Symmetric encryption using snake graphs and supermagic covering - Ranasinghe, P.G.R.S.; Bandara, R.M.V.V.; Athapaththtu, A.M.S.L.K. (National Science Foundation: Colombo, 2025)
Cryptography involves the exploration of methods for safeguarding sensitive information. In this pursuit, graph-theoretic approaches play a significant role. Graph labeling, a key aspect of this, assigns labels or values to vertices and edges within a graph, serving as a means to encode information. It is instrumental in designing cryptographic protocols centered around graph-based structures. The sheer variety of labeling methods makes it challenging to discern the specific technique employed and distinguish between the graphs used for encryption. Notably, in 2020, Giridaran utilized super magic labeling as an encryption technique. Building upon this foundation, our present cryptographic scheme leverages graphs with snake vertex labeling to symmetrically encrypt plaintext. This encryption process harnesses the inherent randomness within super magic covering wheel graphs of odd order, in tandem with an advanced shift cipher. In this scheme, both the sender and receiver possess a secret key pair (k,l), carefully selected for the task at hand. The encryption process employs an odd number k, representing the sides of a cyclic graph (polygon), while l is chosen to preserve the symmetries of consecutive snake graphs. The use of graph labeling proves to be an effective tool in the creation of flexible, efficient, and secure cryptographic protocols. Our protocol, tailored for encryption, ensures a high level of security by capitalizing on the intrinsic structure and the stochastic nature of graph labeling. Through the careful selection of the labeling scheme, we have devised a protocol that remains resilient against a range of potential attacks, including impersonation and replay attacks.
Keywords: Shift cipher; Snake vertex labeling; Supermagic covering; Wheel graph.