The security is so important for both storing and transmitting the digital data, the choice of parameters is critical for a security system, that is, a weak parameter will make the scheme very vulnerable to attacks, for example the use of supersingular curves or anomalous curves leads to weaknesses in elliptic curve cryptosystems, for RSA cryptosystem there are some attacks for low public exponent or small private exponent. In certain circumstances the secret sharing scheme is required to decentralize the risk. In the context of the security of secret sharing schemes, it is known that for the scheme of Shamir, an unqualified set of shares cannot leak any information about the secret. This paper aims to show that the well-known Shamir’s secret sharing is not always perfect and that the uniform randomization before sharing is insufficient to obtain a secure scheme. The second purpose of this paper is to give an explicit construction of weak polynomials for which the Shamir’s (k, n) threshold scheme is insecure in the sense that there exist a fewer than k shares which can reconstruct the secret. Particular attention is given to the scheme whose threshold is less than or equal to 6. It also showed that for certain threshold k, the secret can be calculated by a pair of shares with the probability of 1/2. Finally, in order to address the mentioned vulnerabilities, several classes of polynomials should be avoided.

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.

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.