Antimagic Labeling of Bi-Star Graphs for Secure and Efficient Cryptographic Data Transformation

Graph labeling is a fundamental concept in graph theory with applications in networks, cryptography, and data security. Graph-based cryptographic models and ECC-based methods provide partial solutions but individually face limitations in randomness, computational efficiency, and scalability. Existing graph-based encryption approaches often rely on classical ciphers, have high computational overhead, and offer limited resistance to sophisticated attacks. These gaps highlight the need for a hybrid, efficient, and high-entropy cryptographic framework. This research introduces a novel Bi-Star + ECC encryption scheme that combines super-edge antimagic total labeling of Bi-Star graphs with Elliptic Curve Cryptography (ECC). Plaintext is first converted into a numerical matrix and mapped onto a Bi-Star graph. Unique labels are assigned to vertices and edges, and edge weights are computed as the sum of connected labels, producing ciphertext with distinct, unpredictable values. ECC integration provides key exchange, hybrid encryption, and robust asymmetric security. The process involves mapping input data to a matrix, constructing a weighted Bi-Star graph, calculating unique edge sums, encrypting with ECC, and decoding by reversing the labeling process. This research is implemented on the Python platform. Performance evaluation demonstrates high efficiency and security: encryption/decryption in 2–18 ms, memory usage 1.2–7.2 MB, and security metrics (Confidentiality = 11, Integrity = 10, Security = 10). The method ensures high entropy, low redundancy, and robust resistance against attacks. Integrating Bi-Star graph labeling with ECC provides a secure, efficient, and practical cryptographic mechanism, addressing the limitations of prior graph-based and ECC-only approaches while enabling scalable and high-performance encryption.