# Protecting Private Communications in Cyber-Physical Systems through Physical Unclonable Functions
## 3 Proposed Encryption Scheme
### Key Generator
#### 3.3.1 Exchange-Bias Effect: Overview  
Discovered by [PERSON] and [PERSON] (2016) in 1956, they describe the EB as a process that occurs as a result of the interaction between two layers of magnetic material composing the magnetic device: a ferromagnetic (FM) and an antiferromagnetic (AFM) layer. The first (and simplest) consequence of this phenomenon is a displacement of the hysteresis cycle showed by magnetic materials affected by a magnetic field (because of the influence of the atomic spins of the FM on the AFM ions in the contact zone of the two materials, or interface). In a physical sense, an EB device is seen as a united set of magnetic domains that do not interact with each other but have an interface with a ferromagnetic layer, so that each one of the domains in the AFM has a magnetic moment ([PERSON] et al., 2016).  
However, in a more practical context, this effect causes the material magnetization to evolve and change when the material is left at room temperature after activation. It is then when the dependence of the (exchange-bias) magnetic field with \(ln(t)\) (logarithm of time instant) becomes noticeable, as stated by [PERSON] et al. (2016) and [PERSON] and [PERSON] (2016). The importance of these results lies in the demonstration that a magnetic device composed of a FM and AFM bilayer behaves depending on the logarithm of time instant and without the intervention of any other variable.  
In order to cause a magnetic bilayer to behave in that way, the material must be activated according to a specific process. The manufacturing methods of exchange-bias materials are not a subject of study in this work, but it is important to mention that the activation requires a distribution of the AF material in grains suitable to achieve this activation and thermal stability ([PERSON] et al., 2016). This manufacturing process, which will be called 'activation', consists of converting the behavior of the AFM from antiferromagnetic  
Figure 4: PUF schematics.  
to paramagnetic in such a way that the spins are oriented in a random manner. This is achieved by heating the material in a temperature range that is between the Neel temperature, \(T_{N}\) (above which an antiferromagnetic material becomes paramagnetic), and the Curie temperature, \(T_{C}\) (above which certain magnetic materials undergo a sharp change in their magnetic properties). This heating is done in the presence of a magnetic field \(H_{ext}\) high enough to saturate the ferromagnetic layer, as shown in Figure 5. Once the antiferromagnetic spins are aligned in a random manner, the sample is cooled below the Neel temperature, in what is called the alignment temperature, \(T_{AL}\). If the presence of the saturation field is maintained, not only the spins of the ferromagnetic will be aligned but also those of the interface of the AFM, due to the influence of the spins of the interface of the FM, as seen in Figure 5.  
Then, as a conclusion, an EB magnetic device presents a behavior that varies with time. This phenomenon enables us to create seeds also varying with time, so the entire secret key stream will dynamically and automatically change with time, as required (see Section 3.2). This dynamic evolution, besides, does not require any key distribution or communication; benefits from a natural phenomenon. Thus, the proposed scheme is more secure than any other previous proposal. REQ#2 is, therefore, fulfilled.  
Although the evolution speed may be quite slow, a Trifork generator can produce very long-period number sequences, fulfilling REQ#1.  
Any case, if any manufacturer or attacker could create an EB material behaving in the same manner as those materials employed in our PUF, no security will be provided by this mechanism (REQ#3 will not be met). Nevertheless, the next section describes how unclonable the behavior of these EB materials is; and how impossible it is in practice to either manufacture two identical or similar EB devices or to manipulate an existing EB-based PUF to be employed by cybercriminals.