This paper represents a new image encryption algorithm based on modifying generalized singular value decomposition (GSVD) by decomposing the plain-image into two segments using GSVD with an exchanged key-image to produce the cipher-image. The exchanged key-image is used as an encrypting and decrypting image. Mathematically, this procedure is represented by transforming the plain-image’s matrix into two different matrices and applying the GSVD with the exchanged key-image’s matrix to obtain the cipher-image’s matrix. The two encoded segments can be kept in several places or assigned to a group of authorized persons. No one can obtain the information of the image easily without the knowledge of the decrypting key. This proposed algorithm is represented as one of the digital image encryption techniques used to enhance the security of images that have been sent between recipients.
In this paper we will search in analysis the matrices (SVD) and (GSVD) in terms of the relationship between their matrices after touching and briefly about the idea of each. Where we will two analyze matrices A(m, p) and B(n, p) using the techniques above and we compare between each of the two analyzes ‘for the purpose of reaching a final relationship connecting between the matrices of the two analyze. This relationship can be utilized it in image processors, encryption and image enhancement as well as text and video. Perhaps in a later research we will focus on determining the relationships between the matrices of other analyzes such as (QR) and (LU) analysis.
Bézier curve of the first rank is a simple equation in terms of form, but it is characterized by the nature of private transactions making it difficult to use in image encryption because the dispersion of color values is not enough, this results in an encrypted image that gives clear references to the original image. This weakness in the equation does not exist in the case of text encryption where enough to change the numerical values of the components of the text to get a digital matrix representing the encrypted text.Through this algorithm we have used the Bézier curve technique from the first order of image coding we used a new method to generate the coefficients of the equation where we simulated the Bazier equation where it became as follows:
• y=x_1*(t-1)+x_2*t
• Where 0<t<1
To illustrate the work of this technology in image encoding the core of our work is in choosing a vector (1 × 4) with four numerical components )k_1, k_2, k_3, k_4 ( So that k_1<k_2 and k_3 <k_4, k_1 and k_2 have the same signal, as well as k_3 and k_4 also have the same reference to give them t_1 and t_2 Where t_1=k_1/k_2 and t_2=k_3/k_4 which will ensure that both have t_1 and t_2 have positive values less than 1. We have thus designed the equation of Bézier curve suitable for a scattering of color values of the image process, as well we’ll see it by explaining the way in detail below and tables of readings and global standards that have been inferred by the application of the algorithm
The purpose from the research to choose the correct and best type of cement that is prevail able by mass quantity in the markets and different types. To construction the infrastructures needs the best types but the worthy mentioned the world specifications depend on compressive strength after (28) days that means the target to recognize the cements, to exploit the times can be used the chemical analysis for cement composition and calculate the compressive strength on the alkali and alit during hours instead of (28) days practically. The advanced devices used to analysis the cement composition is (X-ray) device.
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