QLight-IIoT: A Quantum-Resistant Lightweight Authentication and Key Agreement Scheme for Resource-Constrained IIoT Environments Baisakhi Upadhyaya, Amaresh Chandra Panda, Swagat Sourav Mohanty, Ayushi Pati, Prasant Mohapatra IEEE Internet of Things Journal, 2026 The Industrial Internet of Things (IIoT) enables smart manufacturing through advanced sensing, monitoring, and control capabilities. However, securing these resource-constrained IIoT devices poses critical challenges due to limited memory and energy resources, while the emergence of quantum computing threatens existing security mechanisms. This study addresses the urgent need for practical quantum-resistant security solutions for deployment in resource-limited industrial environments. It presents QLight-IIoT, a quantum-resistant authentication and key agreement (AKA) scheme established solely on hash-based hardness assumption, demonstrating that lightweight quantum-resistant authentication is achievable without relying on computationally intensive primitives like lattices or codes. The proposed scheme is deployed and tested over Raspberry Pi 4 to demonstrate its practicality in real-world IIoT environments. Experimental validation shows that the scheme ensures mutual authentication with session key establishment with an average key generation time of 0.3200 seconds. The security of the proposed QLight-IIoT scheme is systematically evaluated using the Real-or-Random (ROR) model, the Scyther tool, and the Automated Validation of Internet Security Protocols and Applications (AVISPA) framework. Performance evaluation reveals significant efficiency improvements, achieving 9.29–77.36% reduction in communication cost and 4.41–95.37% reduction in Computational overhead relative to existing schemes. The scheme requires minimal storage of 632 bits per IIoT device, resulting in up to 64.84% reduction in total system storage cost. Comparative security analysis further validates the scheme’s security against various attack vectors. This work provides a practical pathway for industrial organizations to prepare IIoT infrastructure for quantum-resistant security challenges while maintaining compatibility with current resource-constrained hardware.
Study of the crossing number associated with strong product of path with cycle and triangular snake graph Mhaid Mhdi Alhajjar, Amaresh Chandra Panda, Siva Prasad Behera International Journal of Reasoning Based Intelligent Systems, 2025 In 2018, Ouyang et al. presented the first efforts related to the crossing number of strong product of the path Pm to the cycle Cn. They proved that cr(P2 ⊠ Cn) = n for n ≥ 3 together with introducing a general conjecture as follows: cr(Pm ⊠ Cn) = (m - 1)n: ∀ m, n ≥ 3. Here, we prove that Ouyang et al. conjecture is also true for n = 3 and m ≥ 3, together with exhibiting an optimal drawing of it. Furthermore, we start to study new case in relation to the strong product of path with triangular snake graph TSn by proving that cr(P2 ⊠ TSn) = 3⌊n/2⌋ for n ≥ 3.
On the Crossing Number of the Cartesian Product of a Triangular Snake Graph with Path, Cycle, Star and 3-Vertex Graphs Iaeng International Journal of Applied Mathematics, 2024
The crossing number of Cartesian product of sunlet graph with path and complete bipartite graph Mhaid Alhajjar, Amaresh Chandra Panda, Siva Prasad Behera Discrete Mathematics Algorithms and Applications, 2024 The crossing number of a graph [Formula: see text], denoted by [Formula: see text], is defined to be the minimum number of crossings that arise among all its drawings in the plane. This concept has been of interest to many researchers who have studied it for many families of graphs. In this paper, we introduce the crossing number of Cartesian product of sunlet graph [Formula: see text] with path [Formula: see text]. Further, we prove that the crossing number of [Formula: see text] is equal to [Formula: see text], along with giving a conjecture for the general case. In addition, we utilize the vertex’s rotation concept in order to prove some necessary conditions for the complete bipartite graph [Formula: see text] to be optimal when it is drawn in the plane, by presenting an upper bound for the crossing number of any subgraph in it together with determining the exact number of crossings in case the vertices of subgraph have the same rotation.
