Abdelrahman Abdelrahman Ibrahim Karawia

RESEARCH INTERESTS

My interests are in linear system algorithms, inverse matrix algorithms, wavelets, image denoising, image compression, cryptography, and steganography.

Scopus Publications

Image Features Hiding by Permutation of Pixels Locations
Mohammed Abdul-Hameed
Science Research Society
After completing a scientific research project on image encryption using third-order differential equations, we will focus on designing a new algorithm to conceal the features of the image by exchanging pixel positions in a calculated, precise, and reversible mathematical manner. The exchange will occur in five stages, where the first four stages involve flipping the pixels in a way that resembles paper flipping, causing the pixels to interleave, making their features almost 90% disappear. It is quite natural to significantly increase the disappearance ratio of the image features, reaching up to 99%, by increasing the stages of pixel flipping in different and interleaved positions. However, this is not necessary as we will make the fifth stage of pixel position swapping using a chaotic map, which has the great ability to completely obscure the image features to a ratio of 100%. We applied this algorithm to several images, and the results were excellent. It is worth mentioning that, despite completely hiding the image features, this algorithm is not considered an encryption algorithm because a crucial aspect of encryption, namely the encryption key, is not present. However, it serves as a prelude to the encryption process, we have accomplished through our previous research, where the encryption here is more secure from a security perspective. Additionally, we note that it is possible to enhance this algorithm by adding a key, making it a key-based encryption algorithm, thus obtaining a new encryption algorithm


A New AI System for Precise Grading of HCC Based on Analyzing DW-MRI Radiomics and Alpha-fetoprotein as Liver Cancer Clinical Marker
Abdelrhman Elkhouly, Ahmed Alksas, Gehad A. Saleh, Mohamed Shehata, Abdelrahman Karawia, Mohammed Ghazal, Sohail Contractor, and Ayman El-Baz
Springer Nature Switzerland



Advanced color image encryption using third-order differential equations and three-dimensional logistic map
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.


An image steganography algorithm via a compression and chaotic maps
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.


Image Encryption Algorithm Using Differential Equations
Mohammed Abdul Hameed Jassim Al-Kufi
Science Research Society
After several prior works in image encryption, where we utilized algebraic mathematical tools within matrix algebra to perform operations that scatter the color values of the image, transforming the image into an encrypted matrix that no longer represents the original image, we decided to explore the field of differential equations as a mathematical tool for image encryption. In this algorithm, we employed third-order ordinary differential equations along with first-degree equations to encode the image. We treated the color values of the original image as coefficients for the independent variable ????. Then, we selected another image as an encryption key, considering its color values as the powers associated with the independent variable ????. This process yielded a system of third-order differential equations, the number of which elements equaled the number of color values in the original image.We approached this system of differential equations by integrating with respect to the independent variable ???? three times for each system of differential equations obtained, treating the integration constant as zero. Ultimately, we obtained a system of ordinary equations with the independent variable ????, where the coefficients of this variable represented alternative values for the color values of the original image. These coefficients represented a scattering of the color values of the original image, and the new matrix formed by these values represented the encryption matrix for the original image.For the purpose of decryption and recovering the original image, we referred to the key image used during the encryption process. We followed these steps: We took the numerical values of the encrypted matrix and converted them into coefficients for the independent variable ????. We considered the color values of the key matrix as the powers associated with the independent variable ???? after adding 3 to them. This step yielded a system of ordinary equations with the number of elements corresponding to the number of color values in the original image. Subsequently, we differentiated each equation in the system of ordinary equations mentioned above. We repeated the differentiation process three times, ultimately obtaining a system of differential equations with the independent variable ????, where the coefficients of this variable represented the color values of the image after decryption. These values matched the color values of the original image prior to decryption, confirming that the error value equaled zero.The results we obtained were excellent and matched high standards of accuracy, which we will discuss later.


An Image-Encipherment Algorithm Using a Combination of a One-Dimensional Chaotic Map and a Three-Dimensional Piecewise Chaotic Map
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.


A new cryptographic algorithm via a two-dimensional chaotic map
Aesha Elghandour, Ahmad Salah, and Abdelrahman Karawia
Elsevier BV



Medical image steganographic algorithm via modified LSB method and chaotic map
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.


New Encryption Algorithm Using Bit-Level Permutation and Non-Invertible Chaotic Map
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.


An Image Encryption Algorithm Based on Bisection Method and One-Dimensional Piecewise Chaotic Map
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.


Cryptographic algorithm using newton-raphson method and general bischi-naimzadah duopoly system
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.


Image encryption based on Fisher-Yates shuffling and three dimensional chaotic economic map
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.


An algorithm of image encryption using logistic and two-dimensional chaotic economic maps
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.


Encryption algorithm of multiple-image using mixed image elements and two dimensional chaotic economic map
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.


Cryptographic algorithm based on pixel shuffling and dynamical chaotic economic map
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.


A new recursive algorithm for inverting a general comrade matrix




On the inverse of general cyclic heptadiagonal matrices




Image encryption algorithm based on chaotic economic model
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.


On solving pentadiagonal linear systems via transformations
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.


Female facial beauty analysis for assesment of facial attractivness




Symbolic algorithm for solving comrade linear systems based on a modified stair-diagonal approach
A.A. Karawia
Elsevier BV



Inversion of general cyclic heptadiagonal matrices
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 new algorithm for general cyclic heptadiagonal linear systems using Sherman-Morrison-Woodbury formula




Two algorithms for solving general backward pentadiagonal linear systems
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.


The use of the Sherman-Morrison-Woodbury formula to solve cyclic block tri-diagonal and cyclic block penta-diagonal linear systems of equations
Milan Batista and Abdel Rahman A. Ibrahim Karawia
Elsevier BV

RECENT SCHOLAR PUBLICATIONS

Advanced color image encryption using third-order differential equations and three-dimensional logistic map
M Abdul-Hameed, H El-Metwally, S Askar, AM Alshamrani, ...
AIP Advances 14 (7) 2024



An image steganography algorithm via a compression and chaotic maps
M Abdelhakm, A Salah, S Askar, M Abouhawwash, AA Karawia
AIP Advances 14 (4) 2024



An image-encipherment algorithm using a combination of a one-dimensional chaotic map and a three-dimensional piecewise chaotic map
S Askar, A Alshamrani, A Elghandour, A Karawia
Mathematics 11 (2), 352 2023



Image encryption via a 2-d logistic-baker map and fractional discrete meixner moments
AA Karawia, YM Fouda
2022



A Breakdown Free Numerical Algorithm for Inverting General Tridiagonal Matrices
M El-Mikkawy, A Karawia
arXiv preprint arXiv:2208.12843 2022



A Hybrid Numerical Algorithm for Evaluating n-th Order Tridiagonal Determinants
M El-Mikkawy, AR Karawia
arXiv preprint arXiv:2207.11157 2022



A new cryptographic algorithm via a two-dimensional chaotic map
A Elghandour, A Salah, A Karawia
Ain Shams Engineering Journal 13 (1), 101489 2022



Medical image steganographic algorithm via modified LSB method and chaotic map
AA Karawia
IET Image Processing 15 (11), 2580-2590 2021



New encryption algorithm using bit-level permutation and non-invertible chaotic map
AA Karawia, YA Elmasry
IEEE Access 9, 101357-101368 2021



An image encryption algorithm based on bisection method and one-dimensional piecewise chaotic map
AN Elghandour, AM Salah, YA Elmasry, AA Karawia
IEEE Access 9, 43411-43421 2021



Cryptographic algorithm using newton-raphson method and general bischi-naimzadah duopoly system
A Karawia
Entropy 23 (1), 57 2020



Image encryption based on fisher‐yates shuffling and three dimensional chaotic economic map
A Karawia
IET Image Processing 13 (12), 2086-2097 2019



An algorithm of image encryption using logistic and two-dimensional chaotic economic maps
SS Askar, AA Karawia, A Al-Khedhairi, FS Al-Ammar
Entropy 21 (1), 44 2019



Encryption algorithm of multiple-image using mixed image elements and two dimensional chaotic economic map
AA Karawia
Entropy 20 (10), 801 2018



Cryptographic algorithm based on pixel shuffling and dynamical chaotic economic map
SS Askar, AA Karawia, FS Alammar
IET Image Processing 12 (1), 158-167 2018



A New Recursive Algorithm For Inverting A General Comrade Matrix
AA Karawia
ARS COMBINATORIA 130, 205-213 2017



On solving comrade linear systems via transformations
AA Karawia, SS Askar
British J Math Comput Sci 18, 1-8 2016



On the inverse of general cyclic heptadiagonal matrices
AA Karawia
ARS COMBINATORIA 125, 161-171 2016



Research Article On Solving Pentadiagonal Linear Systems via Transformations
SS Askar, AA Karawia
2015



Image encryption algorithm based on chaotic economic model
SS Askar, AA Karawia, A Alshamrani
Mathematical Problems in Engineering 2015 (1), 341729 2015

MOST CITED SCHOLAR PUBLICATIONS

Inversion of general tridiagonal matrices
M El-Mikkawy, A Karawia
Applied Mathematics Letters 19 (8), 712-720 2006
Citations: 131



An algorithm of image encryption using logistic and two-dimensional chaotic economic maps
SS Askar, AA Karawia, A Al-Khedhairi, FS Al-Ammar
Entropy 21 (1), 44 2019
Citations: 76



Image encryption algorithm based on chaotic economic model
SS Askar, AA Karawia, A Alshamrani
Mathematical Problems in Engineering 2015 (1), 341729 2015
Citations: 62



A computational algorithm for solving periodic penta-diagonal linear systems
AA Karawia
Applied mathematics and computation 174 (1), 613-618 2006
Citations: 46



A new cryptographic algorithm via a two-dimensional chaotic map
A Elghandour, A Salah, A Karawia
Ain Shams Engineering Journal 13 (1), 101489 2022
Citations: 44



Encryption algorithm of multiple-image using mixed image elements and two dimensional chaotic economic map
AA Karawia
Entropy 20 (10), 801 2018
Citations: 42



Cryptographic algorithm based on pixel shuffling and dynamical chaotic economic map
SS Askar, AA Karawia, FS Alammar
IET Image Processing 12 (1), 158-167 2018
Citations: 40



On solving pentadiagonal linear systems via transformations
SS Askar, AA Karawia
Mathematical Problems in Engineering 2015 (1), 232456 2015
Citations: 31



An image encryption algorithm based on bisection method and one-dimensional piecewise chaotic map
AN Elghandour, AM Salah, YA Elmasry, AA Karawia
IEEE Access 9, 43411-43421 2021
Citations: 28



The use of the Sherman–Morrison–Woodbury formula to solve cyclic block tri-diagonal and cyclic block penta-diagonal linear systems of equations
M Batista, ARAI Karawia
Applied Mathematics and Computation 210 (2), 558-563 2009
Citations: 28



Image encryption based on fisher‐yates shuffling and three dimensional chaotic economic map
A Karawia
IET Image Processing 13 (12), 2086-2097 2019
Citations: 26



New encryption algorithm using bit-level permutation and non-invertible chaotic map
AA Karawia, YA Elmasry
IEEE Access 9, 101357-101368 2021
Citations: 25



Medical image steganographic algorithm via modified LSB method and chaotic map
AA Karawia
IET Image Processing 15 (11), 2580-2590 2021
Citations: 15



Two algorithms for solving comrade linear systems
AA Karawia
Applied mathematics and computation 189 (1), 291-297 2007
Citations: 11



Symbolic algorithm for solving comrade linear systems based on a modified Stair-Diagonal Approach
AA Karawia
Applied Mathematics Letters 26 (9), 913-918 2013
Citations: 9



On solving a general bordered tridiagonal linear system
AA Karawia, QM Rizvi
International Journal of Mathematics and Mathematical Sciences 33, 1160-1163 2013
Citations: 9



Female facial beauty analysis for assesment of facial attractivness
QM Rizvi, AA Karawia, S Kumar
2013 2nd international conference on information management in the knowledge 2013
Citations: 7



Two algorithms for solving general backward pentadiagonal linear systems
AA Karawia
International Journal of Computer Mathematics 87 (12), 2823-2830 2010
Citations: 7



New double periodic and solitary wave solutions to the modified Kawahara equation
A Elgarayhi, AA Karawia
International Journal of Nonlinear Science 7 (4), 414-419 2009
Citations: 7



Two algorithms for solving a general backward tridiagonal linear systems
AA Karawia
Applied mathematics and computation 194 (2), 534-539 2007
Citations: 6