The construction of encryption key by using a super H-antimagic total graph

Abstract

The strength of cryptosystem relays on the management of encryption key. The key should be managed such that it is hard for any intruder to analyze the key. Thus, the main issue is how to make the relation between plaintext, ciphertext and the key is hidden. This paper will study the use of super (a, d)-H antimagic total graph in developing an encryption key to achieve the security. Let H be a simple, connected and undirected graph. A graph G = (V, E) is said to be a super (a, d)-H-antimagic total graph if there exist a one-to-one map f : V (G) ∪ E(G) → {1, 2, . . . , |V (G)| + |E(G)|} such that for all subgraphs isomorphic to H, the total H-weights w(H) = P v∈V (H) f(v) + P f(e) form an arithmetic sequence {a, a + d, a + 2d, ..., a + (s − 1)d}, where a and d are pos- itive integers and s is the number of all subgraphs isomorphic to H, and f : V (G) → {1, 2, . . . , |V (G)|}. The resulting super (a, d)-H antimagic total graph can potentially generates a complex key, thus by using such graph we can get a secure cryptosystem.