground on novel full chaotic maps and S-boxes. The algorithm uses Arnold transformation to interfere with the color images and replaces them with S-boxes, and then the encrypted images are obtained by diffusion through the modulo addition operation. Simulation results demonstrate that this new secure image encryption scheme has a preferable encryption performance on the image and high execution efficiency, which can prevent various attacks and ensure the security of the image.
... Chaotic systems have excellent cryptographic characteristics such as high initial value sensitivity, long-term unpredictability, pseudo-randomness and ergodicity [3], which makes it widely used in secure communication. At present, many researchers have proposed some image encryption schemes by combining chaos theory and various technologies [4][5][6][7][8][9][10][11][12][13][14][15]. For example, Wang et al [4] proposed an encryption scheme based on matrix semi-tensor product theory and Boolean network. ...
Article
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With the rapid development of information technology in the field of electronic medicine, the confidentiality of medical images has received increasing attention. The research on the encryption of multiple medical images holds greater practical significance. In this paper, the encryption algorithm is designed specifically for the region of interest (ROI) in medical images. Different techniques and methods are used to encrypt ROI and region of non-interest (RONI) respectively. By combining improved Zigzag scrambling, DNA coding, and the Fisher-Yates shuffle, we place an emphasis on protecting the ROI, and achieve secure encryption for medical images of any number and size. In addition, a new one-dimensional chaotic system S-LCS with larger parameter space and better chaotic properties is proposed. In this encryption scheme, the information about the ROI serves as the secret key, and the initial values and parameters of the chaotic sequences required for encryption are calculated from this key. This strengthens the relationship between the key and the plaintext, enhancing the security of the key. Through testing and comparative analysis, it has been found that the encryption algorithm has high enough security, can resist various attacks, and has high encryption efficiency in the application scenario of multi-image encryption.
... For instance, recent studies have investigated and proposed encryption methods based on chaotic systems that boast lower algorithm complexity, ensuring faster encryption and decryption processes. Advancements have also been made in terms of strengthening resistance against chosen-plaintext attacks, known-plaintext attacks, and other security vulnerabilities [29]. Researchers have explored methods to enhance image encryption schemes' robustness against noise interference, ensuring better reconstruction of the original image post-decryption. ...
Article
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This research explores the application of chaotic systems in generating pseudo-random numbers for encryption protocols, offering a novel perspective on addressing the challenges posed by limited computer precision in cryptographic applications. Chaotic systems, while promising for encryption, often suffer from degradation in their chaotic properties when implemented on computers with finite precision. Previous studies have primarily aimed to mitigate this issue, with limited consideration of harnessing finite-precision errors as a potential source of randomness. In this study, we propose an innovative encryption method that leverages finite-precision errors within chaotic systems. The algorithm generates a keystream based on lower bound error and employs standard MATLAB routines to describe its main steps, including initialization and image factor addition, Chua’s circuit simulation, error sequence generation, normalization, reshaping of the normalized sequence, and the encryption process. Comprehensive performance evaluations were conducted using benchmark images, including Cameraman, Peppers, and Catherine, each with dimensions of 256 × 256 pixels. Evaluation criteria encompassed key space analysis, pixel correlation, entropy of information, histogram analysis, and resistance to noise attacks. The results highlight the effectiveness and security of the proposed method, showcasing its practical utility in real-world encryption scenarios. This research not only contributes a novel approach to encryption but also provides valuable insights into the potential of utilizing finite-precision errors to enhance randomness generation in chaotic systems for cryptographic applications.
... Wang et al. constructed a two-parameters chaotic system and combined it with truth table diffusion for image encryption [35]. Zhou et al. used the finite precision of computers to generate chaotic signals and applied it to image encryption, and achieves good encryption results [36]. The performance of chaotic systems will influence the encryption results and therefore some new proposed chaotic systems are committed to solving periodic windows, wide parameter range, and high randomness issues. ...
Article
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Image encryption is an effective method for protecting the security of image information, and chaotic maps are generally applied to realize some random operations. Inspired by the nonlinear characteristic of optimization test functions, a chaotic map called drop-wave map developed from the two-dimensional (2D) drop-wave function is proposed in this paper. The drop-wave map has a wide range of parameters and uniform phase trajectories. Utilizing the generated pseudo-random sequences with the proposed drop-wave map, a novel multi-layer image encryption algorithm is presented through processing bit-planes using bit circle-shift, bit-plane permutation using Baker map, intra-layer permutation, and multi-direction diffusion. First, the bit circle-shift operation is performed on each pixel to change values initially, where the shifted digits are determined with one pseudo-random sequence. Second, the Baker map is used to scramble the bit positions in each bit-plane and the timestamp is regarded as an extra key. Furthermore, the intra-layer permutation operation with another pseudo-random sequence is performed to permutate the bit positions completely. Finally, the ciphertext image is obtained by using multi-direction diffusion to change pixel values. The main contributions of this work lie in the design of a 2D drop-wave map and a combination of multi-layer operations to enhance the security of image encryption. Simulation results and security analysis verify the validity and feasibility of the proposed algorithm through statistical analysis and robustness analysis.
... In the existing image chaos-based algorithms [28]- [32], the chaotic variables were constructed directly by changing the fixed or floating point representation of the chaotic variables with the secret key bits. However, the proposed KCVG modifies the chaotic point indirectly; in which a chaotic perturbation method that uses the secret key bits' value and location is used to achieve this goal. ...
Article
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The secrecy of various forms of multimedia data constitutes a significant aspect of the cybersecurity field. In this case, chaos-based image ciphers can be adapted. Chaotic image encryption has been investigated in the literature using different transformation domains, such as spatial, discrete Fourier transform, wavelet transform, etc. Although some frequency-based cryptosystems exhibit favorable confusion properties, they may suffer in terms of diffusion properties and fail in terms of some statistical characteristics, which make them vulnerable to various statistical, analytical, and differential attacks. In this regard, we adopt a dual-domain (wavelet and spatial domains) image cryptosystem and propose a novel diffusion process in the wavelet domain to address the problem of weak resilience against the aforementioned attacks. The proposed diffusion process in the wavelet domain is applied only on 1/16 of the pixels of the plain image, which makes it computationally more efficient compared to the existing wavelet domain-based works. In addition, the proposed cryptosystem solves the bell shape histogram problem associated with some frequency-based cryptosystems, which has been verified using different performance metrics in our simulation results. We also introduce a novel key-dependent chaotic variable generator to generate the required initial conditions and control parameters for the adopted enhanced chaotic map. The superiority of the proposed algorithm compared to some of the existing state-of-the-art has been verified through various performance metrics. These include different types of correlation coefficients, histogram visualization, histogram deviation, irregular deviation, mean square error, chi-square test, entropy test, and differential analysis.
... The foundational work by Robert Matthews [2] introduced the chaotic encryption method [3], which revolutionized the approach to secure image transmission. Chaotic systems pro-vide an ideal foundation for cryptosystems designed to protect digital images. ...
Article
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In the current era of digital communication, it has become increasingly apparent that transmitting images, often containing personal and/or confidential information, over the Internet is insecure, thus making image security a top priority. Many encryption algorithms have been proposed in the literature to address this issue. However, these algorithms have limitations, such as low-key space, high computational overhead, and susceptibility to differential attacks. To overcome these limitations, this paper proposes Z-Crypt, a novel two-stage image encryption approach that combines a substitution-permutation network (SPN) and a chaotic logistic map (CLM) with the Chirp Z-Transform (CZT) to enhance security and resist attacks. The CLM-generated matrices introduce confusion and diffusion, while SPN creates a dissociation of the cipher from the plaintext. Lastly, the CZT strengthens the encryption by transforming the image into the frequency domain. This creates multiple layers of confusion and diffusion to make a strong encryption algorithm. We have evaluated the proposed Z-Crypt’s security using various metrics, including correlation coefficient, entropy, peak signal-to-noise ratio (PSNR), and key sensitivity analysis. Experimental results verify that the proposed algorithm outperforms existing methods, achieving high security while maintaining computational efficiency.
... As a result, there has been a growing need for a secure transmission environment to accommodate the diverse forms of data exchanged [4][5][6]. Among these, images stand out as a highly visual and commonly shared form of data that typically contains a significant amount of private and sensitive information [7][8][9]. Therefore, the application of image encryption techniques has emerged as a valuable approach to safeguarding important data from potential leakage during transmission [10][11][12]. By employing such techniques, the confidentiality and integrity of transmitted images can be effectively maintained [13][14][15], ensuring the preservation of privacy and the mitigation of unauthorized access or malicious attacks [16][17][18]. ...
Article
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In response to the vulnerability of image encryption techniques to chosen plaintext attacks, this paper proposes a secure image communication scheme based on two-layer dynamic feedback encryption and discrete wavelet transform (DWT) information hiding. The proposed scheme employs a plaintext correlation and intermediate ciphertext feedback mechanism, and combines chaotic systems, bit-level permutation, bilateral diffusion, and dynamic confusion to ensure the security and confidentiality of transmitted images. Firstly, a dynamically chaotic encryption sequence associated with a secure plaintext hash value is generated and utilized for the first round of bit-level permutation, bilateral diffusion, and dynamic confusion, resulting in an intermediate ciphertext image. Similarly, the characteristic values of the intermediate ciphertext image are used to generate dynamically chaotic encryption sequences associated with them. These sequences are then employed for the second round of bit-level permutation, bilateral diffusion, and dynamic confusion to gain the final ciphertext image. The ciphertext image hidden by DWT also provides efficient encryption, higher level of security and robustness to attacks. This technology offers indiscernible secret data insertion, rendering it challenging for assailants to spot or extract concealed information. By combining the proposed dynamic closed-loop feedback secure image encryption scheme based on the 2D-SLMM chaotic system with DWT-based hiding, a comprehensive and robust image encryption approach can be achieved. According to the results of theoretical research and experimental simulation, our encryption scheme has dynamic encryption effect and reliable security performance. The scheme is highly sensitive to key and plaintext, and can effectively resist various common encryption attacks and maintain good robustness. Therefore, our proposed encryption algorithm is an ideal digital image privacy protection technology, which has a wide range of practical application prospects.
... The disclosure of image information may lead to leakage of personal privacy information, and may also affect business secrets or national security [2]. Accordingly, image encryption has become an important technology to protect image information [3,4]. Image cryptography is dissimilar to text cryptography in that there is great redundancy and high pixel correlation [5][6][7]. ...
Article
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Chaotic systems are applicable to image cryptography with their inherent properties. Unfortunately, in numerous existing chaos-based image cryptography, chaotic systems face the problems of uneven chaotic trajectories and narrow chaotic regions, which leads to hidden risks in the encryption approach. To solve these problems, a novel two-dimensional Sine-Arcsin-Cos-Arcsin (2D-SACA) chaotic mo-del is constructed, which can design chaotic systems according to users’ own needs, and then we propose an image encryption approach applying the designed chaotic systems. Compared with the existing chaotic systems in image cryptography, the designed chaotic systems have better randomness, sensitivity, wide chaotic regions and more uniform trajectory distribution. The major contribution of this scheme is to design a 2D-SACA chaotic model, which can generate different superior chaotic systems, and propose an image encryption approach that enables images of different dimensions and categories to be encrypted. Simulation analysis illustrates that this approach has superior performance, high efficiency, strong key sensitivity, and wide key space, thanks to the sensitivity of designed chaotic systems and the extensive chaotic region, which can prevent various attacks. And even with noise interference and data loss, the original image can be successfully restored.
... Al-Hazaimeh et al. proposed an image encryption algorithm utilizing the Lorenz chaotic map, with initial secret keys generated from the hash value of the plaintext image [29]. Wang et al. introduced several new chaotic systems and integrated them into image encryption frameworks, including chaotic signals with finite-precision error [30], an improved ant colony walking path [31], and a newly-designed coupled map lattice [32], among others. Alexan et al. proposed several image encryption methods based on chaotic maps, such as a color image cryptosystem based on Sine chaotic map and 4D Chen hyperchaotic map of fractional-order [33]. ...
Article
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Image encryption serves as a crucial means to safeguard information against unauthorized access during both transmission and storage phases. This paper introduces an integrated encryption algorithm tailored for multiple images, leveraging a novel hyperchaotic system and the Baker map to augment the key space and enhance security measures. The methodology encompasses a permutation-diffusion framework, employing sequences derived from the hyperchaotic system for both permutation and diffusion operations. Initially, the multiple images undergo intermixing, consolidating them into a singular image. Subsequently, the Baker map is employed to further scramble this amalgamated image, thereby extending the scrambling period. Ultimately, the ciphertext image is generated through forward–backward diffusion applied to the pixel sequence of the Zigzag scanned image. Experimental findings substantiate the high-security efficacy of the proposed scheme, demonstrating resilience against diverse threats.
... In recent years, chaotic systems have attracted considerable attention as a potential source of randomness and nonlinearity for cryptographic applications [12][13][14][15][16]. Chaotic systems display complex dynamic behav-iors that make it difficult for attackers to determine the initial conditions and parameters of the chaotic map, resulting in a high level of security [17][18][19][20][21]. To enhance the security of chaotic image encryption algorithms, they are often combined with techniques from other disciplines [22][23][24]. ...
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With the continuous advancement of information technology, the security of digital images is becoming increasingly important. To ensure the secure transmission of images, this paper proposes an image encryption algorithm based on a two-dimensional dual discrete quadratic chaotic map (2D-DDQCM). The digital sequences generated by the 2D-DDQCM exhibit high randomness and unpredictability, making them suitable as pseudo-random number generators in cryptography. In the first round of encryption, the algorithm generates an initial key using natural noise and transforms the pixel positions and values of the image using a pseudo-random key stream generated by the 2D-DDQCM, achieving confusion and diffusion. To ensure the security of the encryption process, the algorithm employs a feedback key mechanism, which ensures the dynamism and unpredictability of the encryption keys, making it more difficult for attackers to crack. In the second round of encryption, the ciphertext is used as input into a hash function to generate a new key. Through a series of pixel-level operations, the security of the ciphertext is further enhanced. The algorithm is tested on a set of standard test images, and the information entropy of the ciphertext was found to be 7.9993, with correlations in the three directions being 0.0006, 0.0003, -- 0.0012, respectively. Additionally, compared with existing image encryption algorithms, the results indicate that the image encryption algorithm based on the 2D-DDQCM and the feedback key mechanism provides an effective solution for the secure transmission of images.
... The proposed method is to resist various attacks. Zhou et al. [28] have suggested a method based on limited computational precision, which was applied to simulate three novel chaotic signals using different chaotic systems and disturbance techniques. According to the results, the suggested algorithm demonstrates a high level of security. ...
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... In existing research on image encryption, chaotic systems [4,5] serve as a critical component of encryption. Zhou et al [6][7][8] proposed various novel chaotic systems for image encryption, considering limitations in computer precision and other issues. For example, the systems employ new random numbers obtained using chaotic signals and true random numbers to perform XOR operations on the encrypted image, enhancing security. ...
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In response to the large size of remote sensing images and the limitations of existing image compression and encryption algorithms, this paper proposes a novel compression and encryption algorithm. The proposed algorithm utilizes a new type of memristive chaotic mapping in combination with PSO-BP neural networks and multi-threaded parallelism. Specifically, the proposed novel two-dimensional memristive chaotic mapping involves a combination of new memristors based on HP memristors and Cubic chaotic mapping. Compared to existing chaotic systems, this method exhibits stronger randomness and hyperchaotic characteristics. Additionally, to improve the reconstruction accuracy of compressed images, a traditional BP neural network with an added hidden layer is combined with the PSO algorithm for image compression and reconstruction. Furthermore, to enhance the encryption efficiency of remote sensing images, a multi-threaded parallel encryption method is employed, enabling simultaneous permutation within and among threads. Experimental results demonstrate that the proposed algorithm achieves good compression reconstruction accuracy, excellent encryption performance, and resistance to attacks.
... UACI and NPCR tests: The attacker usually makes some minor modifications to the plaintext and then observes the ciphertexts generated from the modified and un-modified data to discover the encryption rules for cracking the target scheme. To invalidate such attack methods, all newly designed data encryption schemes should pass the differential attack test, which includes the Number of Pixels Change Rate (NPCR) and the Uniform Average Changing Intensity (UACI) [41]. In the following, we consider a plain image Im 1 and the corresponding cipher image En Im _ . 1 If the minor modification is applied to Im , 1 this lead to Im 2 and the corresponding encrypted version En Im _ . 2 Therefore, the NPCR and the UACI can be determined by: It can be seen from table 2 that the NPCR values are between 0.9955 and 0.9958 while the UACI values are between 0.3269 and 0.3287. ...
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Given the increasing demand for privacy preservation of medical data, a novel medical image encryption scheme is proposed based on Invertible Neural Network (INN) in this paper. Firstly, a new High-Order Hopfield Neural Network (HOHNN) is designed to yield a cipher flow as the conditional input, thereby regulating the encryption process. Moreover, its intrinsic properties as well as various dynamic behaviors are both demonstrated through theoretical analysis and two-parameter Lyapunov exponential charts. Secondly, guided by a multi-objective loss function and a known prior distribution, the original medical image is encrypted into a noise-like cipher image through the proposed encryption scheme. Besides, it is worth mentioning that unlike the existing deep learning-based data encryption schemes, the decryption network shares the identical weight matrix and network structure with the corresponding encryption one in this work. Finally, extensive simulation experiments have validated the feasibility as well as the security of the proposed scheme.
... Combining chaos and gene theory, Gao et al. (2023) propose a colour image encryption scheme based on hyper-chaotic mapping and DNA mutation. Using a finite precision error system, an image encryption algorithm based on new chaotic signals and truly random numbers was proposed by Zhou et al. (2023). An image encryption algorithm based on compressed sensing and integer wavelet transform was proposed by Huang et al. (2023), which has a good hiding effect and can resist known plaintext attacks and selected plaintext attacks. ...
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To study the influence of chaotic systems on wheat image encryption, a method to determine the optimal chaotic system encryption based on a wheat image is proposed. Ten different chaotic system schemes were combined to encrypt the wheat images using 13 common chaotic maps. The best chaotic system scheme was obtained by considering the anti-attack capability of these encryption schemes, which analyzed eight commonly used image encryption performance evaluation indexes. The experimental results show that the new four-dimensional chaotic system has the best encryption effect and is suitable for wheat image encryption. The proposed scheme for wheat image encryption based on chaotic systems provides a reference for other crop image encryption methods.
... Ref [43]. and Ref [44]. present chaotic encryption schemes. ...
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To improve the salient region security and transmission efficiency of remote sensing images, a multiple remote sensing image (MRSIs) encryption scheme based on saliency extraction and magic cube circular motion is proposed in this paper. The scheme provides two tiers of privacy protection for salient regions (airport locations) in remote sensing images. First, a 4D improved discrete tabu learning neuron (4D-IDTLN) chaotic system is proposed. The analysis of phase diagrams, the Lyapunov exponents (LEs) spectrum and bifurcation diagrams of the system show that the system exhibits rich dynamic behaviors. Second, the salient regions of remote sensing images are classified and extracted via knowledge-oriented saliency (KOS) and vision-oriented saliency (VOS) techniques to create a mask contour positioning model (MCPM) for the salient regions, which is then encrypted. Then, the MRSIs are fused into a cube, which is encrypted using magic cube circular motion and chaotic sequences and further encrypted using closed-loop diffusion. Finally, the security of the proposed encryption scheme is evaluated. The results indicate that the scheme provides higher security and better transmission efficiency for MRSIs.
... This characteristic sensitivity is why chaotic maps have become a cornerstone in the realm of cryptography. They are prized for their ability to generate sequences that are inherently unpredictable, making them invaluable for securing cryptographic processes [26][27][28][29][30][31]. ...
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This study introduces an innovative hash function based on a one-dimensional chaotic map, showcasing its strong security capabilities through extensive experimental validation. The development of hash functions has received increasing attention in recent years due to their crucial role in a wide range of information and computer science applications, such as cryptography, ensuring data integrity, and facilitating data indexing. Our chaotic map exhibits robust chaotic behavior, characterized by its high sensitivity to initial conditions and its inherent unpredictability, making it an ideal foundation for the hash function. This function is capable of effectively transforming variable-length input data into 256-bit hash values. It can be easily adapted for different output bit lengths with minimal adjustments to the algorithm's grouping length. Comprehensive security assessments, including rigorous testing against various potential attacks, have been conducted to confirm the hash function's resilience. The combined use of experimental and analytical evaluation methods has confirmed the exceptional security of our proposed hash function, highlighting its potential for critical applications in data integrity verification and encryption that demand high security.
... In the realm of academia, the fascination with nonlinear science has intensified, with chaos theory-characterized by sensitivity to initial conditions and unpredictability in sequence generation [3,4]-standing out as a hallmark of nonlinear systems. Given their widespread application in encryption [5][6][7][8][9][10][11][12][13][14][15], chaotic systems prompt us to devise a key extension algorithm that leverages their inherent security benefits. Traditional one-dimensional chaotic systems, however, are plagued by limitations such as discontinuous chaotic intervals and predictable behaviors [16,17]. ...
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The round key is pivotal to the integrity of block encryption algorithms, derived from the initial key via the key expansion process to enhance security measures. This study introduces an innovative key expansion algorithm, underpinned by a high-performance four-dimensional chaotic map and a durable S-box, distinguishing itself through key sensitivity and independence, thereby enhancing defense against diverse cryptographic attacks. We debut a four-dimensional chaotic map, lauded for its exceptional dynamic qualities as evidenced through rigorous behavior analysis. Furthermore, we develop an S-box generation method utilizing operations in the finite field GF(2 ⁸ ), producing an S-box characterized by its high nonlinearity and fortified security. This S-box is meticulously designed to avoid common vulnerabilities such as fixed points, reverse fixed points, and brief periods, rendering it ideal for key expansion purposes. Leveraging the strengths of the chaotic map and S-box, we detail our key expansion algorithm and validate its security efficacy through comprehensive analysis, highlighting its potential as a robust tool in cryptographic security.
... In academic circles, interest in nonlinear science has grown, with chaos theorymarked by sensitivity to initial conditions and unpredictability in sequence generation [3,4]-emerging as a key feature of nonlinear systems. Owing to their extensive use in encryption [5][6][7][8][9][10][11][12][13][14][15], chaotic systems inspire us to develop a key extension algorithm that capitalizes on their security advantages. However, traditional one-dimensional chaotic systems are limited by issues such as discontinuous chaotic intervals and predictable behaviors [16,17]. ...
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The round key plays a critical role in the security of block encryption algorithms, being derived from the initial key through the key expansion process to bolster security. In this study, we introduce a novel key expansion algorithm powered by a high-performance four-dimensional chaotic map and a robust S-box, notable for its sensitivity and independence of keys, thereby strengthening defense against various cryptographic attacks. We present a four-dimensional chaotic map, celebrated for its outstanding dynamic properties as confirmed through detailed behavior analysis. Additionally, we propose an S-box generation technique based on operations in the finite field GF(2 ⁸ ), resulting in an S-box with high nonlinearity and enhanced security. This S-box is carefully crafted to eliminate typical weaknesses such as fixed points, reverse fixed points, and short periods, making it suitable for key expansion applications. Utilizing the advantages of the chaotic map and S-box, we elaborate on our key expansion algorithm and demonstrate its security effectiveness through thorough evaluation, showcasing its promise as a potent instrument in cryptographic security.
... With the rapid development of communication technology and network technology, various forms of data and information can be more frequently and widely disseminated through the network, which brings convenience to people's lives while posing new challenges to information security [1][2][3]. As one of the most intuitive and common data types in information dissemination, images contain a large amount of private information [4][5][6]. ...
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Due to the finite computing precision, all orbits of a digital chaotic system fall into a cycle when this system is realized on digital computers and digital signal processors. To counteract this degradation, a dynamical perturbation-feedback mixed control (DPFMC) method is proposed by using a novel pseudorandom sequence. We choose a ciphertext sequence as the pseudorandom sequence, and it is used to perturb the digital chaotic system, while it also acts as the coefficient of the dynamical feedback control scheme. The simulation and analysis results show that the proposed method has better dynamical characteristics than traditional methods. Furthermore, we construct a new pseudorandom number generator (PRNG) and determine that it has good randomness. Thus the proposed method can be applied to cryptography and other potential applications.
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We propose a new image encryption algorithm based on the spatiotemporal chaos of the mixed linear–nonlinear coupled map lattices. This spatiotemporal chaotic system has more outstanding cryptography features in dynamics than the logistic map or the system of coupled map lattices does. In the proposed image encryption, we employ the strategy of bit-level pixel permutation which enables the lower bit planes and higher bit planes of pixels permute mutually without any extra storage space. Simulations have been carried out and the results demonstrate the superior security and high efficiency of the proposed algorithm.
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It is shown how the existence of low-dimensional chaotic dynamical systems describing turbulent fluid flow might be determined experimentally. Techniques are outlined for reconstructing phase-space pictures from the observation of a single coordinate of any dissipative dynamical system, and for determining the dimensionality of the system's attractor. These techniques are applied to a well-known simple three-dimensional chaotic dynamical system.