# An Intrusion Resistant SCADA Framework Based on Quantum and Post-Quantum Scheme
## 1 Introduction  
Many industries and organizations have adopted Supervisory Control and Data Acquisition (SCADA) systems to control and monitor industrial processes such as water management, oil and gas industry, traffic management, and nuclear power plants. The significance of SCADA systems is directly proportional to the required security level to protect them from cyber attacks [1, 2]. Existing standards, including the American Gas Association (AGA)-12, used in SCADA systems are vulnerable to traditional and quantum attacks. The primary quantum algorithms to crack traditional cryptographic schemes are [PERSON]'s algorithm [3] and [PERSON]'s algorithm [4]. [PERSON]'s algorithm is an approach to solve the factoring problem by finding the order or period of the particular function in the problem. A classical computer can easily calculate the periods of a function. However, for large numbers, we need a quantum computer using superposition to solve the order-finding problem efficiently. [PERSON]'s approach is a quantum search algorithm to find a particular element, given an array of \(m\) elements [5, 6]. AGA-12 mainly adopts three algorithms; namely, Rivest-Shamir-Adleman (RSA) for key management, Advanced Encryption Standard (AES) for encryption and Elliptic Curve Digital Signature (ECDSA) for digital signature with the Secure Hash Algorithm (SHA-1) hash function [1]. The boom of quantum computing is both beneficial and detrimental to cyber-physical systems. [PERSON] et al. [7] practically proved that the [PERSON]'s algorithm is capable of cracking RSA-2048 within 8 hours with 20 million qubits. However, while a classical searchalgorithm takes \(O(N)\), an exhaustive search by [PERSON]'s algorithm takes \(O(\sqrt{N})\). Thus, it weakens the key strength of AES-256 to only 64 bits. A hash algorithm should be both preimage and collision-resistant. However, Google has cracked SHA-1 by launching a collision attack [8]. The SHA-2,3 remains safe at present. An attack on SHA-2,3 requires on the order of \(2^{256}\) queries in a non-quantum setting and, \(2^{128}\) queries in a quantum setting [8]. Thus, SHA-2,3 has _security level_ on the order of \(2^{256}\) in classical hardware and \(2^{128}\) in quantum hardware. Quantum computing endangers stable cyber-physical security, and researchers are developing solutions to mitigate the quantum threat. The solutions involve quantum and post-quantum cryptography to secure cyber-physical systems from future attacks by quantum computing [9]. Quantum cryptography involves quantum key distribution protocols that exploit the laws of quantum physics, superposition and entanglement principle to secure against [PERSON]'s algorithm [10; 11]. Whereas, post-quantum cryptography uses algorithms based on mathematical operations that are quantum-resistant and can inter-operate with classical network protocols [12]. One of the many post-quantum cryptography areas is the set of hash-based algorithms to generate a digital signature, which is secure against preimage and collision attacks by a quantum computer [13]. A first preimage attack attempts to recover a message \(m\) from only the hash value such that \(H=\textit{hash}(m)\). A second preimage attack finds another message \(n\) such that \(m\
eq n\) and _hash(m)=hash(n)_. A collision attack aims to retrieve two different messages \(m\) and \(n\), such that _hash(m) = hash(n)_[8; 14]. SPHINCS-256 is a high-security post-quantum stateless hash-based signature scheme that uses two types of signatures, namely, an extension of Winternitz One-time Signature (WOTS+) and Hash to Obtain Random Subset (HORS) signature with Tree (HORST) for few time signature [13]. SPHINCS-256 uses a pseudo-random number generator based on Chacha-12, for generating the HORST secret-key. In 2008, [PERSON] et al. [15] proposed Chacha, a cryptanalysis-resistant stream cipher algorithm that maps an input stream to a novel and irreversible output stream [16]. Chacha-12 is an extension of Chacha [17]. However, [PERSON] et al.