Enhanced Integer Factorization Method: Sequential and Parallel Approaches Ehab T. Alnfrawy, Hazem M. Bahig, Hatem M. Bahig, Reda Elbarougy Symmetry, 2026 Integer factorization plays a foundational role in asymmetric cryptography systems, notably the Rivest, Shamir, and Adleman (RSA) cryptosystem. This paper presents an improvement of the integer factorization from both sequential and parallel computational perspectives. The algorithm is based on polynomial evaluation and the greatest common divisor. The objectives of these improvements are to decrease the execution time and memory consumption associated with the process of finding prime factors. Experimentally, we use different values of parameters (1) the number of bits n, (2) the difference between two factors, and (3) the number of processors in the parallel model. The experimental results indicate that both proposed methods, sequential and parallel, yield significant improvements regarding running time and memory usage when the difference between the two factors is n1/3 and n1/4. The average improvement observed is 99% in running time, with memory consumption reduced to a constant. This characteristic is important for limited hardware devices. Furthermore, the proposed parallel method demonstrates scalability and achieves sublinear speedup.
CT-to-PET Synthesis in the Head–Neck and Thoracic Region via Conditional 3D Latent Diffusion Modeling Mohammed A. Mahdi, Mohammed Al-Shalabi, Reda Elbarougy, Ehab T. Alnfrawy, Muhammad Usman Hadi, et al. Bioengineering, 2026 Background: Positron emission tomography (PET) provides physiologic information central to oncologic staging and treatment assessment, but its availability is limited by cost, radiation exposure, and scanner access. Synthesizing PET from computed tomography (CT) is attractive but challenging, as tracer uptake is only partially constrained by anatomy, making the mapping inherently one-to-many. Methods: We propose a conditional 3D latent diffusion framework (3D-LDM) for CT-to-PET synthesis in the head–neck and thoracic region. The pipeline localizes anatomy by segmenting lungs in CT and restricting the volume to reduce irrelevant variability. PET volumes are encoded into a compact latent space using a KL-regularized 3D autoencoder, and a conditional 3D diffusion U-Net learns to generate PET latents conditioned on CT via a denoising diffusion process. The model was trained and evaluated on 900 paired PET/CT studies. Performance was assessed in SUV space using MAE, PSNR, and SSIM, and compared against transformer-, CNN-, and GAN-based baselines. Results: On the held-out test cohort, 3D-LDM achieved the best overall quantitative fidelity (MAE = 303.05 ± 22.16 SUV units, PSNR = 32.64 ± 1.79, SSIM = 0.86 ± 0.03), outperforming all baselines with statistically significant differences (p < 0.001). At the lesion level, the model achieved a precision of 0.76 (95% CI: 0.71, 0.81) and recall of 0.76 (95% CI: 0.72, 0.80), detecting an average of 3.19 lesions per scan with a false-positive rate of 0.72/scan. Lesion-wise NMSE was 11.37%, significantly outperforming GAN and transformer baselines. Conclusions: 3D-LDM enables efficient, high-fidelity PET synthesis in the head–neck and thoracic regions, substantially improving lesion-level accuracy over state-of-the-art baselines. While it is not a replacement for diagnostic PET, these results support the model’s potential as a clinical decision support tool.
3D Latent Diffusion Model for MR-Only Radiotherapy: Accurate and Consistent Synthetic CT Generation Mohammed A. Mahdi, Mohammed Al-Shalabi, Ehab T. Alnfrawy, Reda Elbarougy, Muhammad Usman Hadi, et al. Diagnostics, 2025 Background: The clinical imperative to reduce patient ionizing radiation exposure during diagnosis and treatment planning necessitates robust, high-fidelity synthetic imaging solutions. Current cross-modal synthesis techniques, primarily based on GANs and deterministic CNNs, exhibit instability and critical errors in modeling high-contrast tissues, thereby hindering their reliability for safety-critical applications such as radiotherapy. Objectives: Our primary objective was to develop a stable, high accuracy framework for 3D Magnetic Resonance Imaging (MRI) to Computed Tomography (CT) synthesis capable of generating clinically equivalent synthetic CTs (sCTs) across multiple anatomical sites. Methods: We introduce a novel 3D Latent Diffusion Model (3DLDM) that operates in a compressed latent space, mitigating the computational burden of 3D diffusion while leveraging the stability of the denoising objective. Results: Across the Head & Neck, Thorax, and Abdomen, the 3DLDM achieved a Mean Absolute Error (MAE) of 56.44 Hounsfield Units (HU). This result demonstrates a significant 3.63% reduction in overall error compared to the strongest adversarial baseline, CycleGAN (MAE = 60.07 HU, p < 0.05), a 10.76% reduction compared to NNUNet (MAE = 67.20 HU, p < 0.01), and a 20.79% reduction compared to the transformer-based SwinUNeTr (MAE = 77.23 HU, p < 0.0001). The model also achieved the highest structural similarity (SSIM = 0.885 ± 0.031), significantly exceeding SwinUNeTr (p < 0.0001), NNUNet (p < 0.01), and Pix2Pix (p < 0.0001). Likewise, the 3D-LDM achieved the highest peak signal-to-noise ratio (PSNR = 29.73 ± 1.60 dB), with statistically significant gains over CycleGAN (p < 0.01), NNUNet (p < 0.001), and SwinUNeTr (p < 0.0001). Conclusions: This work validates a scalable, accurate approach for volumetric synthesis, positioning the 3DLDM to enable MR-only radiotherapy planning and accelerate radiation-free multi-modal imaging in the clinic.
CT-to-PET Synthesis in the Head–Neck and Thoracic Region via Conditional 3D Latent Diffusion Modeling MA Mahdi, M Al-Shalabi, R Elbarougy, ET Alnfrawy, MU Hadi, RF Ali Bioengineering 13 (5), 534 , 2026 2026
Enhanced Integer Factorization Method: Sequential and Parallel Approaches ET Alnfrawy, HM Bahig, HM Bahig, R Elbarougy Symmetry 18 (5), 780 , 2026 2026
DAIRE: A lightweight AI model for real-time detection of controller area network attacks in the internet of vehicles S Alam, A Jameel, Z Parveen, E Alnfrawy, A Ashraf, R Uddin, J Aqib Machine Learning with Applications, 100859 , 2026 2026
Cone-beam CT to synthetic CT translation using conditional 3D latent diffusion-based model M Al-Shalabi, MA Mahdi, R Elbarougy, ET Alnfrawy, MU Hadi, RF Ali IEEE Access , 2026 2026 Citations: 1
3D Latent Diffusion Model for MR-Only Radiotherapy: Accurate and Consistent Synthetic CT Generation MA Mahdi, M Al-Shalabi, ET Alnfrawy, R Elbarougy, MU Hadi, RF Ali Diagnostics 15 (23), 3010 , 2025 2025 Citations: 3
SHRED: An Ensemble-Based Machine Learning Model to Sift Email Messages for Real-Time Spam Detection S Alam, A Jameel, Z Parveen, E Alnfrawy IEEE Access , 2025 2025 Citations: 2
Security Flaws in Wireless Sensor Networks and Authentication Procedures for Internet of Things KF Reyazur Rashid Irshad, Faisal Shaman, Mohammed Mehdi, Asharul Islam ... Journal of Nanoelectronics and Optoelectronics 18 (2) , 2023 2023 Citations: 1
A Novel Whale Based Optoelectronics System for Securing Healthcare Data in Internet of Things (IoT)-Based Cloud Environment RG Reyazur Rashid Irshad, Faisal Shaman, Mohammed Mehdi, Asharul Islam ... Journal of Nanoelectronics and Optoelectronics 18 (2) , 2023 2023 Citations: 1
Towards an Efficient Public Key Cryptosystem ET Alnfrawy Faculty of Computers and Info. , Cairo University , 2010 2010
Efficient scalar multiplication based on window algorithm with 2's complement applied for elliptic curve cryptosystems MAE Mohamed, TA Ehab, AF Aly 2010 10th International Conference on Intelligent Systems Design and … , 2010 2010 Citations: 1
Addition-Subtraction Chain for 160 bit Integers by using 2’s Complement MM Abd-Eldayem, ET Alnfrawy, AA Fahmy Egyptian Computer Science Journal 34 (5) , 2010 2010 Citations: 3
On the Complexity of Computing Discrete Logarithms ET Alnfrawy Faculty of Science, Cairo University , 2004 2004
Generalized Extended Euclidean Algorithm ET Alnfrawy Computer Division, Mathematics Department, Faculty of Science, Cairo University , 2004 2004
Frobenus Operator over Matrices ET Alnfrawy 1995
Ada Implementation of Dynamic Programming ET Alnfrawy 1995
MOST CITED SCHOLAR PUBLICATIONS
3D Latent Diffusion Model for MR-Only Radiotherapy: Accurate and Consistent Synthetic CT Generation MA Mahdi, M Al-Shalabi, ET Alnfrawy, R Elbarougy, MU Hadi, RF Ali Diagnostics 15 (23), 3010 , 2025 2025 Citations: 3
Addition-Subtraction Chain for 160 bit Integers by using 2’s Complement MM Abd-Eldayem, ET Alnfrawy, AA Fahmy Egyptian Computer Science Journal 34 (5) , 2010 2010 Citations: 3
SHRED: An Ensemble-Based Machine Learning Model to Sift Email Messages for Real-Time Spam Detection S Alam, A Jameel, Z Parveen, E Alnfrawy IEEE Access , 2025 2025 Citations: 2
Cone-beam CT to synthetic CT translation using conditional 3D latent diffusion-based model M Al-Shalabi, MA Mahdi, R Elbarougy, ET Alnfrawy, MU Hadi, RF Ali IEEE Access , 2026 2026 Citations: 1
Security Flaws in Wireless Sensor Networks and Authentication Procedures for Internet of Things KF Reyazur Rashid Irshad, Faisal Shaman, Mohammed Mehdi, Asharul Islam ... Journal of Nanoelectronics and Optoelectronics 18 (2) , 2023 2023 Citations: 1
A Novel Whale Based Optoelectronics System for Securing Healthcare Data in Internet of Things (IoT)-Based Cloud Environment RG Reyazur Rashid Irshad, Faisal Shaman, Mohammed Mehdi, Asharul Islam ... Journal of Nanoelectronics and Optoelectronics 18 (2) , 2023 2023 Citations: 1
Efficient scalar multiplication based on window algorithm with 2's complement applied for elliptic curve cryptosystems MAE Mohamed, TA Ehab, AF Aly 2010 10th International Conference on Intelligent Systems Design and … , 2010 2010 Citations: 1
CT-to-PET Synthesis in the Head–Neck and Thoracic Region via Conditional 3D Latent Diffusion Modeling MA Mahdi, M Al-Shalabi, R Elbarougy, ET Alnfrawy, MU Hadi, RF Ali Bioengineering 13 (5), 534 , 2026 2026
Enhanced Integer Factorization Method: Sequential and Parallel Approaches ET Alnfrawy, HM Bahig, HM Bahig, R Elbarougy Symmetry 18 (5), 780 , 2026 2026
DAIRE: A lightweight AI model for real-time detection of controller area network attacks in the internet of vehicles S Alam, A Jameel, Z Parveen, E Alnfrawy, A Ashraf, R Uddin, J Aqib Machine Learning with Applications, 100859 , 2026 2026
Towards an Efficient Public Key Cryptosystem ET Alnfrawy Faculty of Computers and Info. , Cairo University , 2010 2010
On the Complexity of Computing Discrete Logarithms ET Alnfrawy Faculty of Science, Cairo University , 2004 2004
Generalized Extended Euclidean Algorithm ET Alnfrawy Computer Division, Mathematics Department, Faculty of Science, Cairo University , 2004 2004
Frobenus Operator over Matrices ET Alnfrawy 1995
Ada Implementation of Dynamic Programming ET Alnfrawy 1995
