Search results for: local differential privacy

Authors: Ananya Gangavarapu

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Convolutional Neural Networks (CNN) based models are providing diagnostic capabilities on par with the medical specialists in many specialty areas. However, collecting the medical data for training purposes is very challenging because of the increased regulations around data collections and privacy concerns around personal health data. The gathering of the data becomes even more difficult if the capture devices are edge-based mobile devices (like smartphones) with feeble wireless connectivity in rural/remote areas. In this paper, I would like to highlight Federated Learning approach to mitigate data privacy and security issues.

Keywords: deep learning in healthcare, data privacy, federated learning, training in distributed environment

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Authors: Prajwal Eachempati, Laurent Muzellec, Ashish Kumar Jha

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We use Facebook as a case study to investigate the complex relationship between the firm’s public discourse (and actions) surrounding data privacy and the performance of a business model based on monetizing user’s data. We do so by looking at the evolution of public discourse over time (2004–2021) and relate topics to revenue and stock market evolution Drawing from archival sources like Zuckerberg We use LDA topic modelling algorithm to reveal 19 topics regrouped in 6 major themes. We first show how, by using persuasive and convincing language that promises better protection of consumer data usage, but also emphasizes greater user control over their own data, the privacy issue is being reframed as one of greater user control and responsibility. Second, we aim to understand and put a value on the extent to which privacy disclosures have a potential impact on the financial performance of social media firms. There we found significant relationship between the topics pertaining to privacy and social media/technology, sentiment score and stock market prices. Revenue is found to be impacted by topics pertaining to politics and new product and service innovations while number of active users is not impacted by the topics unless moderated by external control variables like Return on Assets and Brand Equity.

Keywords: public discourses, data protection, social media, privacy, topic modeling, business models, financial performance

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Authors: N. Meddeb, A. M. Makhlouf, M. A. Ben Ayed

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Due to the real-time requirement of message in Vehicular Ad hoc NETworks (VANET), it is necessary to authenticate vehicles to achieve security, efficiency, and conditional privacy-preserving. Privacy is of utmost relevance in VANETs. For this reason, we have proposed a new protocol called ‘Multilevel Authentication Protocol’ (MAP) that considers different vehicle categories. The proposed protocol is based on our Multilevel Authentication protocol for Vehicular networks (MAVnet). But the MAP leads to human safety, where the priority is given to the ambulance vehicles. For evaluation, we used the Java language to develop a demo application and deployed it on the Network Security Simulation (Nessi2). Compared with existing authentication protocols, MAP markedly enhance the communication overhead and decreases the delay of exchanging messages while preserving conditional privacy.

Keywords: Vehicular Ad hoc NETworks (VANET), vehicle categories, safety, databases, privacy, authentication, throughput, delay

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Authors: Lev Idels, Arcady Ponosov

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Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others.

Keywords: delay equations, operator methods, stochastic noise, weak solutions

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Authors: H. Niranjan, S. Sivasankaran

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Heat and mass transfer near a steady stagnation point boundary layer flow of viscous incompressible fluid through porous media investigates along a vertical plate is thoroughly studied under the presence of magneto hydrodynamic (MHD) effects. The fluid flow is steady, laminar, incompressible and in two-dimensional. The nonlinear differential coupled parabolic partial differential equations of continuity, momentum, energy and specie diffusion are converted into the non-similar boundary layer equations using similarity transformation, which are then solved numerically using the Runge-Kutta method along with shooting method. The effects of the conjugate heat transfer parameter, the porous medium parameter, the permeability parameter, the mixed convection parameter, the magnetic parameter, and the thermal radiation on the velocity and temperature profiles as well as on the local skin friction and local heat transfer are presented and analyzed. The validity of the methodology and analysis is checked by comparing the results obtained for some specific cases with those available in the literature. The various parameters on local skin friction, heat and mass transfer rates are presented in tabular form.

Keywords: MHD, porous medium, slip, convective boundary condition, stagnation point

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Authors: Farida Prihatini

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As a largest Muslim country in the world with around 215 Muslim inhabitants, Indonesia interestingly is not an Islamic country. Yet, Indonesia is not a secular country as well. The country has committed to be a unity in diversity country where people from various socio-political background may be coexistent live in this archipelago country. However, many provinces and Muslim groups are disposed of special regulation for Muslim people, namely local ordinances with sharia nuances, applied specifically in provinces, cities or regions where Muslim inhabitants are the majority. For the last two decades, particularly since Indonesia reform movement of 1998, a lot of local ordinances (Peraturan Daerah) with Sharia nuance have been enacted and applied in several provinces, cities and regions in Indonesia. The local ordinances are mostly deal with restriction of alcohol, prohibition of prostitution, Al Qur'an literacy, obligation to wear Muslim attire and zakat or alms management. Some of local ordinances have been warmly welcomed by society, while other ordinances have created tension. Those who oppose the ordinances believe that such things regulated by the ordinances are in violation of human rights and democracy, part of privacy rights of the people and must not be regulated by the State or local government. This paper describes the dynamic of local Ordinances with sharia nuances in Indonesia, in this research is limited to three ordinances: on the restriction of alcohol, prohibition of prostitution and obligation to wear Muslim attire. The researcher employs a normative method by studying secondary data and local ordinances in selected areas in Indonesia. The findings of the paper are that local ordinances with sharia nuances are indeed part of the needs of society, yet, in their implementation must take the pluralism of Indonesia and the state basic foundation, which is Pancasila (five pillars) into account.

Keywords: local, ordinances, sharia, rights

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Authors: Taekyun Doo, Cheongmin Ji, Manpyo Hong

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Like a closed-circuit television (CCTV), video surveillance system is widely placed for gathering video from unspecified people to prevent crime, surveillance, or many other purposes. However, abuse of CCTV brings about concerns of personal privacy invasions. In this paper, we propose an encryption method to protect personal privacy system in H.264 compressed video bitstream with encrypting only regions of interest (ROI). There is no need to change the existing video surveillance system. In addition, encrypting ROI in compressed video bitstream is a challenging work due to spatial and temporal drift errors. For this reason, we propose a novel drift mitigation method when ROI is encrypted. The proposed method was implemented by using JM reference software based on the H.264 compressed videos, and experimental results show the verification of our proposed methods and its effectiveness.

Keywords: H.264/AVC, video encryption, privacy protection, post compression, region of interest

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Authors: N. A. Badrul

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People are concerned that they are vulnerable as a result of what is exposed about them on the internet. Users are increasingly aware of their privacy and are making various efforts to protect their personal information. However, besides individuals themselves, organisations are also exposing personal information of their staff to the general public by publishing it on their official website. This practice may put individuals at risk and particularly vulnerable to threats. This preliminary study explores explicitly the amount and types of personal information disclosure from organisational websites. Threats and risks related to the disclosures are discussed. In general, all the examined organisational websites discloses personal information with varies identifiable degree of data.

Keywords: personal information, privacy, e-government, information disclosure

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Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

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An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

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Authors: Yuval Reinfeld

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This paper explores the European Union’s expanding influence as a global regulatory power, particularly in the realms of legal, security, and privacy challenges within the digital landscape. As digital regulation becomes increasingly vital, the EU has positioned itself as a leading exporter of privacy and cybersecurity standards through landmark frameworks like the General Data Protection Regulation (GDPR), the Artificial Intelligence Act (AIA), and the Digital Services Act (DSA). These regulations have set global benchmarks, extending their influence well beyond Europe’s borders by shaping legal frameworks in third countries and guiding the development of global digital governance. Central to this regulatory diffusion is the European Court of Justice (CJEU), whose rulings consistently reinforce and extend the reach of EU standards on an international scale. Through mechanisms such as trade agreements, adequacy decisions, and multilateral cooperation, the EU has constructed a regulatory ecosystem that other jurisdictions increasingly adopt. This paper investigates key CJEU cases to illustrate how the EU’s legal instruments in privacy, security, and AI contribute to its role as a global standard-setter. By examining the intersection of digital governance, international law, and normative power, this research provides a thorough analysis of the EU’s regulatory impact on global privacy, cybersecurity, and AI frameworks.

Keywords: digital privacy, cybersecurity, GDPR, European Union Law, artificial intelligence, global normative power

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Lina Wu, Ye Li

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An equivalent relation between a harmonic form and a closed co-closed form is established on a complete non-compact manifold. This equivalence has been generalized for a differential k-form ω from Lq spaces to non-Lq spaces when q=2 in the context of p-balanced growth where p=2. Especially for a simple differential k-form on a complete non-compact manifold, the equivalent relation has been verified with the extended scope of q for from finite q-energy in Lq spaces to infinite q-energy in non-Lq spaces when with 2-balanced growth. Generalized Hadamard Theorem, Cauchy-Schwarz Inequality, and Calculus skills including Integration by Parts as well as Convergent Series have been applied as estimation techniques to evaluate growth rates for a differential form. In particular, energy growth rates as indicated by an appropriate power range in a selected test function lead to a balance between a harmonic differential form and a closed co-closed differential form. Research ideas and computational methods in this paper could provide an innovative way in the study of broadening Lq spaces to non-Lq spaces with a wide variety of infinite energy growth for a differential form.

Keywords: closed forms, co-closed forms, harmonic forms, L^q spaces, p-balanced growth, simple differential k-forms

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Dhananjay Singh, M. Abdullah-Al-Wadud

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The Internet of Things is a concept of a large scale ecosystem of wireless actuators. The actuators are defined as things in the IoT, those which contribute or produces some data to the ecosystem. However, ubiquitous data collection, data security, privacy preserving, large volume data processing, and intelligent analytics are some of the key challenges into the IoT technologies. In order to solve the security requirements, challenges and threats in the IoT, we have discussed a message authentication mechanism for IoT applications. Finally, we have discussed data encryption mechanism for messages authentication before propagating into IoT networks.

Keywords: Internet of Things (IoT), message authentication, privacy, security

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: Devika Tanna

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'Biometrics' means 'life measurement' but the term is usually associated with the use of unique physiological characteristics to identify an individual. It is important to secure the privacy of digital face image that is stored in central database. To impart privacy to such biometric face images, first, the digital face image is split into two host face images such that, each of it gives no idea of existence of the original face image and, then each cover image is stored in two different databases geographically apart. When both the cover images are simultaneously available then only we can access that original image. This can be achieved by using the XM2VTS and IMM face database, an adaptive algorithm for spatial greyscale. The algorithm helps to select the appropriate host images which are most likely to be compatible with the secret image stored in the central database based on its geometry and appearance. The encryption is done using GEVCS which results in a reconstructed image identical to the original private image.

Keywords: adaptive algorithm, database, host images, privacy, visual cryptography

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Authors: Ahmed Machmoum, Malika El Kyal

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We consider iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays tobe substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: computer, multi-splitting methods, asynchronous mode, differential algebraic systems

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Authors: Farbod Behnaminia, Saeed Samet

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The COVID-19 pandemic has paralyzed many lives until a vaccine was available, which caused the so-called “new normal.” According to the World Health Organization (WHO), COVID-19 is an infectious disease. It can cause significant illness or death in anyone. Governments and health officials tried to impose rules and regulations to avoid and slow down transmission. Therefore, software engineers worldwide developed applications to trace and track patients’ movements and notify others, mainly using Bluetooth. In this way, everyone could be informed whether they come in close contact with someone who has COVID-19 and takes proper safety precautions. Because most of the applications use technologies that can potentially reveal the user’s identity and location, researchers have debated privacy preservation and how to improve user privacy during such pandemics. Thanks to Distributed Ledger Technology (DLT), there have been some proposed methods to develop privacy-preserving Patient Tracking Systems in the last two years. As an instance of the DLT, Blockchain is like a decentralized peer-to-peer database that maintains a record of transactions. Transactions are immutable, transparent, and anonymous in this system. We conducted a comprehensive evaluation of the literature by looking for papers in the relevant field and dividing them into pre- and post-pandemic systems. Additionally, we discussed the many uses of blockchain technology in pandemic control. We found that two major obstacles facing blockchain implementation across many healthcare systems are scalability and privacy. The Polkadot platform is presented, along with a review of its efficacy in tackling current concerns. A more scalable healthcare system is achievable in the near future using Polkadot as well as a much more privacy-preserving environment.

Keywords: blockchain, electronic record management, EHR, privacy-preserving, patient tracking, COVID-19, trust and confidence, Polkadot

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Authors: Abdullah Al Mamun, Talal Alkharobi

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As data size is growing up, people are became more familiar to store big amount of secret information into cloud storage. Companies are always required to need transfer massive business files from one end to another. We are going to lose privacy if we transmit it as it is and continuing same scenario repeatedly without securing the communication mechanism means proper encryption. Although asymmetric key encryption solves the main problem of symmetric key encryption but it can only encrypt limited size of data which is inapplicable for large data encryption. In this paper we propose a probable approach of pretty good privacy for encrypt big data using both symmetric and asymmetric keys. Our goal is to achieve encrypt huge collection information and transmit it through a secure communication channel for committing the business and personal privacy. To justify our method an experimental dataset from three different platform is provided. We would like to show that our approach is working for massive size of various data efficiently and reliably.

Keywords: big data, cloud computing, cryptography, hadoop, public key

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Yunyong Guo, Man Wang, Bryan Guo, Nathan Guo

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This paper introduces an advanced security and privacy model tailored for Telehealth systems, emphasizing end-to-end protection across IoT, Fog, and Cloud components. The proposed model integrates encryption, key management, intrusion detection, and privacy-preserving measures to safeguard patient data. A comprehensive simulation study evaluates the model's effectiveness in scenarios such as unauthorized access, physical breaches, and insider threats. Results indicate notable success in detecting and mitigating threats yet underscore areas for refinement. The study contributes insights into the intricate balance between security and usability in Telehealth environments, setting the stage for continued advancements.

Keywords: cloud, enhancing security, fog, IoT, telehealth

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Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

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The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: closed surfaces, high-order approachs, numerical solutions, reaction-diffusion systems

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Mahdad M’hamed, Belaidi Idir

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This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole

Keywords: numerical computation, element-free Galerkin (EFG), moving least squares (MLS), meshless methods

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Suman Podder

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As Australian ‘Open Banking’ allows customers to share their financial data with accredited Third-Party Providers (‘TPPs’), it is necessary to evaluate whether the regulators have achieved the balance between protecting customer data privacy and promoting data-related innovation. Recognising the need to increase customers’ influence on their own data, and the benefits of data-related innovation, the Australian Government introduced ‘Consumer Data Right’ (‘CDR’) to the banking sector through Open Banking regulation. Under Open Banking, TPPs can access customers’ banking data that allows the TPPs to tailor their products and services to meet customer needs at a more competitive price. This facilitated access and use of customer data will promote innovation by providing opportunities for new products and business models to emerge and grow. However, the success of Open Banking depends on the willingness of the customers to share their data, so the regulators have augmented the protection of data by introducing new privacy safeguards to instill confidence and trust in the system. The dilemma in policymaking is that, on the one hand, lenient data privacy laws will help the flow of information, but at the risk of individuals’ loss of privacy, on the other hand, stringent laws that adequately protect privacy may dissuade innovation. Using theoretical and doctrinal methods, this paper examines whether the privacy safeguards under Open Banking will add to the compliance burden of the participating financial institutions, resulting in the undesirable effect of stifling other policy objectives such as innovation. The contribution of this research is three-fold. In the emerging field of customer data sharing, this research is one of the few academic studies on the objectives and impact of Open Banking in the Australian context. Additionally, Open Banking is still in the early stages of implementation, so this research traces the evolution of Open Banking through policy debates regarding the desirability of customer data-sharing. Finally, the research focuses not only on the customers’ data privacy and juxtaposes it with another important objective of promoting innovation, but it also highlights the critical issues facing the data-sharing regime. This paper argues that while it is challenging to develop a regulatory framework for protecting data privacy without impeding innovation and jeopardising yet unknown opportunities, data privacy and innovation promote different aspects of customer welfare. This paper concludes that if a regulation is appropriately designed and implemented, the benefits of data-sharing will outweigh the cost of compliance with the CDR.

Keywords: consumer data right, innovation, open banking, privacy safeguards

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Authors: Zhan Chen, Wenquan Bi

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This paper focuses on examining the strength of Midori against impossible differential attack. The Midori family of light weight block cipher orienting to energy-efficiency is proposed in ASIACRYPT2015. Using a 6-round property, the authors implement an 11-round impossible differential attack on Midori64 by extending two rounds on the top and three rounds on the bottom. There is enough key space to consider pre-whitening keys in this attack. An impossible differential path that minimises the key bits involved is used to reduce computational complexity. Several additional observations such as partial abort technique are used to further reduce data and time complexities. This attack has data complexity of 2 ⁶⁹·² chosen plaintexts, requires 2 ¹⁴·⁵⁸ blocks of memory and 2 ⁹⁴·⁷ 11- round Midori64 encryptions.

Keywords: cryptanalysis, impossible differential, light weight block cipher, Midori

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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