1D Chaotic System Research Articles

An improved Dijkstra cross-plane image encryption algorithm based on a chaotic system.

While encrypting information with color images, most encryption schemes treat color images as three different grayscale planes and encrypt each plane individually. These algorithms produce more duplicated operations and are less efficient because they do not properly account for the link between the various planes of color images. In addressing the issue, we propose a scheme that thoroughly takes into account the relationship between pixels across different planes in color images. First, we introduce a new 1D chaotic system. The performance analysis shows the system has good chaotic randomness. Next, we employ a shortest-path cross-plane scrambling algorithm that utilizes an enhanced Dijkstra algorithm. This algorithm effectively shuffles pixels randomly within each channel of a color image. To accomplish cross-plane diffusion, our approach is then integrated into the adaptive diffusion algorithm. The security analysis and simulation results demonstrate that the approach can tackle the issue of picture loss in telemedicine by encrypting color images without any loss of quality. Furthermore, the images we utilize are suitable for both standard RGB and medical images. They incorporate more secure and highly sensitive keys, robustly withstanding various typical ciphertext analysis attacks. This ensures a reliable solution for encrypting original images.

Novel chaotic image cryptosystem using dynamic DNA coding

This study aims to solve the problem of small key space in image cryptosystems based on logistic mapping. First, a new one-dimensional (1D) chaotic system, with a wide continuous chaotic interval, a large Lyapunov exponent and obvious chaotic characteristics are presented. Subsequently, a novel image encryption algorithm based on the new 1D chaotic system and dynamic DNA encoding is designed. Compared with other DNA coding methods, the proposed image encryption algorithm encodes chaotic sequences and ensures that the sequence elements at different positions correspond to different DNA coding schemes. This will help to overcome the fixity of DNA coding and make the proposed dynamic DNA coding easy to operate and implement. Finally, the cipher image is obtained by scrambling and bit XOR operation based on the chaotic sequences. The fixed DNA coding method is compared with other chaotic image encryption schemes, and the experimental results indicate that the image encryption algorithm has higher security and can resist common attacks.

Novel Integer Shmaliy Transform and New Multiparametric Piecewise Linear Chaotic Map for Joint Lossless Compression and Encryption of Medical Images in IoMTs

The discrete Shmaliy moment transform (DST) is a type of discrete orthogonal moment transform that is widely used in signal and image processing. However, DST is not suitable for lossless image applications due to its non-integer reversible nature. To overcome this limitation, we introduce the integer discrete Shmaliy transform (IDST) that performs integer-to-integer encoding, leading to a perfect and unique reconstruction of the input image. Next, a new 1D chaotic system model, the 1D multiparametric piecewise linear chaotic map (M-PWLCM), is presented as an extension of the existing 1D PWLCM. The M-PWLCM includes eight control parameters defined over an unlimited interval. To demonstrate the relevance of IDST and M-PWLCM in reversible image processing applications, they are used in a new scheme for lossless compression and encryption of medical images in the internet of medical things (IoMTs). On the one hand, the simulation results show that our scheme offers a good compression ratio and a higher level of security to resist differential attacks, brute force attacks and statistical attacks. On the other hand, the comparative analysis carried out shows the overall superiority of our scheme over similar state-of-the-art ones, both in achieving a higher compression ratio and better security when communicating medical images over unsecured IoMTs.

Chaotic image encryption based on spiral traversal and finite field bidirectional diffusion

In this paper, a new sinusoidal cascade chaotic map model is proposed, which constructs chaotic system by sinusoidal cascade of two identical 1D chaotic maps. This model can generate 1D chaotic system with wider parameter range and wider chaotic region. To verify its application in image encryption, a chaotic image encryption algorithm based on spiral traversal and finite field bidirectional diffusion is proposed. The pseudo-random sequences generated by three kinds of 1D chaotic maps improved by the sinusoidal cascade chaotic map model are used as the ciphers of the cryptosystem. Among them, SHA-256, SHA-512 and plain image are combined to generate the initial value of the system. The experimental results and security analysis show that the encryption algorithm designed in this paper can effectively resist exhaustive attack, differential attack, noise attack and so on, and the proposed model has superior performance in encryption speed and security.

Secure image encryption scheme based on a new robust chaotic map and strong S-box

Because the characteristics of chaotic systems are very consistent with the requirements of cryptosystem, chaotic systems are widely used in the encryption of big data, especially the chaos based image encryption is particularly feasible. In this paper, a one-dimensional (1D) piece-wise quadratic polynomial chaotic map (PWQPCM) is proposed to obtain a new system model with better chaotic characteristics. Compared with some existing 1D chaotic systems, the proposed PWQPCM system has better dynamic performance. In particular, it exhibits robust chaotic behavior over a larger continuous parameter range, which is more suitable for cryptographic applications. In addition, a strong S-box construction method and a secure image encryption algorithm based on PWQPCM model are proposed. In this encryption algorithm, a new method of pixel segmentation encryption, S-box substitution and diffusion encryption is combined. The cryptosystem proposed in this paper has the advantages of good performance against data loss, low time cost and flexible adjustment of security strength. Simulation experiments and security analysis verified the above good performance of the encryption system, showing its good application potential in real-time image security communication.

A Cross-Plane Color Image Encryption Algorithm Based on 1D-SLM

With the rapid development of 5G technology, it has become fast and easy for people to transmit information on the Internet. Digital images can express information more intuitively, so transmitting information through images has excellent applications. This paper uses a new chaotic system called 1D-Sin-Logistic-Map (1D-SLM). 1D-SLM has two control parameters, which can provide larger parameter space, and the parameter space in the chaotic state is continuous. Through Lyapunov exponent analysis (LE), bifurcation diagrams analysis, spectral entropy analysis (SE), and 0-1 test, it is verified that 1D-SLM has complex dynamic behavior and is very suitable for cryptography. Compared with other 1D chaotic systems, the 1D-SLM has a larger Lyapunov exponent (LE) and spectral entropy (SE). For color image encryption algorithms, only relying on chaotic mapping is not enough to ensure security. So combined with 1D-SLM, we design a color image encryption algorithm, which is implemented by plane expansion, which reduces the correlation between the three channels of color images. The experimental results show that the proposed cross-plane color image encryption algorithm is safe and resistant to common attack methods.

Novel One‐Dimensional Chaotic System and Its Application in Image Encryption

Designing a chaotic system with a simple structure and complex dynamic behavior is one of the main tasks of chaotic cryptography. This paper designs a new 1D chaotic system called 1D two‐parameters‐sin‐cos (1D‐TPSC). Compared with high‐dimensional chaotic systems, the 1D‐TPSC has a simple structure and is easy to implement with software. The Lyapunov exponent analyzes the parameter space of the 1D‐TPSC in a chaotic state. Furthermore, using sensitivity analysis, cobweb plot, and bifurcation diagram to verify that the sequence generated by 1D‐TPSC has good performance. In addition, the 1D‐TPSC has also been applied in chaotic image encryption. Arnold mapping is used to scramble the plaintext, and random XOR is used to diffuse the scrambled image. Simulation experiments show that the method can remarkably resist standard attack methods.

Securing Digital Images through Simple Permutation-Substitution Mechanism in Cloud-Based Smart City Environment

Data security plays a significant role in data transfer in cloud-based smart cities. Chaotic maps are commonly used in designing modern cryptographic applications, in which one-dimensional (1D) chaotic systems are widely used due to their simple design and low computational complexity. However, 1D chaotic maps suffer from different kinds of attacks because of their chaotic discontinuous ranges and small key-space. To own the benefits of 1D chaotic maps and avoid their drawbacks, the cascading of two integrated 1D chaotic systems has been utilized. In this paper, we report an image cryptosystem for data transfer in cloud-based smart cities using the cascading of Logistic-Chebyshev and Logistic-Sine maps. Logistic-Sine map has been utilized to permute the plain image, and Logistic-Chebyshev map has been used to substitute the permuted image, while the cascading of both integrated maps has been utilized in performing XOR procedure on the substituted image. The security analyses of the suggested approach prove that the encryption mechanism has good efficiency as well as lower encryption time compared with other related algorithms.

A novel 1D chaotic system for image encryption, authentication and compression in cloud

To solve the privacy image problem stored in cloud, we propose a compressive sensing (CS) based image compression, authentication, encryption algorithm in cloud, which can implement computation outsourcing to get rid of the expensive storage and computation costs. To achieve these goals, combined with the logistic-tent-sine chaotic map, a logistic-tent-sine chaotic map (LTSS) is proposed for it has larger chaotic ranges and better chaotic behaviors than simple 1D chaotic map such as a logistic chaotic map. Then, the LTSS chaotic system is employed for image protection algorithm in cloud, which contains three parts: data owner, cloud services and data user. The primary role of the data owner part is to compress and encrypt the image while embedding the owner’s Palmprint discriminative and binary features for authentication. The low-frequency part of the image is encrypted using the proposed Binary Data Cyclic Encryption algorithm (BDCE) while the owner’s palmprint features are embedded for authentication of the data owner. The high-frequency data are randomized for compression by the CS and following encrypted by the Double Random Phase Encoding (DRPE). For the cloud services, authentication services depend on the key and palmprint features and the high computational compressed sensing reconstruction is implemented in cloud can reduce the user burden. For data users, a user should provide the correct key and right palmprint, and then obtain an image available from the cloud service. The algorithm has better quality compared with the common compressive sensing based algorithms and robust to noise and occlusion for using the discrete wavelet transform. What is more, theoretical analysis and empirical evaluations show that the proposed algorithm can resist to exhaustive attack, differential attack and classical attacks.

An Image Encryption Algorithm Based on Compressive Sensing and M Sequence

In this article, a new image encryption algorithm based on compressive sensing (CS) and M sequence is proposed to decrease the image communication load and improve the security of image communication in the internet of things. Most of the available image encryption schemes are based on chaotic systems to shuffle the image pixels. Before shuffling the image pixels, the random sequence, which is produced by a chaotic system, need to be sorted. This sorting operation is avoided by utilizing a modified linear feedback shift register (LFSR) state sequence. Then, the security of the proposed scheme is improved by combining CS with an improved 1D chaotic system, which is used to construct a measurement matrix. The computational complexity is reduced by the use of the improved 1D chaotic system. Simultaneously, the amount of image data is reduced. Simulation results and performance analyses demonstrate that the proposed encryption scheme can greatly reduce the amount of image data and has good security and robustness.

A novel color image LSB steganography using improved 1D chaotic map

Conventional one-dimensional (1D) chaotic map have a simple structure, which is easy to implement and has a low computational cost, but has a drawback that the range of chaotic behaviors is narrow and the distribution of key sequence is uniform. In order to overcome the drawback, we proposed an improved 1D chaotic system model and evaluate the proposed model through experiments with the logistic map and a sine map. Simulation and performance evaluation shows that the 1D chaotic map improved by the proposed model can overcome the existing defects sufficiently. We also proposed a color image LSB steganography algorithm using the improved 1D chaotic map. Through experiments, we confirmed the accuracy of the proposed color image LSB steganography algorithm. Experimental results proved that the algorithm has a better performance than the previous methods, showing an excellent performance against statistical analysis attacks. We also analyzed the effect of secret data type on the quality of stego image.

An image encryption algorithm based on substitution technique and chaos mixing

These recent years, countless chaos-based image encryption algorithms have been proposed to meet security needs in real time multimedia communication. However, many of these have exhibited flaws due to the chaotic map inadequacy. In this paper, we proposed a fast and secure image encryption algorithm by using new 1D chaotic systems, with better chaotic properties in the range of their control parameters. These new chaotic systems were obtained from well-known 1D chaotic maps (Logistic, May, Gaussian, Gompertz) with flaws in their chaotic properties. From the chaotic systems designed, we extracted a pseudo random number sequence (PRNS) and generated S-boxes. Then a novel technique of plain image substitution was used to enhance the sensitivity of the original image pixels, followed by a scrambling-masking technique using the generated S-box. Security tests and evaluation metrics confirmed that the proposed cryptosystem was efficient, practicable, and reliable, with high potential to be adopted for network security and secure communications because of its high encryption speed.

A chaotic image encryption algorithm based on 3-D bit-plane permutation

There are two shortcomings existing in the current color image encryption. One is that high correlation between R, G, B components of the original image may be neglected, the other is that the encryption has little relationship with the plain image, and then it is vulnerable to be broken. In order to solve these two problems and present secure and effective image encryption scheme, we introduce a novel chaos-based image encryption algorithm for color images based on three-dimensional (3-D) bit-plane permutation. In the proposed algorithm, the color plain image is firstly converted to 24 bit planes by RGB splitting and bit plane decomposition, next three-dimensional bit-plane permutation is performed on bit planes, position sequences for permutation are obtained from the 3D Chen chaotic system, and then the three confused components are gotten. Secondly, three key matrices are generated by a 1D chaotic system and a multilevel discretization method, and finally, the color cipher image is obtained by diffusing the confused components using key matrices. The SHA 256 hash function value of the plain image is obtained and combined with the given parameters to calculate the parameters and initial values of the chaotic system, so that the proposed scheme highly depends on the plain image and it may effectively withstand known-plaintext and chosen-plaintext attacks. Simulation results and security analyses demonstrate that our algorithm not only has good encryption effect, but can also resist against common attacks, so it is reliable to be applied for image secure communications.

An efficient and secure chaotic cipher algorithm for image content preservation

This paper proposes a new chaotic cipher algorithm for efficient and secure image content preservation, this method is specialized for both standard and medical images, and it consists of two modules which are iteratively performed: chaotic confusion and pixel diffusion. An improved 1D chaotic system (i.e., Logistic Tent System (LTS)) is employed in both confusion and diffusion modules, where its initial conditions are dynamically generated and controlled by the external secret key and SHA-256 hash value of the plain image, conducted to random-like generating key-streams, elevated the sensitivity to small changes on the plain image, and hence ensured the immunity of the proposal against known/chosen plain image attacks. The confusion module is governed by a novel nonlinear bit-shuffling and circular-shifting technique, aiming to achieve bit balancing effect, mixing effect of the pixel value, and certain diffusion mechanism. The diffusion module is ruled by means of an improved XOR operation (eXOR), to further promote the sensitivity to plain image, and accelerate the diffusion mechanism of the overall cipher algorithm. Given that the diffusion mechanism with respect to pixel value mixing are contributed by the two modules, only one encryption round is needed to make a good combination between computational performance, and sufficient security. The obtained results indicate the high performance in terms of execution-time and security level of the proposed cipher algorithm, and validate its robustness against cryptographic attacks, and hence confirm its efficiency for real-time secure image transmission.

Cryptanalysis of image encryption scheme based on a new 1D chaotic system

This paper demonstrates cryptanalysis of an image encryption scheme based on a new 1D chaotic system proposed by Zhou et al. (2014). It is claimed to possess high strength because of better chaotic properties of employed chaotic system, and use of random pixel insertion. On the contrary, several issues are identified in this image encryption scheme including improper definition of key-stream generator used in substitution step, static permutation leading to predictable diffusion and no contribution to confusion, fixed and small number of rounds, practical infeasibility of random-pixel insertion step with one-time use of utilized random values.For practical usability, one-time use condition is required to be dropped. In this case, it is analyzed that M × N cipher image can be represented as a set of linear equations (of original pixel values) derivable using O(M.N) chosen plain text images. Original image is then completely recoverable using differential cryptanalysis with single differential image represented as a set of M.N linear equations solvable with O((M.N)3) complexity. Experimental results demonstrate that the original image is completely recovered without any information regarding key or equivalent key-stream making author's claim of large key-space insignificant. Improvements have been proposed, with security analysis, to enhance strength of existing scheme.

On the design of henon and logistic map-based random number generator

The key sequence is one of the main elements in the cryptosystem. True Random Number Generators (TRNG) method is one of the approaches to generating the key sequence. The randomness source of the TRNG divided into three main groups, i.e. electrical noise based, jitter based and chaos based. The chaos based utilizes a non-linear dynamic system (continuous time or discrete time) as an entropy source. In this study, a new design of TRNG based on discrete time chaotic system is proposed, which is then simulated in LabVIEW. The principle of the design consists of combining 2D and 1D chaotic systems. A mathematical model is implemented for numerical simulations. We used comparator process as a harvester method to obtain the series of random bits. Without any post processing, the proposed design generated random bit sequence with high entropy value and passed all NIST 800.22 statistical tests.

A novel image encryption scheme based on DNA sequence operations and chaotic systems

In the paper, a novel image encryption algorithm based on DNA sequence operations and chaotic systems is proposed. The encryption architecture of permutation and diffusion is adopted. Firstly, 256-bit hash value of the plain image is gotten to calculate the initial values and system parameters of the 2D Logistic-adjusted-Sine map (2D-LASM) and a new 1D chaotic system; thus, the encryption scheme highly depends on the original image. Next, the chaotic sequences from 2D-LASM are used to produce the DNA encoding/decoding rule matrix, and the plain image is encoded into a DNA matrix according to it. Thirdly, DNA level row permutation and column permutation are performed on the DNA matrix of the original image, inter-DNA-plane permutation and intra-DNA-plane permutation can be attained simultaneously, and then, DNA XOR operation is performed on the permutated DNA matrix using a DNA key matrix, and the key matrix is produced by the combination of two 1D chaotic systems. Finally, after decoding the confused DNA matrix, the cipher image is obtained. Experimental results and security analyses demonstrate that the proposed scheme not only has good encryption effect, but also is secure enough to resist against the known attacks.

An image encryption scheme combining chaos-memory cellular automata and weighted histogram

This paper presents a new symmetric scheme for enciphering digital images. The proposal is based on the combination of chaos and cellular automata (CA) under the scenarios of one round enciphering/deciphering and permutation–diffusion architecture. All the generated key-streams in the proposed cryptosystem are based on the use of an improved one-dimensional (1D) chaotic system [i.e., logistic–tent system (LTS)] with excellent chaotic properties. These key-streams are related to both the secret key and the characteristics of the plain image. Before applying the encryption process, one pixel of the plain image at a random position is overwritten by inserting the weighted histogram value as a new measure to represent the plain image’s features, this pixel withholds the encryption routine and further will be used to guarantee the resistance to known/chosen plain image attacks (CPA secure). In the confusion phase, a bit-level permutation is adopted with the generated one-time key-streams using an improved 1D chaotic system. This strategy of shuffling is handled in which besides to the modification of each pixel’s position, its value is also changed, to further render the achievement of both confusion and diffusion possible within just this phase. The diffusion phase is divided into two subphases: In the first one, the value of each pixel is changed sequentially by means of an improved one-dimensional chaotic system, to fasten the diffusion process and spread the influence of a single bit over the others, and in the second subphase, two-dimensional reversible memory cellular automata are associated with quadtree decomposition strategy and applied to the output of the first subphase, to enhance both the security and the diffusion effect of the cryptosystem. Security analysis shows the capacity of the proposed scheme to resist the commonly known attacks besides to its competitive speed that traces its suitability for practical image encryption.

An image encryption algorithm based on bit level Brownian motion and new chaotic systems

In this paper, a new image encryption algorithm based on Brownian motion and new 1D chaotic system is introduced. Firstly, SHA 256 hash value of the plain image is used to generate the initial values and system parameters of chaotic systems for confusion and diffusion process. Then, 8 bitplanes of the plain image are scrambled based on Brownian motion, respectively, and the position and value of all pixels are changed simultaneously. After the confusion process, a two directional diffusion process is carried out, and it is made up of row diffusion (RD) and column diffusion (CD). The whole process can be repeated many rounds in order to get better encryption effect. Simulation results and security analysis show that our scheme has properties of large key space, high sensitivity to key, strong resisting statistical and differential attack. So, it has high security and important practical application in image transmission and image encryption.

A new color image encryption scheme based on DNA sequences and multiple improved 1D chaotic maps

This paper proposes a new encryption scheme for color images based on Deoxyribonucleic acid (DNA) sequence operations and multiple improved one-dimensional (1D) chaotic systems with excellent performance. Firstly, the key streams are generated from three improved 1D chaotic systems by using the secret keys and the plain-image. Transform randomly the key streams and the plain-image into the DNA matrices by the DNA encoding rules, respectively. Secondly, perform the DNA complementary and XOR operations on the DNA matrices to get the scrambled DNA matrices. Thirdly, decompose equally the scrambled DNA matrices into blocks and shuffle these blocks randomly. Finally, implement the DNA XOR and addition operations on the DNA matrices obtained from the previous step and the key streams, and then convert the encrypted DNA matrices into the cipher-image by the DNA decoding rules. Experimental results and security analysis show that the proposed encryption scheme has a good encryption effect and high security. Moreover, it has a strong robustness for the common image processing operations and geometric attack.