##### International Journal of Mathematical Sciences and Computing (IJMSC)

IJMSC Vol. 8, No. 3, Aug. 2022

#### MECS Press Journal

REGULAR PAPERS

##### Revised Method for Sampling Coefficient Vector of GNR-enumeration Solution

DOI: https://doi.org/10.5815/ijmsc.2022.03.01, Pub. Date: 8 Aug. 2022

For selecting security parameters in lattice-based cryptographic primitives, the exact manner of BKZ algorithm (as total cost and specification of output basis) should be estimated in high block sizes. The simulations of BKZ are used to predict (estimate) the exact manner of BKZ algorithm which cannot be studied by practical running of BKZ algorithm for higher block sizes. Sampling method of GNR (Gamma-Nguyen-Regev) enumeration solution vector v is one of the main components of designing BKZ-simulation and it includes two phases: sampling the norm of solution vector v and sampling corresponding coefficient vectors. Our work, by Moghissi and Payandeh in 2021, entitled as “Better Sampling Method of Enumeration Solution for BKZ-Simulation”, introduces a simple and efficient idea for sampling the norm and coefficient vectors of GNR enumeration solution v. This paper proposes much better analysis for approximating the expected value and variance of the entries of these coefficient vectors. By this analysis, our previous idea for sampling the coefficient vectors is revised, which means that the expected value and variance of every entry in these coefficient vectors sampled by our new sampling method, are more close to the expected value and variance of corresponding entries in original sampling method, while these new sampled coefficient vectors include no violation from main condition of GNR bounding function (i.e., our new sampling method is not a rejection sampling).

##### Outlier Detection Algorithm Based on Fuzzy C-Means and Self-organizing Maps Clustering Methods

DOI: https://doi.org/10.5815/ijmsc.2022.03.02, Pub. Date: 8 Aug. 2022

Data mining and machine learning methods are important areas where studies have increased in recent years. Data is critical for these areas focus on inferring meaningful conclusions from the data collected. The preparation of the data is very important for the studies to be carried out and the algorithms to be applied. One of the most critical steps in data preparation is outlier detection. Because these observations, which have different characteristics from the observations in the data, affect the results of the algorithms to be applied and may cause erroneous results. New methods have been developed for outlier detection and machine learning and data mining algorithms have been provided with successful results with these methods. Algorithms such as Fuzzy C Means (FCM) and Self Organization Maps (SOM) have given successful results for outlier detection in this area. However, there is no outlier detection method in which these two powerful clustering methods are used together. This study proposes a new outlier detection algorithm using these two powerful clustering methods. In this study, a new outlier detection algorithm (FUSOMOUT) was developed by using SOM and FCM clustering methods together. With this algorithm, it is aimed to increase the success of both clustering and classification algorithms. The proposed algorithm was applied to four different datasets with different characteristics (Wisconsin breast cancer dataset (WDBC), Wine, Diabetes and Kddcup99) and it was shown to significantly increase the classification accuracy with the Silhouette, Calinski-Harabasz and Davies-Bouldin indexes as clustering success indexes.

##### Smart Contract Obfuscation Technique to Enhance Code Security and Prevent Code Reusability

DOI: https://doi.org/10.5815/ijmsc.2022.03.03, Pub. Date: 8 Aug. 2022

Along with the advancements in blockchain technology, many blockchain-based successful projects have been done mainly on the ethereum platform, most of which deal with transactions. Still, it also carries various risks when it comes to security, as evident from past attacks. Most big projects like uniswap, decentraland, and others use smart contracts, deployed on the ethereum platform, leading to similar projects via code reuse. Code reuse practice is quite frequent as a survey suggests 26% of contract code deployed is via code reuse. Smart contract code obfuscation techniques can be used on solidity code that is publicly verified, published (in the case of Ethereum), and on the deployment address. All the above techniques work by replacing characters with their random counterpart, known as statistical substitution. A statistical substitution is a process of transforming an input string into a new string where each character has been replaced by a random character drawn from a stock of all possible 'random' characters. Therefore, we proposed numerous methods in this paper to solve the above problems using various smart contract code obfuscation techniques. These techniques can be really useful in blockchain projects and can save millions of dollars to investors & companies by enhancing code security and preventing code reusability. Techniques mentioned in this paper when compared with other techniques. Our methods are not expensive to implement, very easy to use, and provide a developer-friendly selective increment in code complexity.

##### Energy Efficient Multipath Routing in Zone-based Mobile Ad-hoc Networks: Mathematical Formulation

DOI: https://doi.org/10.5815/ijmsc.2022.03.04, Pub. Date: 8 Aug. 2022

A wireless mobile ad hoc network (MANET) is a dynamic network that can be built without the need for any central governance system and pre-existing infrastructure, in which each node can act as a router. During the transmission of information in any network, energy consumption is an important factor for the efficiency and lifetime of the network. A reduction in energy consumption is achieved by detecting the energy consumption at the node at each stage of transmission.

The main objective of this paper is to formulate mathematical models of energy consumption. A mathematical model of the energy consumption of a network is to be built on the basis of available nodes and links to formulate mathematical models related to energy. When constructing this mathematical model for the challenge related to mobility and low connectivity due to limited battery power in the network, the failure of the links present in the network and the estimated energy consumption are taken into account. Due to the greater mobility of this type of network, nodes rapidly change their positions, causing nodes to drain the battery very quickly, thus reducing network performance. So we need a mathematical model which helps in developing a mathematical model after developing a conceptual model. Which helps in predicting the quantitative behavior of a system. Weaknesses and strengths of a model can be identified from the quantitative results of a mathematical model.