كرار ضياء محمد السبتي

Abstract The need of making important information that is being exchanged between participants through unsecure websites has intersted cryptoligists to create and modify some secure cryptosytems to prevent these information from getting hacked or cracked.In this paper, a particular strategy in thepublic key cryptosystem called RSA Cryptosystem is presented to be applied over gray and color images with the help of MATLAB Program. Since the RSA cryptosystem is a well-known secure cryptosystem, we use MATLAB to apply this cryptosystem over gray and color images. Moreover, that would be generating two algorithms for the encryption and decryption procedures. These algorithms can be applied over the plain image and cipher image after reading them in the matrices forms. However, the image is partitioned into blocks that are n x m matrices. Since the RSA cryptosystem is a secure public key cryptosystem since its security based on the difficulty of the factoring problem, which is factoring a positive integer R into a product of two primes, we apply this cryptosystem over images using MATLAB with increasing the number of the primes in R. This gives the modified RSA cryptosystem has a higher security than the RSA cryptosystem, because decrypting any encrypted images requires factoring the large integer composed of the product of many large primes, and it requires knowing the size of the blocks that are formed from plain matrix. Therefore, this approach of encrypting and decrypting images using RSA cryptosystem with some modifications more immune against any attacks in the transmission of images in all agencies in the era of the information technology.

Abstract This study concerned with comparing correlation coefficient (correlation) to copula functions (copulas) throughout their correlations, which are defined by means of their copulas . Indeed, it is an attempt to answer the following question, why copula functions (copula) is preferred in modern statistical inference to correlation?. We will discuss each topic individually, to make a right decision about the question above. For making our decision clear we have recalled some of the basic concepts related to correlation and copulas so that we can show the characteristics and differences of using each one.

Abstract Linear regression model is proposed to construct a proper estimation of parameters of Gumbel distribution as influences that effect on manufactured items, for example, bulbs, electrical machines, and so on. Such type of distributions and its properties that relevant to Gamma-distribution has been shown in this study. Some contributions of other extreme value distributions types such as Weibull distribution, and Fr!́chet distribution were introduced in general forms as models used for lifetime data. Maximum likelihood estimation (M.L.E) method was suggested to estimate the values of parameters because of its effective ability to obtain the best approximation for fitting data compared with other estimation methods like least square method, moments method, and other estimation methods. Another important fact of choosing this method is that this method regarded as a best method for small sample sizes.

In this paper ,we introduce a new method as a modified of the (LTB) algorithm for image compression, by using the standard MV-algebra (A, 212  , ~ ,0), where A=[0,1] is the unit interval of real numbers with the internal binary operation  which is defined by x  y=min {1, x+y }and the internal unary operation ~ x =1-x, for all x,y belong to A and a constant 0. We prove some mathematical properties of standard MV-algebra to use them as a mathematical support in our modified method, we call this method (CSLTB). A comparison was made between our method and (LTB algorithm , JPEG algorithm) by the PSNR (Peak signal Noise Ratio) and RMSE (Root Mean Square Error).Show that our method has better performance.