Synthesis of Index Difference Graph Structures for Cryptographic Implementation

Cryptography stands out as a scientific methodology for safeguarding communication against unauthorized access. This article proposes a newly formulated graph termed the Index Difference Graph (IDG). The proposed graph model serves as the secret key in the encryption process. Furthermore, we present a new graph-based algorithm, the Index Difference Modular Cryptographic (IDMC) Algorithm, and analyze it using centipede and path graphs. The goal of this graph-based approach is to increase the encryption rate while maintaining computational efficiency. This research investigates different types of index difference graphs and analyzes the time and space complexity of the algorithm. IDMC exhibits a lower collision probability, thereby enhancing encryption security. When employing a graph that admits an Index Difference Graph structure in the cryptographic algorithm, both the sender and receiver must be aware of the graph’s precise structure, as this strengthens the robustness of the cryptographic key. The application of the index difference centipede graph Pn⊙2k1 in cryptography, examined through the IDMC algorithm, demonstrates exceptionally high brute-force resistance estimated at approximately 2.6×1039 for smaller instances with n≤7 and escalating to 6.93×10163 for larger graphs with n≥20. This resistance underscores the algorithm’s efficiency and cryptographic resilience.