Chaos theory has been widely used in the design of image encryption schemes. Some low-dimensional chaotic maps have been proved to be easily predictable because of their small chaotic space. On the ...other hand, high-dimensional chaotic maps have a larger chaotic space. However, their structures are too complicated, and consequently, they are not suitable for real-time image encryption. Motivated by this, we propose a new fractional one-dimensional chaotic map with a large chaotic space. The proposed map has a simple structure and a high chaotic behavior in an extensive range of its control parameters values. Several chaos theoretical tools and tests have been carried out to analyze and prove the proposed map’s high chaotic behavior. Moreover, we use the proposed map in the design of a novel real-time image encryption scheme. In this new scheme, we combine the substitution and permutation stages to simultaneously modify both of the pixels’ positions and values. The merge of these two stages and the use of the new simple one-dimensional chaotic map significantly increase the proposed scheme’s security and speed. Besides, the simulation and experimental analysis prove that the proposed scheme has high performances.
This article investigates fields of discovering community structures, which is an essential key to understanding and uncovering organizational principles in complex networks. This tool is of ...theoretical interest and practical significance in modern science. Commonly, the community can be defined as a set of similar nodes led by a node core. Many algorithms use the above definition to find the community structure. However, most of them cannot reveal the node cores and failed to give excellent similarity precision. To overcome the above limitations, we propose a new weighted similarity WS that computes with high precision the closeness between the nodes and clusters based on all local information, including the weight information. A new metric called node strength NS is also proposed to extract the node core of each community. Furthermore, we propose an original method to detect the community structure based on jungle law. Our jungle algorithm (JA) detects the communities with a three-phase strategy: first, the network will be updated by re-weighting and removing the noisy edges. Second, considering the network as a jungle, the strongest or most influential nodes will attract by force just the neighboring weak nodes. Finally, we merge the obtained groups according to the proposed metrics until the community criterion is steady. The experiments on real-world networks are carried out, and the obtained results demonstrate that our JA and WS outperform several community detection methods and similarities.
In this paper, we propose a new real one-dimensional cosine fractional (1-DCF) chaotic map. Several chaos-theory analysis tests demonstrate that the proposed map has many good cryptography ...properties, such as a highly chaotic behavior, a large chaotic range, an infinite number of unstable fixed points, and a widely superior sensitivity to the initial conditions than most of the low-dimensional chaotic maps. Regarding these attractive features, we use the 1-DCF map to design a novel fast image encryption scheme for real-time image processing. Unlike most of the existing encryption schemes, we adopt a permutation-less architecture to increase the encryption speed. Regardless of the permutation phase absence, a high-security level is obtained by using a substitution process with a high sensitivity to the plain image. Moreover, we replace the natural row-order encryption with a more secure random-like encryption order generated from the secret key. Experimentation and simulations show that the new scheme is better than many recently proposed encryption schemes in both security and rapidity.
•A new one-dimensional chaotic map is proposed. The new map offers a complex chaotic behavior with high sensitivity and randomness.•We introduce a new sensitivity function with respect to the plain ...image. The proposed function is recommended to many existing schemes to improve their ability toward the chosen plain text attack.•A new approach called mutual encryption is introduced to improve the security level.•The new scheme is based on a dynamic encryption process that gives and unique encryption way to each image.•The experiments indicate that the new scheme satisfies the theoretical criteria with a fast encryption speed.
In this research paper, we propose a novel one-dimensional chaotic system based on the fraction of cosine over sine (1-DFCS). Evaluation of 1-DFCS indicates the existence of a complex chaotic behavior, an infinite chaotic range, and a high initial state sensitivity. We further propose a new sensitive dynamic mutual image encryption scheme (SDME) using 1-DFCS. SDME is designed with a dynamic diffusion and confusion, which gives a unique encryption process for each image. To ensure the dynamicity, SDME is enriched with a new proposed plain image sensitivity function (PISF). PISF uses the 1-DFCS, plain image, and secret key, which makes it unpredictable and sensitive to a tiny change. PISF is recommended to many image encryption schemes to raise their ability toward the differential attacks. Besides, we propose a mutual part encryption technique. This technique refers to two parties encrypting each other, where a small change in one part reflects the other part. These three characteristics make our scheme able to achieve a high-security level in a single round, which provides a combination of security and time efficiency. The experiment results prove that SDME provides better performance when compared with several state-of-the-art image encryption systems.
In this paper, we propose a new real one-dimensional cosine polynomial (1-DCP) chaotic map. The statistical analysis of the proposed map shows that it has a simple structure, a high chaotic behavior, ...and an infinite chaotic range. Therefore, the proposed map is a perfect candidate for the design of chaos-based cryptographic systems. Moreover, we propose an application of the 1-DCP map in the design of a new efficient image encryption scheme (1-DCPIE) to demonstrate the new map further good cryptographic proprieties. In the new scheme, we significantly reduce the encryption process time by raising the small processing unit from the pixels level to the rows/columns level and replacing the classical sequential permutation substitution architecture with a parallel permutation substitution one. We apply several simulation and security tests on the proposed scheme and compare its performances with some recently proposed encryption schemes. The simulation results prove that 1-DCPIE has a better security level and a higher encryption speed.
In the last decades, a big number of image encryption schemes have been proposed. Most of these schemes reach a high-security level, however, their slow speeds due to their complex process make them ...unusable in real-time applications. Motivated by this, we propose a new efficient and high-speed image encryption scheme based on the Bülban chaotic map. Unlike most of the existing schemes, we make a wisely use of this simple chaotic map to generate only a few numbers of random rows and columns. Moreover, to further increase the speed, we raise the processing unit from the pixel level to the row/column level. Security of the new scheme is achieved through a substitution-permutation network, where we apply a circular shift of rows and columns to break the strong correlation of adjacent pixels. Then, we combine the XOR operation with the Modulo function to mask the pixels values and prevent any leak of information. High-security tests and simulation analysis have been carried out to demonstrate that the scheme is extremely secure and highly fast for real-time image processing at 80 fps (frames per second).
The detection of community structure has aroused wide attention since it can reveal the underlying properties of complex networks in biology, as well as physical and social sciences. Many community ...detection algorithms have been proposed to detect the communities in the un-weighted networks. However, the recently high-level of interest in complex weighted networks gives rise to a need to develop new methods and measures to take the weights of links into account. To fulfill the above needs, we propose a new generalization of the clustering coefficient that retains the information encoded in the weights of links and thus fully capture the richness of the information contained in the data. We also define a new generation of the complete graph (CG) of a weighted network based on the maximal weight attached to each node. Furthermore, we use the weighted clustering coefficient (WCC) and CG to design a novel community detection algorithm based on a proposed pyramidal clustering. It performs in three main steps. In the first step, the CG is generated, and the WCC is computed for all the nodes. The second step uses CG and WCC to divide the network into a set of pyramidal clusters (PCs), where each PC has a score. For the final steps, we propose a measure for the clusters, called connectivity, that computes the degree of connectivity between the PCs. Pairs of PCs with high connectivity are merged until the degree of connectivity between all the clusters is low. The experiment results on weighted and un-weighted real-world networks show that the proposed method outperforms other state-of-art algorithms in terms of normalized mutual information and modularity.
