An Application for Pair Sum Modulo Labeling in Cryptography

Abstract

In the dynamic realm of cybersecurity, it is important to create a strong cryptographic technique to protect sensitive data against advanced threats. This paper introduces an innovative encryption and decryption technique leveraging graph theory and matrix algebra, especially through the use of pair sum modulo (PSM) labeling of graphs, adjacency matrices, and self-invertible matrices. The PSM labeling for a simple undirected graph G(VG, EG)with |VG| = p and |EG| = q, is an 1-1 map FG:VG → {±1,±2,...,±p}, and there is an induced edge labeling bijective function gG:EG → {0,1,2,...,(q − 1)} such that gG (uv) = [FG(u)+FG(v)](mod q) is distinct for each edge uv. A graph that satisfies PSM labeling is known as a PSM graph. Building on recent developments in graph labeling and matrix applications in cryptography, our method enhances security. It improves resistance to brute force attacks by utilizing a large key space. Additionally, it leverages the complexity of matrix inversion to make cryptanalysis more difficult. The amalgamation of these mathematical groundworks reinforces the entropy and resistance to bit-flipping, thereby stimulating the ciphertext against statistical and cryptanalytic threats. We utilize the core principles of PSM labeling and algorithmic encryption methods, as defined in prior research, to develop an innovative cryptographic algorithm. The sustainability of the proposed method is verified through a thorough evaluation of its encryption efficacy, computational complexity, and a comparative study with existing cryptographic techniques. This work not only contributes to a new approach to the cryptographic domain but also opens avenues for further research into the integration of advanced mathematical structures in encryption algorithms.

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