Abdelrahman Abdelrahman Ibrahim Karawia
@mans.edu.eg
Mathematics Department, Faculty of Science
Mathematics Department, Faculty of Science, Mansoura University, Egypt
RESEARCH INTERESTS
My interests are in linear system algorithms, inverse matrix algorithms, wavelets, image denoising, image compression, cryptography, and steganography.
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
Abdelrhman Elkhouly, Ahmed Alksas, Gehad A. Saleh, Mohamed Shehata, Abdelrahman Karawia, Mohammed Ghazal, Sohail Contractor, and Ayman El-Baz
Springer Nature Switzerland
M. Abdul-Hameed, H. El-Metwally, S. Askar, A. M. Alshamrani, M. Abouhawwash, and A. A. Karawia
AIP Publishing
Image encryption stands out as a crucial technique employed to securely transmit images across the Internet. In this paper, we introduce a novel algorithm for encrypting color images. The algorithm is built upon the principles of differential equations, XOR operations, and chaotic maps. First, the plain image is three-dimensional pixel shuffled via a logistic map. Afterward, the differential equations are used as a mathematical tool for encrypting images. The third-order ordinary differential equations are used to encrypt the shuffled images. The color values of the plain image are considered coefficients for the independent variable X. Subsequently, an alternate matrix of the same size is generated using a three-dimensional logistic map, taking into account its color values as the exponents linked to the independent variable X. A set of third-order differential equations emerged, containing an equivalent number of elements as the color values present in the plain image. This set of differential equations is addressed in the following manner: combining XOR and integration three times with respect to the independent variable X for each set of obtained differential equations while treating the integration constant as zero. Ultimately, a set of ordinary equations involving the independent variable X is derived, where the coefficients of X represent color values for the cipher image. The results from experiments and the security analysis affirm the resilience of the proposed algorithm against established security attacks. It exhibits a substantial key space, heightened key sensitivity, and a strong encryption effect.
M. Abdelhakm, A. Salah, S. Askar, M. Abouhawwash, and A. A. Karawia
AIP Publishing
Steganography is widely recognized as an effective method for protecting information via digital media. This paper presents an innovative image steganography algorithm incorporating image compression, chaotic maps, and the least significant bit. The process begins with the compression of a confidential medical image using Huffman encoding. The compressed image then undergoes shuffling, facilitated by the chaotic logistic map. The bits from the shuffled image are discreetly embedded into randomly selected pixels of the cover image, guided by the chaotic piecewise smooth map. The resulting stego image is generated. Statistical analyses are applied to both the cover and stego images for evaluation. The proposed algorithm is compared against state-of-the-art algorithms, and the results demonstrate its superiority over existing methods.
Sameh Askar, Ahmad Alshamrani, Aesha Elghandour, and Abdelrahman Karawia
MDPI AG
One-dimensional and three-dimensional piecewise chaotic maps are used to propose an image-encipher technique in this article. First, the logistic map is used to construct the pseudo-random sequence. After that, this sequence is used to scramble the plain image. Next, the three-dimensional piecewise chaotic map has produced a mask of the chaotic sequence. After doing some preprocessing steps on the mask, a bit-wise XOR operation with the mask is applied to the shuffled image. The suggested algorithm is used to encipher and decipher a different range of images. To check the algorithm security and efficiency, the algorithm performance was calculated using multiple statistical tests and compared to several recent algorithms. Furthermore, numerical simulations and experimental data are also used to validate the proposed algorithm’s resistance to various attacks.
Aesha Elghandour, Ahmad Salah, and Abdelrahman Karawia
Elsevier BV
A. A. Karawia
Institution of Engineering and Technology (IET)
Many methods of hiding information in an image are existing now. The least significant bit is the famous method used in steganographic algorithms. Medical image steganography is a technique used to make the transmission of these images secure so that the decision of the Specialist physician based on these images is not affected. In this paper, medical image steganographic algorithm using modified least significant bit and chaotic map is proposed. The main problem is that the selection of embedding pixels within the host image is not protected enough in most existing methods. So, the author used two-dimensional piecewise smooth chaotic map to select the positions of these pixels randomly. On the other hand, all bits in the secret medical image are transmitted without losing any bit. To do that, the secret medical image is encrypted using one-dimensional piecewise chaotic map (Tent map). Then, the steganographic algorithm is used to hide the bits of the encrypted secret medical image. The bits of each embedded pixel are shuffled before the embedding pro-cess randomly. After that, the stego image is created. The host image and stego image are analysed with the peak signal-to-noise ratio, the mean square error, histogram test, image quality measure and relative entropy test. The stego image displays acceptable result when comparing with the host image. Also, the chi-square attack test is performed and the stego image can resist it. The proposed algorithm can assist the sending of medical images via communication media.
Abdelrahman A. Karawia and Yasser A. Elmasry
Institute of Electrical and Electronics Engineers (IEEE)
Recently, a little research into image encryption has been used on chaotic economic maps. The current paper suggests a bit-level permutation and a non-invertible chaotic economic map to encrypt an image. Firstly, the secret key generation is linked to the plain image. So, the suggested algorithm may resist both known-plaintext and chosen-plaintext attacks. Then a bit-level permutation is performed for all the binary bits of the plain image’s pixels, using the logistic map (permutation stage). It is used to improve the algorithm’s security. Then pixel diffusion is applied using the 2D non-invertible chaotic economic map and bit-wise XOR operations. It is used to change the pixels’ values and make them highly random. The results of the experiments and the security analyses show that the given image encryption algorithm is efficient with higher security. Some comparisons showed that the proposed algorithm outperformed many recent algorithms. Finally, the proposed algorithm may be able to withstand a variety of attacks.
Aesha N. Elghandour, Ahmed M. Salah, Yasser A. Elmasry, and Abdelrahman A. Karawia
Institute of Electrical and Electronics Engineers (IEEE)
In this article, an image encryption algorithm via bisection method and one-dimensional piecewise chaotic map is proposed. It depends on the permutation-substitution model. Firstly, the pseudo-random sequence is defined using polynomial values at selected points by repeat interval of the bisection method. The plain image is shuffled using this sequence. Bit-wise XOR operation with a mask generated from the Tent chaotic map is applied on shuffled image to increase the protection of the proposed algorithm. Various types of images are tested using the proposed algorithm. The effectiveness of this algorithm is measured using several statistical tests and compared to a set of other algorithms to verify the security and performance of the algorithm. Furthermore, experimental results and Numerical simulations are performed to verify their ability to resist various attacks.
Abdelrahman Karawia
MDPI AG
Image encryption is an excellent method for the protection of image content. Most authors used the permutation-substitution model to encrypt/decrypt the image. Chaos-based image encryption methods are used in this model to shuffle the rows/columns and change the pixel values. In parallel, authors proposed permutation using non-chaotic methods and have displayed good results in comparison to chaos-based methods. In the current article, a new image encryption algorithm is designed using combination of Newton-Raphson’s method (non-chaotic) and general Bischi-Naimzadah duopoly system as a hyperchaotic two-dimensional map. The plain image is first shuffled by using Newton-Raphson’s method. Next, a secret matrix with the same size of the plain image is created using general Bischi-Naimzadah duopoly system. Finally, the XOR between the secret matrix and the shuffled image is calculated and then the cipher image is obtained. Several security experiments are executed to measure the efficiency of the proposed algorithm, such as key space analysis, correlation coefficients analysis, histogram analysis, entropy analysis, differential attacks analysis, key sensitivity analysis, robustness analysis, chosen plaintext attack analysis, computational analysis, and NIST statistical Tests. Compared to many recent algorithms, the proposed algorithm has good security efficiency.
Abdelrahman Karawia
Institution of Engineering and Technology (IET)
Recently, few researchers investigated algorithms of image encryption using different chaotic economic maps (CEMs). However, the authors investigated the effect of these maps on the encryption of the plain image. In the current study, an image encryption algorithm via Fisher–Yates shuffling (FYS) combined with a three-dimensional (3D) CEM is given. FYS is used to generate the random permutation of a finite sequence. First, it is used to shuffle the rows and the columns of the plain image. Second, the 3DCEM is used in the substitution stage to confuse the pixels of the shuffling image. The proposed algorithm is applied to several types of images. Many measurements are performed to check the security and performance of the proposed algorithm. In addition, numerical simulations and experimental results have been implemented to verify that the proposed algorithm can resist different attack types.
Sameh Askar, Abdel Karawia, Abdulrahman Al-Khedhairi, and Fatemah Al-Ammar
MDPI AG
In the literature, there are many image encryption algorithms that have been constructed based on different chaotic maps. However, those algorithms do well in the cryptographic process, but still, some developments need to be made in order to enhance the security level supported by them. This paper introduces a new cryptographic algorithm that depends on a logistic and two-dimensional chaotic economic map. The robustness of the introduced algorithm is shown by implementing it on several types of images. The implementation of the algorithm and its security are partially analyzed using some statistical analyses such as sensitivity to the key space, pixels correlation, the entropy process, and contrast analysis. The results given in this paper and the comparisons performed have led us to decide that the introduced algorithm is characterized by a large space of key security, sensitivity to the secret key, few coefficients of correlation, a high contrast, and accepted information of entropy. In addition, the results obtained in experiments show that our proposed algorithm resists statistical, differential, brute-force, and noise attacks.
William Bruce Sherwin
MDPI AG
This article discusses how entropy/information methods are well-suited to analyzing and forecasting the four processes of innovation, transmission, movement, and adaptation, which are the common basis to ecology and evolution. Macroecologists study assemblages of differing species, whereas micro-evolutionary biologists study variants of heritable information within species, such as DNA and epigenetic modifications. These two different modes of variation are both driven by the same four basic processes, but approaches to these processes sometimes differ considerably. For example, macroecology often documents patterns without modeling underlying processes, with some notable exceptions. On the other hand, evolutionary biologists have a long history of deriving and testing mathematical genetic forecasts, previously focusing on entropies such as heterozygosity. Macroecology calls this Gini–Simpson, and has borrowed the genetic predictions, but sometimes this measure has shortcomings. Therefore it is important to note that predictive equations have now been derived for molecular diversity based on Shannon entropy and mutual information. As a result, we can now forecast all major types of entropy/information, creating a general predictive approach for the four basic processes in ecology and evolution. Additionally, the use of these methods will allow seamless integration with other studies such as the physical environment, and may even extend to assisting with evolutionary algorithms.
Sameh S. Askar, Abdelrahman A. Karawia, and Fatmah S. Alammar
Institution of Engineering and Technology (IET)
In the literature, different types of algorithms that are organised to encrypt and decrypt images have been introduced. Some of these depend on chaotic systems where bifurcation routes to chaos exist. Those algorithms have advantages and disadvantages so far as their security level and computational speed are concerned. This study proposes a robust algorithm based on a pixel shuffling and a one-dimensional chaotic economic map for encrypting and decrypting images. The proposed algorithm is implemented on many images. The security and performance of the proposed method are analysed thoroughly by using key space, key-sensitivity, correlation of two adjacent pixels, information entropy, contrast and differential attack. On the basis of the obtained experimental results, the proposed algorithm is characterised by a large size of key space, a high sensitivity to the secret key, very low correlation coefficients, a good information entropy and a high contrast. Finally, the experiments are confirmed that the proposed algorithm can resist statistical and differential attacks with high efficiency.
S. S. Askar, A. A. Karawia, and Ahmad Alshamrani
Hindawi Limited
In literature, chaotic economic systems have got much attention because of their complex dynamic behaviors such as bifurcation and chaos. Recently, a few researches on the usage of these systems in cryptographic algorithms have been conducted. In this paper, a new image encryption algorithm based on a chaotic economic map is proposed. An implementation of the proposed algorithm on a plain image based on the chaotic map is performed. The obtained results show that the proposed algorithm can successfully encrypt and decrypt the images with the same security keys. The security analysis is encouraging and shows that the encrypted images have good information entropy and very low correlation coefficients and the distribution of the gray values of the encrypted image has random-like behavior.
S. S. Askar and A. A. Karawia
Hindawi Limited
Many authors have studied numerical algorithms for solving the linear systems of pentadiagonal type. The well-known fast pentadiagonal system solver algorithm is an example of such algorithms. The current paper describes new numerical and symbolic algorithms for solving pentadiagonal linear systems via transformations. The proposed algorithms generalize the algorithms presented in El-Mikkawy and Atlan, 2014. Our symbolic algorithms remove the cases where the numerical algorithms fail. The computational cost of our algorithms is better than those algorithms in literature. Some examples are given in order to illustrate the effectiveness of the proposed algorithms. All experiments are carried out on a computer with the aid of programs written in MATLAB.
A. A. Karawia
Hindawi Limited
We describe a reliable symbolic computational algorithm for inverting general cyclic heptadiagonal matrices by using parallel computing along with recursion. The computational cost of it is operations. The algorithm is implementable to the Computer Algebra System (CAS) such as MAPLE, MATLAB, and MATHEMATICA. Two examples are presented for the sake of illustration.
A. A. Karawia
Informa UK Limited
In this paper, we present efficient computational and symbolic algorithms for solving backward penta-diagonal linear systems. The implementation of the algorithms using computer algebra systems (CAS) such as MAPLE, MACSYMA, MATHEMATICA, and MATLAB is straightforward. Two examples are given in order to illustrate the algorithms. The symbolic algorithm is competitive with other methods for solving a backward pentadiagonal linear systems.
Milan Batista and Abdel Rahman A. Ibrahim Karawia
Elsevier BV
A.A. Karawia
Elsevier BV
A.A. Karawia
Elsevier BV