In this paper, we introduced new definitions of the system of homogenous difference equations of order two; namely homogenous and semi homogenous system, where we focused on finding the equivalents for these definitions of order one as well as of order greater than one for the system of difference equations of the second order and given some examples. We also a given formula to find the power of the matrix that we used in this research.
<span>Image security is still one of the important fields in multimedia processing because it’s used in our daily lives. Watermarking, steganography, and ciphering are three directions to keep an image secret. Encryption defined as the process of changing information (which called plaintext) into an unreadable secret format (which called cipher-text). A new ciphering algorithm based on binary decomposition and binary codes conversion is proposed in this paper. The key is constructed in a flexible way based on the size of a secret image using some logical operations to increase the security levels. Three test images in different sizes were used to evaluate the performance of the proposed algorithm. The results of the visual scene and statistical factors proved that the suggested method was ciphering the image with high security. The proposed work was validated to confirm its effectiveness. As conclusions, the uses of decomposition and simple binary operations have given high-level image security. Also, key construction is an important step to face several types of attackers.</span>
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