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This document is a retraction note for an article titled "A novel image encryption technique based on Hénon chaotic map and S8 symmetric group." The article has been retracted by the editor-in-chief and the publisher due to concerns raised during an investigation. These concerns include citations that do not support the claims made in the text, non-standard phrasing, and image irregularities. The author, Majid Khan, disagrees with the retraction. The original article can still be found online. [Extracted from the article]

This document is a retraction note for an article titled "A copyright protection using watermarking scheme based on nonlinear permutation and its quality metrics." The article has been retracted by the editor-in-chief and the publisher due to concerns found during an investigation, including unsupported citations, non-standard phrasing, and image irregularities. The author Majid Khan disagrees with the retraction, and the publisher has been unable to contact the other author, Tariq Shah. Springer Nature, the publisher, remains neutral regarding jurisdictional claims and institutional affiliations. The original article can still be found online. [Extracted from the article]

This document is a retraction note for an article titled "An efficient chaotic image encryption scheme." The article has been retracted by the editor-in-chief and the publisher due to concerns raised during an investigation. These concerns include citations that do not support the claims made in the text, non-standard phrasing, and image irregularities. The editor-in-chief no longer has confidence in the results and conclusions of the article. The author Majid Khan disagrees with the retraction, and the publisher has been unable to contact the other author, Tariq Shah. Springer Nature, the publisher, remains neutral regarding jurisdictional claims and institutional affiliations. [Extracted from the article]

This document is a retraction note for an article titled "Construction of S-box based on chaotic Boolean functions and its application in image encryption." The article has been retracted by the editor-in-chief and the publisher due to concerns found during an investigation, including unsupported citations, non-standard phrasing, and image irregularities. The author Majid Khan disagrees with the retraction, and the publisher has been unable to contact the other authors. The original article can still be found online. [Extracted from the article]

The strength of any block cipher depends on the key size, total number of rounds and the strength of confusion component against differential cryptanalysis. Data encryption standard (DES) as a block cipher has enjoyed a worldwide acceptance for more than three decades. It is a symmetric block cipher and considered to be very strong against all known attacks at that time. It uses 64-bit key size and block size, but the advancement in technology results in increasing the speed of the computers and thus makes DES not secure any more. The shorter key size is the weak area of DES. In this article, we have increased the block size as well as the key size from 64 to 128 bits. The internal structure of our proposed mechanism ultimately changed all other components of DES accordingly. By this improvement, our anticipated scheme is more secure due to its robust due to its confusion and diffusion components. The algorithm is applied on the plain text and on images. We have performed the standard benchmarks statistical analyses on our suggested encryption scheme in order to authenticate the anticipated mechanism. [ABSTRACT FROM AUTHOR]

In this article, our aim is to design a new and efficient digital information confidentiality mechanism. We have offered an encryption scheme which is based on fractals and multiple chaotic iterative maps in order to add more confusion and diffusion capability. Due to randomness nature and unique repetitive pattern of fractal increases key space to hundreds of bits and enhance security level of proposed cryptosystem. The projected algorithm is authenticated by utilizing security performance analyses. The security performances elucidate that our suggested technique is quite competent for digital image encryption. [ABSTRACT FROM AUTHOR]

In this communication, we present a technique to synthesize resilient nonlinear mechanisms for the construction of substitution box. The proposed nonlinear component assists in transforming the intelligible message or plaintext into an enciphered format by the use of Gingerbreadman chaotic map and S8 permutations. The proposed substitution box is sensitive to the initial conditions provided to the chaotic system, which are subsequently used as parameters in creating an instance. The simulation results show that the use of the proposed substitution box to image encryption scheme provides an efficient and secure way for real-time communications. [ABSTRACT FROM AUTHOR]

In numerous encryption frameworks, the first information is changed into encoded form by applying nonlinear substitutions and affecting diffusion. The goal of the nonlinear change is to accomplish high level of randomness in the image content. The choice of the source of randomness is critical because the success in cryptanalysis is demarked by the characteristics identified in the encrypted data. The chaotic frameworks show random conduct that is suitable for encryption applications where nonlinear transformations are needed in the middle of plaintext and the scrambled information. The application of nonlinear functional chaos-based system with embedded chaotic systems and binary chaotic sequences can prompt randomness and diffusion in the information. In addition to the high state of randomness, the requirement for various round keys is needed in a run of the mill substitution-permutation process. The proposed strategy kills the requirement for different round keys, which is suitable for high-speed communication frameworks. The measurable analyses performed on the proposed nonlinear algorithm which show improvement in encryption quality and safety against numerous brute-force and statistical attacks. Also, the proposed framework demonstrates high safety against differential and linear cryptanalysis. [ABSTRACT FROM AUTHOR]

In this communication, we have presented a technique to synthesize resilient nonlinear mechanisms for the construction of substitution box for image encryption that utilizes a multiplicative group of nonzero elements of Galois field of order 256. The proposed nonlinear component assists in transforming the intelligible message or plaintext into an enciphered format by the use of exponential and Tinkerbell chaotic maps. The proposed substitution box is sensitive to the initial conditions provided to the chaotic system, which are subsequently used as parameters in creating an instance. The simulation results show that the use of the proposed substitution box to image encryption scheme provides an efficient and secure way for real-time communications. [ABSTRACT FROM AUTHOR]

The advancement of the Internet stretched as frequently as it can in the openness of modernized data, for instance, image, audio and video for public usage. Digital watermarking is a building that delivers surety and support to data check, security and copyright protection of cutting-edge media. This paper combines the purpose of investment study watermarking definition, thought and the guideline responsibilities in this field, for instance, orders of watermarking process that advice which watermarking procedure should be used. It starts with defining some basics and proposing scheme which is based on nonlinear permutation, least significant bits, chaotic logistic and Gauss maps. Finally, distance metrics for proposed scheme discussed to assure the watermark in test image. [ABSTRACT FROM AUTHOR]

The structure of cryptographically resilient substitution boxes (S-boxes) plays a central role in devising safe cryptosystems. The design of chaos-based S-boxes by means of chaotic maps obtained more devotion in current ages. We have suggested novel S-boxes based on the chaotic maps and S symmetric group. We have experimented our chaos-based S-box for image encryption applications and analyze its strength with statistical analyses. [ABSTRACT FROM AUTHOR]

In this manuscript, we have proposed a novel methodology for watermarking which is a gigantic exploration territory that is dynamically developing. This scheme is basically based on applying the Galois field GF(2), S permutation and least significant bits. The investigation of these methods prompts systems for assaults and countermeasures which are utilized to discover blames and limitations in applications, empowering the improvement of better ones. Computerized watermarking is distinctive relying upon its strategies and applications. The extent of this examination is invisible computerized image watermarking for color and gray-scale images. The exploratory consequences of the proposed strategies are dissected utilizing entropy, contrast, homogeneity, energy, means square error, root mean square error, mean absolute error, peak signal-to-noise ratio, universal image quality index, mutual information, structural similarity, structural dissimilarity and structure content are used to measure the similarity between the cover image and watermarked image. [ABSTRACT FROM AUTHOR]

In this study, we present the homotopy analysis transform method for finding solution of fractional diffusion-type equations. We can attain these equations by substituting a first-order time derivative by a fractional-order derivative in regular diffusion equation. We add some examples in order to illustrate the usefulness and efficiency of our novel proposed technique for fractional diffusion equations. [ABSTRACT FROM AUTHOR]

In this paper, we designed a reliable recipe of homotopy analysis method and Laplace decomposition method namely homotopy analysis transform method to solve fuzzy fractional heat and wave equations. This method overcomes the difficulties arise in other analytical method and removes the restrictive condition of nonlinearity and assumptions of small and large parameters. [ABSTRACT FROM AUTHOR]