Block Encryption and Decryption of a Sentence Using Decomposition of the Turan Graph

Encryption and decryption are the two processes in cryptography to conceal and convey important information to an authorized person without third-party interruption in a network. Cryptography is a branch of computer science in which the system has to be updated every second. It mainly depends on mathematical concepts like number theory and algebra. Recently, graph theory concepts are employed in cryptography to make it stronger. The usage of complex graphs in cryptosystems makes it difficult to hack. In this paper, we proposed a cryptosystem using the Turan graph which has a complex graph structure. The advantage of using a Turan graph is that it is a unique multipartite complete graph with more edges than other multipartite complete graphs. This adds robustness to the cryptosystem. The novelty of this paper is the decomposition of the Turan graph into paths and stars and applying edge labeling to them to encrypt and decrypt a sentence of k words. The algorithms for encryption and decryption are also proposed in this paper.

Automated summary

Encryption and decryption are two processes in cryptography that protect and transmit important information without interruption by third parties in a network. Cryptography, a branch of computer science, requires frequent system updates and relies on mathematical concepts such as number theory and algebra. Recently, graph theory concepts have been utilized to enhance the strength of cryptography. This paper proposes a cryptosystem using the Turan graph, which has a complex graph structure. The use of Turan graph adds robustness to the cryptosystem, as it is a unique multipartite complete graph with more edges. The paper presents the decomposition of the Turan graph into paths and stars, along with the application of edge labeling for encryption and decryption of sentences consisting of k words. Encryption and decryption algorithms are also introduced.