# An Intrusion Resistant SCADA Framework Based on Quantum and Post-Quantum Scheme
## 2 Related Work
### Quantum Key Distribution  
In a traditional key exchange protocol, the key strength depends on the mathematical complexity. Moreover, classical computers operate with 'bits' with a state 0 or 1. [PERSON]'s algorithm on quantum hardware has been proven to crack traditional cryptography like RSA. However, we can mitigate attacks based on quantum algorithms, which factorize large numbers, by using quantum key distribution (QKD). Existing QKD protocols exploit quantum physics laws and make it difficult to measure the quantum state of a qubit without disturbing its a state. The quantum computers operate with 'qubits' as the basic unit of information with a state 0 or 1 or a superposed state [9; 10; 24]. The two QKD protocol categories, based on the principles used, are mainly, [PERSON]'s uncertainty principle and quantum entanglement. In any QKD protocol using [PERSON]'s uncertainty principle, the protocol prepares a qubit such that it is not possible to copy the state of qubit without disturbing its state. It is based on the No-Cloning theorem [25]. During the transmission from sender to receiver, the disturbance in the qubit state enables the system to detect an eavesdropper. In the entanglement-based QKD protocol, both the sender and receiver use entangled photons to generate the secret key [10; 11; 26]. In this paper, we review two primary examples of [PERSON]'s uncertainty principle-based QKD, namely, BB84 and B92 protocol. The BB84 protocol, proposed by [PERSON] and [PERSON] in 1984 [27], involves two parties generating a secret key using two channels, namely, quantum and public channel. The sender polarizes the photon by using one of the two _bases_, rectilinear and diagonal. The _basis_ refers to the pairs of orthogonal states. \begin{table}
\begin{tabular}{c c} \hline \hline
**Abbreviations/Notations** & **Definitions** \\ \hline \(t\) & Number of HORST secret key elements \\ \hline \(n\) & Security parameter refers to bit-length \\ \hline \(m\) & Bit-length of message \\ \hline \(d\) & Layers of the hypertree \\ \hline \(h\) & Height of the hypertree \\ \hline \(N\) & Number of qubits \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._The rectilinear basis generates either of the two polarization states: \(0^{\circ}\), \(90^{\circ}\). The diagonal basis generates either \(45^{\circ}\) or \(135^{\circ}\)[9; 11]. When the receiver measures the qubits, there is a 50% probability of using the wrong basis. Further, the probability of getting a correct qubit state using the wrong basis is 50%. Thus, 25% of the qubits measured by the receiver are incorrect [9; 24]. In 1992, [PERSON] proposed a simplified version of the BB84 protocol named B92 [28]. It handles only one of two polarization states for each basis. The rectilinear basis encodes a 0-bit state into a \(0^{\circ}\) polarized state. The diagonal basis encodes a 1-bit state into a \(45^{\circ}\) polarized state. In B92, when the receiver selects the wrong basis, it does not measure anything. This condition is called erasure [11]. Both BB84 and B92 algorithms have four main phases, namely, quantum key exchange, key sifting, error calculation, and error correction and privacy amplification. The mechanism in the key sifting phase of B92 differs from that in BB84. In B92, the key sifting is more efficient since a wrong basis does not measure qubits. Unlike BB84, B92 uses only one of two polarization states for each basis, making the protocol more efficient than BB84. In BB84, the wrong basis can be used to measure qubits, and there is a 50% probability of getting the correct qubit and a 50% probability of getting an incorrect qubit. In B92, when the receiver selects the wrong basis, it does not measure anything. This condition is called erasure. Thus, the receiver does not need to worry about reading incorrect bits because of measuring them wrong. [PERSON] et al. [11] provides a survey on QKD protocols involving BB84 and B92, performed simulations that show B92 has a lower error value than BB84.