Browsing by Author "Wijesiri, G. S."

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Block encryption and decryption of a sentence using decomposition of Generalized Peterson graph
(Faculty of Science, University of Kelaniya Sri Lanka, 2024) Dilushani, S. A. S.; Wijesiri, G. S.
In the modern digital era data breaches and cyberattacks threaten the integrity of global communications more frequently. Cryptography stands as the frontline defense, safeguarding sensitive information against unauthorized access. Encryption and decryption are two cryptographic techniques that conceal and transmit critical information to authorized individuals without the interference of a third party in a network. Cryptography relies on mathematical concepts such as number theory, graph theory, group theory, probability theory, statistics and algebra. Graph theory enhances cryptographic security by utilizing the complexity of graphs, which pose significant challenges to potential attackers. There are mainly two types of cryptographic algorithms as private key cryptosystem and public key cryptosystem. This research introduces a novel cryptosystem utilizing the Generalized Peterson graph GP (7,2). After analyzing various generalized Peterson graphs GP(7,2) was selected for its properties in graph decomposition. We use graph decomposition theories to develop the cryptosystem. The main advantage of choosing GP (7,2) is that, by decomposing GP (7,2), 𝐶7, 𝑃4, 2 copies of 𝑃2and 3 copies of 𝑆3 can be generated. An encryption and decryption scheme utilizing GP (7,2) is proposed, incorporating these subgraphs to enhance cryptographic operations. Security is further enhanced by employing 10 lists of arithmetic progression as coding tables. Additionally, the binary digit labeling for path 𝑃4 and an encoding table for frequently used symbols are introduced to increase the robustness of the cryptosystem. An algorithm is developed and tested to validate the proposed methodology, confirming its effectiveness and reliability. Results indicate that the proposed methodology effectively encrypts, and decrypts sentences of variable lengths, showcasing its flexibility compared to other graph based cryptosystems in the current literature. In conclusion, goal of this research was to propose a new private key block crypto system which is based on graphs and graph theory concepts and which could potentially address the limitations in the current literature such as complexity of graph decomposition becoming exponentially difficult with the number of words in the sentence getting higher. And this proposed methodology can be further improved as well. An open area for future work involves expanding the symbol set to include more characters, such as upper and lower case letters, special characters and numbers. This enhancement would accommodate a wider range of inputs in real world scenarios. The decomposition of a Generalized Peterson graph has been chosen, and future work will explore different types of graph techniques to make the cryptosystem stronger and more difficult to hack.
Exploring signed domination number for the cartesian product of two path graphs
(Faculty of Science, University of Kelaniya Sri Lanka, 2024) Samaranayaka, K. V. H. C.; Weerasinghe, M. H. L.; Wijesiri, G. S.
Let 𝐺 = (𝑉, 𝐸) be a graph with the vertex set 𝑉(𝐺) and consider a function 𝑓: 𝑉(𝐺) → {-1, +1}. If the closed neighborhood of 𝑣 contains +1′s more than -1′s for every 𝑣 ∈ 𝑉(𝐺). Then 𝑓 is the signed domination function for the graph 𝐺 (1). 𝛾𝑠(𝐺) denotes the minimum weight of a signed domination function of 𝐺. The Cartesian product of two path graphs forms a grid graph. Specially, the Cartesian product of 𝑃𝑚 and 𝑃𝑛 gives 𝑚 × 𝑛 grid graph (𝑚 rows and 𝑛 columns) with 𝑚𝑛 number of vertices. In this study, we review existing methods for determining the signed domination number of the Cartesian product of two path graphs 𝛾𝑠(𝑃𝑚 × 𝑃𝑛). We then include definitions of open and closed neighborhoods of a graph, the signed domination function and the signed domination number. The theorems which are used to determine 𝛾𝑠(𝑃𝑚 × 𝑃𝑛) when 𝑚 = 3,4,5,6 and 7 were also presented. In exploring the 𝛾𝑠(𝑃𝑚 × 𝑃𝑛) where 𝑚 = 8, we draw upon existing literature which has focused on determining signed domination number for 𝛾𝑠(𝑃𝑚 × 𝑃𝑛) ranging from 𝑚 = 3 to 𝑚 = 7. This foundational knowledge guides our approach as we compile graphical illustrations that depict both trivial and general configurations of signed domination in grid graphs. These illustrations help us identify and categorize specific cases, defining sub-cases essential for the proof of the theorem. Through this process, we establish relationships among these graphical representations and develop a localized function, denoted as |𝐵𝑗|, to capture the relationships within each identified case. Building on these insights, we suggest theoretically valid approaches to completing the calculation for the 𝛾𝑠(𝑃𝑚 × 𝑃𝑛) when 𝑚 = 8, evaluating and refining our results based on the findings obtained from these methodical investigations. Our finding leads to a upper bound for the signed domination number of the grid graph 𝑃8 × 𝑃𝑛. The theorem is, for 𝑛 ≥ 1, if 𝑛 ≡ 0(𝑚𝑜𝑑 4) then 𝛾𝑠(𝑃8 × 𝑃𝑛) ≤ 4𝑛. We also propose a conjecture for the 𝑛 ≡ 1(𝑚𝑜𝑑 4), 𝛾𝑠(𝑃8 × 𝑃𝑛) ≤ 4𝑛 + 2.
Modeling Non-Isothermal wire-coating from a bath using Giesekus fluid.
(International Research Symposium on Pure and Applied Sciences, 2017 Faculty of Science, University of Kelaniya, Sri Lanka., 2017) Karunathilake, N. G. A.; Panda, S.; Mallawaarachchi, D. K.; Wijesiri, G. S.; Hansameenu, W. T. P.
In this paper we extend the recent analysis of Giesekus isothermal viscoelastic fluid model by inclusion of temperature in the uni-axial flow which occurs in the wire-coating process. The wire-coating flow of incompressible non-Newtonian fluid is described by the boundary value problem in terms of the equation of continuity, momentum, and energy with Giesekus constitutive equation. The equations of the uni-axial flow are written in the cylindrical coordinates and the analytical solution for the velocity is obtained. The energy equation which takes into account the viscous dissipation term is then solved to understand the temperature distribution in the flow region. The influences of non-Newtonian rheological parameters like Deborah number, Giesekus parameter and Brinkman number on velocity and temperature distributions are discussed. A comparison of the approximated solutions and the numerical solutions of the exact model equation for the velocity field is given to verify the validity of the approximated solutions. It is observed that the Giesekus parameter influences the temperature profile in the entire fluid domain.
Scalar and multi-scalar multiplication in Elliptic Curve Cryptography using Fibonacci numbers
(Research Symposium on Pure and Applied Sciences, 2018 Faculty of Science, University of Kelaniya, Sri Lanka, 2018) Sandamali, N. P. A. A.; Wijesiri, G. S.
Cryptography is a science, which enables secure communications from various malicious adversaries using mathematical techniques. As a branch of cryptography, Neal Koblitz and Victor Miller introduced the Elliptic Curve Cryptography (ECC), in 1985. ECC provides us several advantages such as higher speed, efficient use of power and less storage. Security of ECC is based on the hardness of Elliptic Curve Discrete Logarithm Problem (ECDLP), which is defined as the problem of determining scalar d of the scalar multiplication Q = dP, when P and Q are given, where P and Q are two points on the elliptic curve. Lot of research are carried out to speed up and improve ECC implementations. Such researches mainly focus on the scalar multiplication, since it is the most important and time-consuming ECC operation. In this work we also focus on scalar as well as multi-scalar multiplication. Although Elliptic Curve Cryptosystems have enormous advantages, side channel attacks can break their common implementations. Finding methods against side channel attacks on elliptic curves is also a very active research. Simple Power Analysis (SPA) is a one type of side channel attack. In SPA, the attackers use the power consumption to monitor each operation and it helps attackers to retrieve secret scalar. Scalar multiplication is considered as a basic operation for elliptic curve cryptosystems. There are various methods to compute scalar multiplication in ECC. Generally, the most popular method is binary method. Unfortunately, although the binary method has excellent features, SPA attackers are able to fully reveal the secret scalar d, by observing the power trace of the binary method. One way to overcome this problem is finding a doubling free addition chain. Our main objective in this research is finding a doubling-free addition chain to compute scalar and multi-scalar multiples. As a solution for this problem, we proposed a new methodology to compute scalar and multi-scalar multiplication using Fibonacci numbers. We propose three algorithms. The first algorithm is for pre-computations in which we get a sequence of Fibonacci numbers to compute multiples. Using the resulting sequence, the second algorithm compute the relevant scalar multiplication. Using the same sequence, the third algorithm can compute the relevant multi-scalar multiplication. The proposed method shows higher performance when we compare new algorithms with traditional binary method.
Symmetric key encryption and decryption using graph theory
(Faculty of Science, University of Kelaniya Sri Lanka, 2023) Fernando, K. K. N.; Wijesiri, G. S.
In the twenty-first century, mathematical proficiency is crucial due to the widespread exchange of data and efficient communication across diverse fields. Data security employs encryption and various mathematical techniques to protect information systems. It safeguards against unwanted access, use, and damage. Graph theory is widely applied in the field of cryptography because a graph can be easily represented as a matrix on computers. The goal of this study is to make a novel connection between private key cryptography and graph theory principles that will safeguard data from unauthorized parties. In the encryption process, the original texts are converted into ciphertext by representing a splitting graph and using a minimum spanning tree, then computed into an adjacency matrix of ciphertext and partitioned it into a block matrix. Finally, obtained the resultant ciphertext using the receiver’s private key. The decryption process follows a similar stage in reverse order. This suggested encryption algorithm demonstrates a new scheme for more complexity and security. The resulting ciphertext size is larger than the plaintext size and checked its validity.
Viscous Dissipation and thermal radiation of Williamson fluid flow over an exponentially stretching sheet
(Karunathilake N. G. A.; Hansameenu W. P. T.; Wijesiri G. S. (2023), Viscous Dissipation and thermal radiation of Williamson fluid flow over an exponentially stretching sheet, Proceedings of the International Conference on Applied and Pure Sciences (ICAPS 2023-Kelaniya) Volume 3, Faculty of Science, University of Kelaniya Sri Lanka. Page 78., 2023) Karunathilake, N. G. A.; Hansameenu, W. P. T.; Wijesiri, G. S.
This study investigates the viscous dissipation and thermal radiation of Williamson fluid flow over an exponentially stretching sheet. The analysis has been started with the governing equations of the fluid flow derived from the conservation of mass, momentum, energy, and concentration. The internal heat generation and absorption effect in the view of getting the influence of temperature difference between the free stream and stretching sheet have been incorporated. The Rosseland approximation and Taylor series expansion formulate the radiative heat flux. The density difference which interacts with the gravitational force, resulting in a natural convection heat and mass transfer process is described by the mass transfer phenomenon with the homogeneous first-order chemical reaction effect. The boundary layer approximations have been introduced to focus on the fluid flow near the stretching sheet. Furthermore, the governing system of partial differential equations has been converted into a nonlinear ordinary differential equation by using similarity transformations. The resulting non-linear coupled system of ordinary differential equations has been solved numerically by shooting techniques. The graphs have simulated and presented the qualitative impact of different flow parameters such as magnetic field, Prandtl number, Williamson number, Grashof number, and thermal radioactive parameter on the radial velocity, temperature, and mass concentration profiles. The study reveals that the Prandtl number intensifies the radial velocity and has a mixed impact on the temperature and concentration, which decreases with an increase in the magnetic parameter but increases temperature and concentration. Further with the increase of the Prandtl number, the velocity and the temperature decrease in general but increase the concentration. The radial velocity increases with the Radioactive parameter but the temperature and the concentration display mixed reactions to the parameter. The Grashof parameter intensifies the radial velocity but reduces the temperature and the concentration. The Williamson parameter does not significantly impact radial velocity, temperature, and concentration.