Information security is one of the important issues in the information age, image encryption algorithms have been increasingly studied to guarantee the secure image transmission over the internet and through wireless networks. In this article, we propose a new approach for image encryption based on polar decomposition and orthogonal matrices. This scheme offers good confusion and diffusion qualities. The proposed algorithm is shown to be secure against important cryptanalytic attacks (statistical attacks, sensitivity dependence, differential attacks, brute force attacks...), theoretical analysis and computer simulations both confirm that it has a high security level.

Recent researches of image encryption algorithms have been increasingly based on chaotic systems. This paper, a new image encryption scheme which employs. The idea is to associate the Hénon attractor and the logistics map, for the construction of a new secret key cryptosystem. We generate values through of the logistics map that will be added to the pixels of the plaintext image. This result modulo 256 will be permuted to another position of the encrypted image. The calculation of this permutation is deducted from the Hénon attractor, which is 2-dimensional, in order to have a significantly increasing the resistance to attacks. The proposed system has the advantage of bigger key space (about 180 bits); high security analysis such as key space analysis, statistical analysis and sensitivity analysis were carried out. The results demonstrate that the proposed system is highly efficient and a robust system.

Electronic health records (EHRs) replaced the old paper-based systems to make patient data more accurate, reliable, and more accessible. Yet, the EHRs system requires high transmission cost, energy, and waste of time for both doctors and patients. Furthermore, EHRs security presents a serious issue threatening the patient's privacy. Most of the third-party hosting systems have some issues related to the users' privacy and data security. Hence, it is necessary to restrict the access control policies and develop efficient mechanisms for cloud-based EHRs data. In this paper, a sensitive and energetic access control (SE-AC) mechanism is proposed for managing the cloud-hosted EHRs and providing a fine-grained access control even in critical situations. The proposed mechanism ensures the confidentiality of the patient's data, where only authorized individuals to have permission to be able to edit or review certain of the patient's data. Each EHR data is encrypted by the managing authority before submitting to the cloud storage. The requesting user can get dynamically changing permissions based on authentication and context attributes. In addition, seven major aspects have been quantified to assess the operation of any access control that could be deployed in the Internet-of-Thing (IoT). The security analysis indicates that the SE-AC mechanism is secure and will prevent any unauthorized access. The results show exceptional compatibility and performance with different setups and configuration.

In this work, we propose a secure version of ElGamal public key cryptosystem, and prove that it is semantically secure assuming the hardness of what we call the two-dimensional decisional Diffie-Hellman (2DDDH) problem, this cryptosystem is distinguished by the speed of encryption and decryption processes and by its resistance to active adversaries. Since the 2DDDH problem is harder than the decisional Diffie-Hellman (DDH) problem (as it will be seen), one may conclude that our model reinforces the exchange security compared to the existed cryptosystems falling within the same context, also we discuss the difficult problems that guarantee its security.

In this paper, we propose a new and practical variant of ElGamal encryption which is secure against every passive and active adversary. Under the hardiness of the decisional Diffie-Hellman assumption, we can prove that the proposed scheme is secure against an adaptive chosen ciphertext attacks in the standard model. Such security verifies not only the confidentiality but also verifies the integrity and the authentication of communications. We display that the modified scheme furthermore achieves anonymity as well as strong robustness.

The security of multimedia documents becomes an urgent need, especially with the increasing image falsifications provided by the easy access and use of image manipulation tools. Hence, usage of image authentication techniques fulfills this need. In this paper, we propose an effective self-embedding fragile watermarking scheme for color images tamper detection and restoration. To decrease the capacity of insertion, a Bayer pattern is used to reduce the color host image into a gray-level watermark, to further improve the security Torus Automorphism permutation is used to scramble the gray-level watermark. In our algorithm, three copies of the watermark are inserted over three components (R, G, and B channels) of the color host image, providing a high probability of detection accuracy and recovery if one copy is destroyed. In the tamper detection process, a majority voting technique is used to determine the legitimacy of the image and recover the tampered regions after interpolating the extracted gray-level watermark. Using our proposed method, tampering rate can achieve 25% with a high visual quality of recovered image and PSNR values greater than 34 (dB). Experimental results demonstrate that the proposed method affords three major properties: the high quality of watermarked image, the sensitive tamper detection and high localization accuracy besides the high-quality of recovered image.

Encryption is the way to ensure confidentiality of different data, digital images have special features as large data, bulky data, and strong correlation between pixels, which makes traditional encryption algorithms not suitable for image encryption. For this concern, we propose a novel lossless encryption scheme for digital images based on combination of matrix transformations and XOR operation. The numerical experimental results confirms that the proposed method achieves high security level against brute force attacks, statistical attacks and sensitivity analysis, moreover the suggested algorithm provides a good randomness properties, thus our method can be applied for image encryption and transmission in sensitive domains.

Nowadays, the security of communication becomes very important with the rapid development of network technology. So, the transmission and distribution of the several digital information must be protected and secured against other users. Many steganography techniques have been proposed for embedding secret digital data in other digital data. In this article, we propose a new steganography algorithm based on a linear algebraic tool that is the polar decomposition (PD) for hiding secret data in an image. A host image is selected and divided into blocks of size 2 × 2, a PD is applied on each block, and the secret data are embedded in suitable blocks. Experimental results show that our proposed algorithm gives a higher hiding capacity, achieves good imperceptibility, and also provides a high degree of security against common types of attacks such as compression attack with quality 10%, gamma correction attack, and impulse noise attack.

The security of multimedia documents becomes an urgent need, especially with the increasing image falsifications provided by the easy access and use of image manipulation tools. Hence, usage of image authentication techniques fulfills this need. In this paper, we propose an effective self-embedding fragile watermarking scheme for color images tamper detection and restoration. To decrease the capacity of insertion, a Bayer pattern is used to reduce the color host image into a gray-level watermark, to further improve the security Torus Automorphism permutation is used to scramble the gray-level watermark. In our algorithm, three copies of the watermark are inserted over three components (R, G, and B channels) of the color host image, providing a high probability of detection accuracy and recovery if one copy is destroyed. In the tamper detection process, a majority voting technique is used to determine the legitimacy of the image and recover the tampered regions after interpolating the extracted gray-level watermark. Using our proposed method, tampering rate can achieve 25% with a high visual quality of recovered image and PSNR values greater than 34 (dB). Experimental results demonstrate that the proposed method affords three major properties: the high quality of watermarked image, the sensitive tamper detection and high localization accuracy besides the high-quality of recovered image.

Wireless capsule endoscopy (WCE) has several benefits over traditional endoscopy such as its portability and ease of usage, particularly for remote internet of things (IoT)-assisted healthcare services. During the WCE procedure, a significant amount of redundant video data is generated, the transmission of which to healthcare centers and gastroenterologists securely for analysis is challenging as well as wastage of several resources including energy, memory, computation, and bandwidth. In addition to this, it is inherently difficult and time consuming for gastroenterologists to analyze this huge volume of gastrointestinal video data for desired contents. To surmount these issues, we propose a secure video summarization framework for outdoor patients going through WCE procedure. In the proposed system, keyframes are extracted using a light-weighted video summarization scheme, making it more suitable for WCE. Next, a cryptosystem is presented for security of extracted keyframes based on 2D Zaslavsky chaotic map. Experimental results validate the performance of the proposed cryptosystem in terms of robustness and high-level security compared to other recent image encryption schemes during dissemination of important keyframes to healthcare centers and gastroenterologists for personalized WCE.

In this paper we consider the problem of the asymptotic expansion of double Laplace-type integrals, in the case when the set γ of points where the phase achieves its absolute minimum is a simple curve. It will be shown that the asymptotic behaviour of such integrals is governed by the order of degeneracy of normal derivatives of the phase with respect to the curve γ. Complete asymptotic expansions will be constructed if that order is constant along γ, and the first two coefficients will be explicitly computed. If not, a uniform asymptotic expansion method, involving special functions, is suggested.

In this paper we consider the problem of the asymptotic expansion of double Laplace-type integrals, in the case when the set γ of points where the phase achieves its absolute minimum is a simple curve. It will be shown that the asymptotic behaviour of such integrals is governed by the order of degeneracy of normal derivatives of the phase with respect to the curve γ. Complete asymptotic expansions will be constructed if that order is constant along γ, and the first two coefficients will be explicitly computed. If not, a uniform asymptotic expansion method, involving special functions, is suggested.

Let E be a n-dimensional vector space over a field k and ω a trivector of Λ3E. We can associate to the trivector ω several invariants either algebraic, arithmetic or geometric. In this paper we consider the following three invariants, the commutant C(ω), the complexity c(ω) and the automorphisms group Aut(ω). We show that there exists a vector space E and a trivector ω of Λ3E for which C(ω) is not a Frobenius algebra. We also show that the complexity c(ω) and the length l(ω) are equal. Finally, we prove the existence of a trivector ω such that Aut(ω) is not a FC-group.

Let E be a n-dimensional vector space over a field k and ω a trivector of Λ3E. We can associate to the trivector ω several invariants either algebraic, arithmetic or geometric. In this paper we consider the following three invariants, the commutant C(ω), the complexity c(ω) and the automorphisms group Aut(ω). We show that there exists a vector space E and a trivector ω of Λ3E for which C(ω) is not a Frobenius algebra. We also show that the complexity c(ω) and the length l(ω) are equal. Finally, we prove the existence of a trivector ω such that Aut(ω) is not a FC-group.

Security is an important issue in image storage and communication, encryption is one of the most common ways to ensure security. Recently, many schemes based on chaotic map have been proposed, but most of this method suffers from small key space, which makes them vulnerable to brute forces attacks. In this study, we design a highly robust novel symmetric image encryption scheme which offer good confusion and diffusion qualities, and a large key space to ensure popular security factor and to overcome the weaknesses of the state of the art encryption schemes. In the security analysis section, we prove that our scheme can resist most known attacks, such as cipher image only attack, known and chosen plain image attacks, differential and exhaustive attacks. It is shown in this paper that the use of polar decomposition with chaotic map can gives a fast and secures encryption.

In this paper, we introduce the homogeneous weight and homogeneous Gray map over the ring R_q=F₂[u₁,u₂,…,u_q]/⟨u²_i=0,u_iu_j=u_ju_i⟩ for q≥1q≥1. We also consider the construction of simplex and MacDonald codes of types α and β over this ring and their covering radius.

In this paper, we define the simplex and MacDonald codes of types αα and β over Z₂Z₄. We also examine the covering radii of these codes. Further, we study the binary images of these codes and prove that the binary image of the simplex codes of type αα meets the Gilbert bound.

In this paper, we show that the asymptotic expansion of a double Laplace-type integral with a non-stationary minimum point, located on the boundary of the domain of integration, is governed by the order of contact between the boundary curve and the level curve of the phase through the minimum point. This achievement will enable us to construct complete asymptotic expansions in more general settings. Especially, the problem will be completely solved if the phase and the boundary curve of the domain of integration are analytic near the minimum point.

In this paper we are concerned with the exit time problem of a dynamic system perturbed by a white noise, in the case where the noiseless dynamics has a global attractor in a given domain. By the use of a singular perturbation technique and recent results on the asymptotic expansion of a class of Laplace-type integrals, new results concerning the problem under investigation will be presented.

In the last decade the need for new and robust watermarking schemes has been increased because of the large illegal possession by not respecting the intellectual property rights in the multimedia in the internet. In this paper we introduce a novel blind robust watermarking scheme which exploits the positive circulant matrices in frequency domain which is the SVD, Different applications such as copyright protection, control and illicit distributions have been given. Simulation results indicate that the proposed method is robust against attacks as common digital processing: compression, blurring, dithering, printing and scanning, etc. and subterfuge attacks (collusion and forgery) also geometric distortions and transformations. Furthermore, good results of NC (normalized correlation) and PSNR (Peak signal-tonoise ratio) have been achieved while comparing with recent state of the art watermarking algorithms.