Supervisory Control and Data Acquisition (SCADA) systems are ubiquitous in industrial control processes, such as power grids, water supply systems, traffic control, oil and natural gas mining, space stations and nuclear plants. However, their security faces the threat of being compromised due to the increasing use of open-access networks. Furthermore, one of the research gaps involves the emergence of quantum computing, which has exposed a new type of risk to SCADA systems. Failure to secure SCADA systems can lead to catastrophic consequences. For example, a malicious attack can take control of the power supply to a city, shut down the water supply system, or cause malfunction of a nuclear reactor. The primary purpose of this paper is to identify the new type of attack based on quantum computing and design a novel security scheme to defend against traditional attacks as well as the quantum attack. The methodology of the proposed signcryption is built on the foundation of the classical Bennett and Brassard 1984 (BB84) cryptographic scheme and does not involve computationally expensive third-party validation. The proposed signcryption scheme provides both encryption and intrusion detection. In particular, it detects the man-in-the-middle attack that can lead to other types of attacks. We have simulated the proposed algorithm using the Quantum Information Toolkit in Python. Furthermore, we have validated and analyzed the proposed design through security verification tools, namely, Scyther and PRISM.