Analyzing cryptographic algorithm efficiency with in graph-based encryption models - Banu, Yashmin; Rath, Biplab Kumar; Gountia, Debasis (Frontiers in Computer Science, 2025)
This research paper investigates the efficiency of cryptographic algorithms within graph-based encryption models such as star graph, focusing on their computational performance and security robustness. In this study, we analyze the performance of RSA and ElGamal cryptographic algorithms by evaluating time and space complexity across various file types, including text, image, audio, and data of different sizes. The encryption process is modeled using graph structures such as the Star graph, along with other well-known algorithms like A*, Dijkstra, Bellman-Ford, and Floyd-Warshall for comparative analysis and performance benchmarking. Consequently, this research conducts a comparative analysis of RSA and ElGamal cryptographic algorithms by applying them to mixed data, including binary, text, and image files. The CPU's internal clock was employed to record the execution time of encryption and decryption operations, facilitating the assessment of time complexity for both algorithms. The CPU's internal memory was employed to monitor and record memory usage during the encryption and decryption operations performed on mixed datasets. Accordingly, the evaluation of the encryption algorithms was conducted using criteria such as encryption time, decryption time, and throughput to determine their relative performance. In evaluating cryptographic approaches, factors such as response time, confidentiality, bandwidth, and integrity are considered. Experimental results indicate that RSA demonstrates superior time efficiency and resource utilization, whereas the ElGamal algorithm exhibits greater memory efficiency and resourcefulness. This study evaluates RSA and ElGamal encryption on text, image, audio, and data files of varying sizes using graph-based models. The Star graph algorithm is adopted for its simplicity and low computational cost, and its performance is compared against A*, Dijkstra, and Bellman-Ford algorithms. Results show that the Star model offers near-optimal paths with significantly reduced processing time, demonstrating high confidence in efficiency for lightweight encryption tasks. We have added computational performance, logical confidence, and optimality conditions of the proposed Star-based encryption model. The Star algorithm, integrated with RSA/ElGamal encryption, is benchmarked against classical pathfinding algorithms like A*, Dijkstra, and Bellman-Ford, commonly used for routing and shortest-path computations. Computational performance of (i) the worst-case time complexity of star algorithm (proposed) is O(bd) where b is the branching factor and d is the depth and space complexity is O(E + V) where E is the number of edges and V is the number of nodes, high (central node access) traversal efficiency, excellent (centralized graph encoding) suitability for graph-based encryption, very high structural simplicity, (ii) the worst case time complexity of A* Algorithm is O(bd) where b is the branching factor and d is the depth and space complexity is O(E + V) where E is the number of edges and V is the number of nodes, high (with good heuristic) traversal efficiency, good (needs proper graph abstraction) suitability for graph-based encryption, moderate structural simplicity, (iii) the average case time complexity and best case time complexity of Dijkstra's Algorithm is O((V + E) log V) and the worst case time complexity is O((V2) logV) and space complexity is O(V) where V is the number of vertices, moderate to high traversal efficiency, fair (efficient in weighted graphs) suitability for graph-based encryption, moderate structural simplicity, and (iv) Bellman-Ford Algorithm is O(V*E) time complexity and O(V) space complexity where V is the number of vertices and E is the number of edges, low traversal efficiency, limited (computationally expensive) suitability for graph-based encryption, moderate structural simplicity.