# Evaluating the Efficiency of Physical and Cryptographic Security Solutions for Quantum Immune IoT
## 3 Quantum Immune Security Solutions
### Quantum Immune Physical Layer Security  
Physical layer security addresses the passive quantum threat model that was described in Section 2. Physical layer security methods can be generally divided into two different categories: secrecy coding methods that secretly convey information using the properties of the wireless medium, and extraction methods that seek to build secret information by adopting the inherent randomness of wireless channels. When it comes to extraction methods, [PERSON] and [PERSON] can agree on the common key by measuring a physical quantity common to both of them in a process commonly referred to as key extraction [43]. Due to the physical properties of the quantity measured, for example, channel impulse response, [PERSON] and [PERSON] obtain highly correlated measurements. On the other hand, the measurements obtained by the eavesdropper [PERSON] are weakly correlated because she is most likely in a different place than [PERSON]. This hypothetical gap of the correlation of measurements between [PERSON] and [PERSON] and the correlation of [PERSON]'s measurements opens the door for a key exchange mechanism with an information reconciliation and privacy amplification step to enable the calculation of a secret key that is almost independent of the adversary's view [43]. Thus, the physical layer key extraction between the two parties, [PERSON] and [PERSON], is based on two basic premises: the measurements of both [PERSON] and [PERSON] are highly correlated, whereas [PERSON]'s measurements are weakly correlated. These assumptions become relevant if the confidentiality of the key agreement is based on the physical layer properties and on the location of the attacker. In secrecy coding methods, the goal is to design a coding scheme--namely, an encoding algorithm and the decoding algorithm--that makes it possible to communicate both reliably and securely between [PERSON] and [PERSON] in the presence of an eavesdropper [PERSON]. The reliability of the secrecy code is quantified by its average probability of error with uniformly distributed messages \(M\). The information leaked to [PERSON] is given by the mutual information between [PERSON]'s message \(M\) and [PERSON]'s observations \(Z^{n}\) where \(n\) denotes the number of samples. A rate \(R\) is said to be achievable under the strong secrecy requirement if there exists a sequence of codes for which both the average probability of error and the information leaked to [PERSON] vanish as \(n\) tends to infinity. The supremum \(C_{s}\) of the achievable rates is known as the secrecy capacity of the channel. In other words, reliable and secure communication is possible only at coding rates below or at secrecy capacity. Figure 3: Simplified NewHope and Frodo key agreement protocols (based on [5; 6]). The definition of secrecy capacity is an information theoretic one, that is, secrecy does not depend on assumptions about computational hardness, and as such secrecy coding is not vulnerable to future developments in computer power such as quantum computing. However, the definition of secrecy capacity is based on the premise that the channel between the legitimate parties, [PERSON] and [PERSON], is statistically better than any of the eavesdropper channels. In practice, [PERSON] may jam [PERSON] by generating an artificial noise-like signal that affects all receivers except the one used by [PERSON] [11]. However, the jamming signal is location and channel dependent. This fact opens the theoretical possibility to attack physical layer security schemes as described in [44]. The basic idea of the attack is that if an attacker's antennas surround [PERSON] and [PERSON] completely and those antennas are cooled to a few degrees Kelvin, the attacker is then able to recover radio signals from [PERSON] and [PERSON] by using the Huygens principle and the Green integral representation of the electromagnetic fields.