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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (28 February 2023) | Viewed by 28858

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Dr. Zhongyun Hua

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School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen 518000, China
Interests: cyberspace security; multimedia security; chaos theory
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Yushu Zhang

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College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
Interests: multimedia security; AI security; blockchain
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Dear Colleagues,

As one of the most fundamental research methods, the mathematical method is highly abstract but instrumental. Algorithms based on the foundation of mathematical models are the most basic concept at the core of computer science. Mathematics has a close relationship with the development of computer science, such as applied mathematics, represented by discrete mathematics, which is focused on the process of transforming continuous models or equations into discrete forms and serves as a bridge between computers and humans. Mathematical proofs also play a growing role in computer science; they are used to certify that software and hardware will always behave correctly, something that no amount of testing can achieve. Unlike using mathematical models and methods to analyze problems that arise in computer science, mathematicians have used computers to assist in the discovery of patterns and formulation of conjectures. Recently, based on numerical methods, language theory, and so on, researchers have begun to use data-driven methods in some subfields, including image processing, knowledge representation, natural language processing, and machine learning. Additionally, neural networks have demonstrated that they can aid mathematicians in discovering new conjectures and theorems, which may bring forth a further technological revolution. This Special Issue of Mathematics is dedicated to original research and recent developments in mathematical methods and computer science. This Special Issue covers all topics related to mathematical methods and computer science.

Dr. Zhongyun Hua
Dr. Yushu Zhang
Guest Editors

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Keywords

mathematics in image processing
mathematics in information security
mathematical methods for detecting and analyzing cyber-attacks
mathematical methods and applications for artificial intelligence

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Published Papers (14 papers)

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Editorial

Jump to: Research

3 pages, 149 KiB

Open AccessEditorial

Preface to the Special Issue on “Mathematical Methods for Computer Science”

by Zhongyun Hua and Yushu Zhang

Mathematics 2023, 11(16), 3608; https://doi.org/10.3390/math11163608 - 21 Aug 2023

Viewed by 800

Abstract

In the last few decades, the relationship between mathematics and algorithms has become increasingly important and influential in computer science [...] Full article

(This article belongs to the Special Issue Mathematical Methods for Computer Science)

Research

Jump to: Editorial

28 pages, 8565 KiB

Open AccessArticle

Security Analysis and Improvement of Dual Watermarking Framework for Multimedia Privacy Protection and Content Authentication

by Ming Li and Yange Yue

Mathematics 2023, 11(7), 1689; https://doi.org/10.3390/math11071689 - 1 Apr 2023

Cited by 2 | Viewed by 1688

Abstract

The demand for using multimedia network infrastructure for transmission grows with each passing day. Research scholars continue to develop new algorithms to strengthen the existing network security framework in order to ensure the privacy protection and content authentication of multimedia content and avoid causing huge economic losses. A new technology for multimedia image copyright protection and content authentication has been proposed. The innovations lie in the use of an inter-block coefficient difference algorithm to embed robust watermarking in the transform domain, and the same fragile watermark is embedded twice in the spatial domain so that any tiny tampering can be identified and located. A new encryption algorithm combined with Arnold transform is used to encrypt data before embedding. However, some security vulnerabilities were found, and successful cryptanalysis and attack were conducted. Subsequently, an improved scheme was proposed to improve the security and tamper detection ability of the original watermarking scheme and recover the tampered robust watermark. The results show that the improved scheme is safer and more reliable and shows good performance in tampering detection and the recovery robustness of the watermark. Full article

(This article belongs to the Special Issue Mathematical Methods for Computer Science)

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29 pages, 9305 KiB

Open AccessArticle

Complete Separable Reversible Data Hiding for Encrypted Digital Images Using Code Division Multiplexing with Versatile Bit Depth Management

by David Mata-Mendoza, Diana Nuñez-Ramirez, Manuel Cedillo-Hernandez, Mariko Nakano-Miyatake and Hector Perez-Meana

Mathematics 2023, 11(4), 1017; https://doi.org/10.3390/math11041017 - 16 Feb 2023

Cited by 3 | Viewed by 1587

Abstract

A reversible data hiding in the encrypted domain (RDH-ED) aims to hide data within encrypted images, protecting its content, while allowing additional information to be distributed. This paper presents a complete separable RDH-ED scheme, whose main contribution is allowing the receiver to extract data and restore the image, either from the cryptogram with hidden data or from the directly decrypted version. With versatile bit-depth management, the most significant bits of each pixel are encrypted with AES-CTR cipher algorithm, while the additional data will be inserted inside the least significant bit planes of the encrypted pixels, by means of the code division multiplexing technique. Considering the marked/encrypted images, and encryption/data-hiding keys, a receiver could: (a) directly decrypt the encrypted image and obtain its approximate version, (b) extract the error-free hidden data, and (c) recover the data and original image. Considering an image approximation version and the data hiding key, a receiver could: (d) extract the hidden data from the plaintext domain, and (e) restore the image to its original state, while accessing the hidden data without any loss. Experimental results show the performance of the developed algorithm, evaluating the capacity and imperceptibility of the proposed scheme with respect to current state of the art. Full article

(This article belongs to the Special Issue Mathematical Methods for Computer Science)

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16 pages, 1867 KiB

Open AccessArticle

PCEP: Few-Shot Model-Based Source Camera Identification

by Bo Wang, Fei Yu, Yanyan Ma, Haining Zhao, Jiayao Hou and Weiming Zheng

Mathematics 2023, 11(4), 803; https://doi.org/10.3390/math11040803 - 4 Feb 2023

Cited by 3 | Viewed by 1348

Abstract

Source camera identification is an important branch in the field of digital forensics. Most existing works are based on the assumption that the number of training samples is sufficient. However, in practice, it is unrealistic to obtain a large amount of labeled samples. Therefore, in order to solve the problem of low accuracy for existing methods in a few-shot scenario, we propose a novel identification method called prototype construction with ensemble projection (PCEP). In this work, we extract a variety of features from few-shot datasets to obtain rich prior information. Then, we introduce semi-supervised learning to complete the construction of prototype sets. Subsequently, we use the prototype sets to retrain SVM classifiers, and take the posterior probability of each image sample belonging to each class as the final projection vector. Finally, we obtain classification results through ensemble learning voting. The PCEP method combines feature extraction, feature projection, classifier training and ensemble learning into a unified framework, which makes full use of image information of few-shot datasets. We conduct comprehensive experiments on multiple benchmark databases (i.e., Dresden, VISION and SOCRatES), and empirically show that our method achieves satisfactory performance and outperforms many recent methods in a few-shot scenario. Full article

(This article belongs to the Special Issue Mathematical Methods for Computer Science)

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21 pages, 927 KiB

Open AccessArticle

Equation-Based Modeling vs. Agent-Based Modeling with Applications to the Spread of COVID-19 Outbreak

by Selain K. Kasereka, Glody N. Zohinga, Vogel M. Kiketa, Ruffin-Benoît M. Ngoie, Eddy K. Mputu, Nathanaël M. Kasoro and Kyamakya Kyandoghere

Mathematics 2023, 11(1), 253; https://doi.org/10.3390/math11010253 - 3 Jan 2023

Cited by 12 | Viewed by 4288

Abstract

In this paper, we explore two modeling approaches to understanding the dynamics of infectious diseases in the population: equation-based modeling (EBM) and agent-based modeling (ABM). To achieve this, a comparative study of these approaches was conducted and we highlighted their advantages and disadvantages. Two case studies on the spread of the COVID-19 pandemic were carried out using both approaches. The results obtained show that differential equation-based models are faster but still simplistic, while agent-based models require more machine capabilities but are more realistic and very close to biology. Based on these outputs, it seems that the coupling of both approaches could be an interesting compromise. Full article

(This article belongs to the Special Issue Mathematical Methods for Computer Science)

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21 pages, 6383 KiB

Open AccessArticle

Trace Concealment Histogram-Shifting-Based Reversible Data Hiding with Improved Skipping Embedding and High-Precision Edge Predictor (ChinaMFS 2022)

by Hui Shi, Baoyue Hu, Jianing Geng, Yonggong Ren and Mingchu Li

Mathematics 2022, 10(22), 4249; https://doi.org/10.3390/math10224249 - 13 Nov 2022

Cited by 2 | Viewed by 1528

Abstract

Reversible data hiding (RDH) is a special class of steganography, in which the cover image can be perfectly recovered upon the extraction of the secret data. However, most image-based RDH schemes focus on improving capacity–distortion performance. In this paper, we propose a novel RDH scheme which not only effectively conceals the traces left by HS but also improves capacity–distortion performance. First, high-precision edge predictor LS-ET (Least Square predictor with Edge Type) is proposed, and the predictor divides pixels into five types, i.e., weak edge, horizontal edge, vertical edge, positive diagonal edge, and negative diagonal edge. Different types of target pixels utilize different training pixels with stronger local consistency to improve accuracy. Then, a novel prediction-based histogram-shifting (HS) framework is designed to conceal embedding traces in the stego images. Finally, we improve both the data-coding method and the skipping embedding strategy to improve the image quality. Experimental results demonstrate that the capacity–distortion performance of the proposed scheme outperforms the other trace concealment schemes and is comparable to the state-of-the-art schemes utilizing sorting technique, multiple histogram modification, and excellent LS-based predictors. Moreover, it can conceal the embedding traces left by the traditional HS schemes to a certain extent, reducing the risk of being steganalyzed. Full article

(This article belongs to the Special Issue Mathematical Methods for Computer Science)

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13 pages, 2849 KiB

Open AccessArticle

Multitask Image Splicing Tampering Detection Based on Attention Mechanism

by Pingping Zeng, Lianhui Tong, Yaru Liang, Nanrun Zhou and Jianhua Wu

Mathematics 2022, 10(20), 3852; https://doi.org/10.3390/math10203852 - 17 Oct 2022

Cited by 8 | Viewed by 2145

Abstract

In today’s modern communication society, the authenticity of digital media has never been of such importance as it is now. In this aspect, the reliability of digital images is of paramount importance because images can be easily manipulated by means of sophisticated software, such as Photoshop. Splicing tampering is a commonly used photographic manipulation for modifying images. Detecting splicing tampering remains a challenging task in the area of image forensics. A new multitask model based on attention mechanism, densely connected network, Atrous Spatial Pyramid Pooling (ASPP) and U-Net for locating splicing tampering in an image, AttDAU-Net, was proposed. The proposed AttDAU-Net is basically a U-Net that incorporates the spatial rich model filtering, an attention mechanism, an ASPP module and a multitask learning framework, in order to capture more multi-scale information while enlarging the receptive field and improving the detection precision of image splicing tampering. The experimental results on the datasets of CASIA1 and CASIA2 showed promising performance metrics for the proposed model (

F_{1}

-scores of 0.7736 and 0.6937, respectively), which were better than other state-of-the-art methods for comparison, demonstrating the feasibility and effectiveness of the proposed AttDAU-Net in locating image splicing tampering. Full article

(This article belongs to the Special Issue Mathematical Methods for Computer Science)

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20 pages, 5419 KiB

Open AccessArticle

On the Physical Layer Security Peculiarities of Wireless Communications in the Presence of the Beaulieu-Xie Shadowed Fading

by Aleksey S. Gvozdarev and Tatiana K. Artemova

Mathematics 2022, 10(20), 3724; https://doi.org/10.3390/math10203724 - 11 Oct 2022

Cited by 3 | Viewed by 1364

Abstract

The article presents an analysis of the physical layer security of a wireless communication system functioning in the presence of multipath fading and a wiretap. Under the assumption of the equal propagation conditions (both for the legitimate receiver and the eavesdropper) described by the shadowed Beaulieu–Xie model, a closed-form expression for the secrecy outage probability was derived. The correctness of the obtained expression was numerically verified via comparison with the direct numerical integration. The truncated version of the obtained expression was analyzed for various channel parameters to establish the requirements for numerically efficient implementation (in terms of the number of summands delivering the desired precision). An in-depth study of the secrecy outage probability dependence from all the possible channel parameters for different fading scenarios was performed, including heavy fading and light fading, with and without strong dominant and multipath components. The performed research demonstrated the existence of the secrecy outage probability non-uniqueness with the respect to the average signal-to-noise ratio in the main channel and the relative distance between the legitimate and wiretap receivers. Full article

(This article belongs to the Special Issue Mathematical Methods for Computer Science)

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19 pages, 6243 KiB

Open AccessArticle

Image Reconstruction with Multiscale Interest Points Based on a Conditional Generative Adversarial Network

by Sihang Liu, Benoît Tremblais, Phillippe Carre, Nanrun Zhou and Jianhua Wu

Mathematics 2022, 10(19), 3591; https://doi.org/10.3390/math10193591 - 1 Oct 2022

Cited by 1 | Viewed by 1427

Abstract

A new image reconstruction (IR) algorithm from multiscale interest points in the discrete wavelet transform (DWT) domain was proposed based on a modified conditional generative adversarial network (CGAN). The proposed IR-DWT-CGAN model generally integrated a DWT module, an interest point extraction module, an inverse DWT module, and a CGAN. First, the image was transformed using the DWT to provide multi-resolution wavelet analysis. Then, the multiscale maxima points were treated as interest points and extracted in the DWT domain. The generator was a U-net structure to reconstruct the original image from a very coarse version of the image obtained from the inverse DWT of the interest points. The discriminator network was a fully convolutional network, which was used to distinguish the restored image from the real one. The experimental results on three public datasets showed that the proposed IR-DWT-CGAN model had an average increase of 2.9% in the mean structural similarity, an average decrease of 39.6% in the relative dimensionless global error in synthesis, and an average decrease of 48% in the root-mean-square error compared with several other state-of-the-art methods. Therefore, the proposed IR-DWT-CGAN model is feasible and effective for image reconstruction with multiscale interest points. Full article

(This article belongs to the Special Issue Mathematical Methods for Computer Science)

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18 pages, 2303 KiB

Open AccessArticle

Research on Improved BBO Algorithm and Its Application in Optimal Scheduling of Micro-Grid

by Qian Zhang, Lisheng Wei and Benben Yang

Mathematics 2022, 10(16), 2998; https://doi.org/10.3390/math10162998 - 19 Aug 2022

Cited by 5 | Viewed by 1425

Abstract

Aiming at the cooperative optimization problem of economy and environmental protection of the traditional microgrid, including micro gas turbine and diesel engine, carbon capture and storage, and a power to gas system which can consume wind and light and deal with carbon dioxide, is introduced, and three optimization scheduling models of the microgrid based on improved BBO algorithm are proposed. Firstly, a micro-grid with a power to gas system is constructed, and an optimal scheduling model is built which takes into account the system operation cost, environmental governance cost and comprehensive economic benefit. Secondly, the ecological expansion operation is introduced, an improved BBO algorithm is explored by improving the mobility model, and its convergence is derived in detail. Finally, the microgrid system energy optimization scheduling is realized based on the improved BBO algorithm. Compared with the scheduling model that only considers the operation cost or pollution gas control cost, the total cost of the comprehensive economic benefit scheduling model is reduced by 15.5% and 5.5%, respectively, which reflects the reasonableness of the scheduling model and the effectiveness of the improved algorithm. Full article

(This article belongs to the Special Issue Mathematical Methods for Computer Science)

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19 pages, 8076 KiB

Open AccessArticle

Steganography with High Reconstruction Robustness: Hiding of Encrypted Secret Images

by Xishun Zhu, Zhengliang Lai, Nanrun Zhou and Jianhua Wu

Mathematics 2022, 10(16), 2934; https://doi.org/10.3390/math10162934 - 15 Aug 2022

Cited by 10 | Viewed by 2111

Abstract

As one of the important methods to protect information security, steganography can ensure the security of data in the process of information transmission, which has attracted much attention in the information security community. However, many current steganography algorithms are not sufficiently resistant to recent steganalysis algorithms, such as deep learning-based steganalysis algorithms. In this manuscript, a new steganography algorithm, based on residual networks and pixel shuffle, is proposed, which combines image encryption and image hiding, named Resen-Hi-Net, an algorithm that first encrypts a secret image and then hides it in a carrier image to produce a meaningful container image. The proposed Resen-Hi-Net has the advantages of both image encryption and image hiding. The experimental results showed that the proposed Resen-Hi-Net could realize both image encryption and image hiding; the visual container image quality was as high as 40.19 dB on average in PSNR to reduce the possibility of being attacked, and the reconstructed secret image quality was also good enough (34.39 dB on average in PSNR). In addition, the proposed Resen-Hi-Net has a strong ability to resist destructive attacks and various steganographic analyses. Full article

(This article belongs to the Special Issue Mathematical Methods for Computer Science)

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24 pages, 6083 KiB

Open AccessArticle

Image Encryption Algorithm Based on Plane-Level Image Filtering and Discrete Logarithmic Transform

by Wei Feng, Xiangyu Zhao, Jing Zhang, Zhentao Qin, Junkun Zhang and Yigang He

Mathematics 2022, 10(15), 2751; https://doi.org/10.3390/math10152751 - 3 Aug 2022

Cited by 51 | Viewed by 2387

Abstract

Image encryption is an effective way to protect image data. However, existing image encryption algorithms are still unable to strike a good balance between security and efficiency. To overcome the shortcomings of these algorithms, an image encryption algorithm based on plane-level image filtering and discrete logarithmic transformation (IEA-IF-DLT) is proposed. By utilizing the hash value more rationally, our proposed IEA-IF-DLT avoids the overhead caused by repeated generations of chaotic sequences and further improves the encryption efficiency through plane-level and three-dimensional (3D) encryption operations. Aiming at the problem that common modular addition and XOR operations are subject to differential attacks, IEA-IF-DLT additionally includes discrete logarithmic transformation to boost security. In IEA-IF-DLT, the plain image is first transformed into a 3D image, and then three rounds of plane-level permutation, plane-level pixel filtering, and 3D chaotic image superposition are performed. Next, after a discrete logarithmic transformation, a random pixel swapping is conducted to obtain the cipher image. To demonstrate the superiority of IEA-IF-DLT, we compared it with some state-of-the-art algorithms. The test and analysis results show that IEA-IF-DLT not only has better security performance, but also exhibits significant efficiency advantages. Full article

(This article belongs to the Special Issue Mathematical Methods for Computer Science)

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17 pages, 2953 KiB

Open AccessArticle

Federated Learning-Inspired Technique for Attack Classification in IoT Networks

by Tariq Ahamed Ahanger, Abdulaziz Aldaej, Mohammed Atiquzzaman, Imdad Ullah and Muhammad Yousufudin

Mathematics 2022, 10(12), 2141; https://doi.org/10.3390/math10122141 - 20 Jun 2022

Cited by 10 | Viewed by 2294

Abstract

More than 10-billion physical items are being linked to the internet to conduct activities more independently and with less human involvement owing to the Internet of Things (IoT) technology. IoT networks are considered a source of identifiable data for vicious attackers to carry out criminal actions using automated processes. Machine learning (ML)-assisted methods for IoT security have gained much attention in recent years. However, the ML-training procedure incorporates large data which is transferable to the central server since data are created continually by IoT devices at the edge. In other words, conventional ML relies on a single server to store all of its data, which makes it a less desirable option for domains concerned about user privacy. The Federated Learning (FL)-based anomaly detection technique, which utilizes decentralized on-device data to identify IoT network intrusions, represents the proposed solution to the aforementioned problem. By exchanging updated weights with the centralized FL-server, the data are kept on local IoT devices while federating training cycles over GRUs (Gated Recurrent Units) models. The ensemble module of the technique assesses updates from several sources for improving the accuracy of the global ML technique. Experiments have shown that the proposed method surpasses the state-of-the-art techniques in protecting user data by registering enhanced performance measures of Statistical Analysis, Energy Efficiency, Memory Utilization, Attack Classification, and Client Accuracy Analysis for the identification of attacks. Full article

(This article belongs to the Special Issue Mathematical Methods for Computer Science)

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23 pages, 7936 KiB

Open AccessArticle

Double Image Encryption Scheme Based on Compressive Sensing and Double Random Phase Encoding

by Rui Zhang and Di Xiao

Mathematics 2022, 10(8), 1242; https://doi.org/10.3390/math10081242 - 10 Apr 2022

Cited by 12 | Viewed by 1955

Abstract

In order to overcome the shortcomings of the standard compressive sensing (CS) encryption framework, a novel fusion application scheme of CS and optical transformation technology is proposed. The proposed scheme, making full use of the feature of CS to achieve compression and encryption simultaneously, compresses and encrypts two images into one image, which not only reduces storage space and transmission bandwidth, but also improves the security performance of encryption. In the proposed scheme, the two original images are first sampled with CS, and then double random phase coding is performed to obtain two small-sized images. Meanwhile, the two original images are directly encrypted with double random phase coding to obtain the authentication information. Next, we combine two small-sized images and authentication information into one image, and finally perform double random phase coding again to obtain the final encrypted image. It should be emphasized that the proposed scheme has the function of image authentication. Experiment results validate the effectiveness and advancement of the proposed fusion application scheme. Full article

(This article belongs to the Special Issue Mathematical Methods for Computer Science)

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