cryptography

In this research, we will hide an image we call the secret image inside another image we call the repository. After converting the color values of both images from decimal to binary, we copy the stored images into four copies and use the eighth and seventh bits of these copies to hide the full bits of the secret image starting with the first. Two to be replaced in the eighth and seventh parts, respectively in the first version, then we hide the third and fourth bits of the secret image in the eighth and seventh parts, respectively, of the second version of the repository images, after that we hide the fourth and fifth parts of the secret image in the eighth and seventh parts of The third version of the repository image, then finally we put the last two bits of the secret image in the eighth and seventh parts of the fourth version of the image After that, we retrieve the color values of the images formed from the binary system to the decimal system so that we have four new warehouse images, but the secret image that did not show any features in the images roduced in order to strengthen the masking process, we encrypt those formed images using one of the mathematical analyzes within the field of analysis Numerical, which is the analysis of LU factors, which analyzes the image or divides it into two images, and we will see this through the working methodology.

Cayley- Purser Algorithm is a public key algorithm invited by Sarah Flannery in 1998. The algorithm of Cayley-Purser is much faster than some public key methods like RSA but the problem of it is that it can be easily broken especially if some of the private key information is known. The solution to this problem is to modify this algorithm to be more secure than before so that it gives its utilizers the confidence of using it in encrypting important and sensitive information. In this paper, a modification to this algorithm based on using general linear groups over Galois field $GF(p^n)$, which is represented by $GL_m(GF(p^n))$ where $n$ and $m$ are positive integers and $p$ is prime, instead of $GL_2(Z_n)$ which is General linear set of inverted matrices $2 times 2$ whose entries are integers modulo $n$. This $GL_m(GF(p^n))$ ensures that the secret key of this algorithm would be very hard to be obtained. Therefore, this new modification can make the Cayley-Purser Algorithm more immune to any future attacks.

RSA is a well-known public-key cryptosystem. It is the most commonly used and currently most important public-key algorithm which can be used for both encryption and signing. RSA cryptosystem involves exponentiation modulo an integer number n that is the product of two large primes p and q. The security of the system is based on the difficulty of factoring large integers in terms of its key size and the length of the modulus n in bits which is said to be the key size. In this paper, we present a method that increases the speed of RSA cryptosystem. Also an efficient implementation of arithmetic and modular operations are used to increase its speed. The security is also enhanced by using a variable key size space. There exist numerous implementations (hardware or software) of RSA cryptosystem, but most of them are restricted in key size. An important improvement achieved in this paper is that the system is designed flexibly in terms of key size according to user security.

Reaction automata direct graph (RADG) is a new technique that uses the automata direct graph method to represent a certain design for encryption and decryption. Jump states are available in the RADG design that enables the encipher to generate different ciphertexts each time from the same plaintext and wherein not a single ciphertext is related to a certain plaintext. This study created a matrix representation for RADG designs that allows the calculation of the number of cases ($F_{Q}$)mathematically possible for any design of the set $Q$. $F_{Q}$ is an important part of the function $mathrm{F}(mathrm{n}, mathrm{m}, lambda)$ that calculates the total number of cases of a certain design for the values $Q, R, sum, psi, J$ and $T$. This paper produces a mathematical equation to calculate $F_{Q}$.

In this research paper, we will present how to hide confidential information in a color image randomly using a mathematical equation; by apply this equation to the number of image bytes after converting the image into a digital image, the number of randomly selected bytes depends on the length of the secret message. After specifying the bytes, we include the secret message in those selected bytes utilizing least significant bit (LSB) of steganography, and return the new bytes in the same place in the original image by using the same mathematical equation, after the hiding process using steganography, and then we encrypt the image and send it to the recipient. Several statistical measures applied to the original image, compared with the image after embedding, and after the image encrypted. The results obtained are very good. The statistical measures were used the histogram, mean square error (MSE) and the peak signal to noise ratio (PSNR). The system is designed to perform these processes, which consists of two stages, hiding stage and extract stage. The first stage contains from four steps, the first step of this stage reading the image and converting it to a digital image and make an index on each byte of the image bytes and the application of the mathematical equation to select the bytes by randomly, second step is the process of hiding the secret message in selected bytes and return those bytes to the original locations, third step is the calculation of the statistical measures to determine the rate of confusion after the inclusion of the confidential message, fourth step to encrypt the image of the message carrier and measure the rate of confusion after the encryption and compare with the original image. The extraction process consists of three steps, the first step is to use the private key to decrypt, and the second step is to apply the same mathematical equation to extract the embedded bytes of the confidential message, third step use the same method of hiding the information and extracting the confidential message.