Secure Message Transmission Using k-Sequential Labeling of Digraphs

In this paper, we propose an innovative encryption method based on the sequential labeling of cycle and star digraphs. This approach harnesses the inherent properties of digraph structures in combination with XOR operations to secure message transmission. Initially, we introduce a method to assign sequential labels to the vertices of cycle and star digraphs, ensuring a unique representation of each vertex. The message to be encrypted is converted into its binary equivalent and then segmented into 4-bit blocks. Each block is represented by a vertex in the digraph, followed by the generation of its adjacent vertices. Entropy analysis indicates a high level of randomness in the encrypted data, demonstrating the method's effectiveness and security. To support this, Welch's t-test was used to compare sequential labeling and random key data. A key component of the encryption is the XOR operation performed between vertex labels and a chosen seed value, resulting in an encrypted binary sequence. Decryption is achieved by applying the inverse XOR operation using the same seed. The proposed method offers a simple yet effective approach to encryption and can be extended to various digraph families. Illustrative examples are provided to demonstrate the construction and application of the encryption and decryption process.