Random numbers are important parameters for the security of cryptographic applications. In this study, a secure and efficient generator is proposed to generate random numbers. The first part of the generator is a true random number generator that consists of chaotic systems implemented on FPGA. The second part of the generator is a post-processing algorithm used to overcome the problems that emerge from the generator or environmental factors. As the post-processing algorithm, Keccak, the latest standard of hash algorithm, was rearranged and used. Random numbers with the proposed approach meet the security requirements for cryptographic applications. Furthermore, the NIST 800-22 test suite and autocorrelation test are used to ensure the generated numbers have no statistical weakness. The successful test results demonstrate the security of the generated numbers. An important advantage of the proposed generator does not cause any data loss and perform 100% efficiency although data loss can be up to 70% in some post-processing algorithms.

Random numbers constitute the most important part of many applications and have a vital importance in the security of these applications, especially in cryptography. Therefore, there is a need for secure random numbers to provide their security. This study is concerned with the development of a secure and efficient random number generator that is primarily intended for cryptographic applications. The generator consists of two subsystems. The first is algorithmic structure, Keccak, which is the latest standard for hash functions. The structure provides to generate secure random numbers. The second is additional input that generates with ring oscillators that are implemented on the FPGA. The additional inputs prevent reproduction and prediction of the subsequent random numbers. It is shown that the proposed generator is satisfies security requirements for cryptographic applications. In addition, NIST 800-22 test suite and autocorrelation test are used to demonstrate that generated random numbers have no statistical weaknesses and relationship among itself, respectively. Successful results from these tests show that generated numbers have no statistical weaknesses. Moreover, important advantage of the proposed generator is that it is more efficient than existing RNGs in the literature.

The graph is a data structures and models that used to describe many real-world problems. Many engineering problems, such as safety and transportation, have a graph-like structure and are based on a similar model. Therefore, these problems can be solved using similar methods to the graph data model. Vertex cover problem that is used in modeling many problems is one of the important NP-complete problems in graph theory. Vertex-cover realization by using minimum number of vertex is called Minimum Vertex Cover Problem (MVCP). Since MVCP is an optimization problem, many algorithms and approaches have been proposed to solve this problem. In this article, Malatya algorithm, which offers an effective solution for the vertex-cover problem, is proposed. Malatya algorithm offers a polynomial approach to the vertex cover problem. In the proposed approach, MVCP consists of two steps, calculating the Malatya centrality value and selecting the covering nodes. In the first step, Malatya centrality values are calculated for the nodes in the graph. These values are calculated using Malatya algorithm. Malatya centrality value of each node in the graph consists of the sum of the ratios of the degree of the node to the degrees of the adjacent nodes. The second step is a node selection problem for the vertex cover. The node with the maximum Malatya centrality value is selected from the nodes in the graph and added to the solution set. Then this node and its coincident edges are removed from the graph. Malatya centrality values are calculated again for the new graph, and the node with the maximum Malatya centrality value is selected from these values, and the coincident edges to this node are removed from the graph. This process is continued until all the edges in the graph are covered. It is shown on the sample graph that the proposed Malatya algorithm provides an effective solution for MVCP. Successful test results and analyzes show the effectiveness of Malatya algorithm.

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Graph structure is widely used to describe problems in different fields. Problems in many areas, such as security and transportation, are among them. The problems can be solved using approaches similar to the graph structure. The independent set problem, which is NP-Complete problem, is one of the main problems of graph theory and is used in modeling many problems. The implementation of the Independent set problem with the most significant possible number of nodes in the graph is called the Maximum Independent set. A lot of algorithm approach are proposed to solve the problem. This study proposes an effective approach for the maximum independent problem. This approach occurs two steps: computing the Malatya centrality value and determining the maximum independent set. In the first step, centrality values are computed for the nodes forming the graph structure using the Malatya algorithm. The Malatya centrality value of the nodes in any graph is the sum of the ratios of the node's degree to the neighboring nodes' degrees. The second step is to determine the nodes to be selected for the maximum independent set problem. Here, the node with the minimum Malatya centrality value is selected and added to the independent set. Then, the edges of this node, its adjacent nodes, and the edges of adjacent nodes are subtracted from the graph. By repeating the new graph structure calculations, all vertexes are deleted so that the maximum independent set is determined. It is observed on the sample graph that the proposed approach provides an effecient solution for the maximum independent set. Successful test results and analyzes denonstrate the effectiveness of the proposed approach.

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