## 2 Related Works
* **One-way--**It must not be possible to calculate the challenge \(c_{i}\) that triggers a PUF to generate \(r_{i}\). * **Tamper evident--**Any attempt to recover the structural aspect of a PUF should alter the original structure and therefore the initial challenge-response pair. Both the fingerprints of a UNO and the challenge-response of a PUF have the purpose of identifying an object. In order to guarantee the uniqueness and robustness of a PUF or a UNO, two metrics are commonly used in the literature. The first is called inter-distance and expresses the distance between two responses of different PUFs [17]. The second is intra-distance and evaluates the distance between two responses of the same PUF. These distances are often summarized using histograms, showing their occurrence observed over a number of CRPs. It is common that the resulting histograms could be approximated by a Gaussian distribution, and are summarized by providing their averages \(\mu_{intra}\), \(\mu_{inter}\) and their standard deviations \(\sigma_{intra}\) and \(\sigma_{inter}\)[17]. The above mentioned means give a very important notion to the evaluation of the PUFs/UNOs. \(\mu_{intra}\) indicates the average noise on the responses, i.e., it measures the average reproducibility of a measured response related to an earlier realization of the same response. \(\mu_{inter}\) indicates the notion of uniqueness, i.e., it measures the average distinguishable responses given by the PUFs/UNOs. Depending on the nature of the PUF response, the distance measure can vary. One distance measure commonly used in PUFs is the Hamming distance, as used in Optical PUFs [19]. Since the appearance of the PUFs in 2001, several object types were proposed as candidates to PUF systems, such as Optical PUFs [19; 20], Image-based PUFs [21; 22], Coating PUFs [23; 24], Silicon PUFs [25], SRAM (Static Random Access Memory) PUFs [26; 27; 28; 29], Paper PUFs [8; 30], Arbiter PUFs [31], Reconfigurable PUFs [32], Ring Oscillator Pufs [33; 34], RFID (Radio-Frequency Identification) PUFs [35], among others. This work focuses on image-based PUFs because as the authors are interested in its scope. Image-based PUFs for anti-counterfeiting applications were introduced in Reference [36]. These kind of PUFs are based on random visual features of physical objects. The process relies on the capture of 2D or 3D images, where the outline of the object is observed. The image-based PUF is physically unclonable, but not necessarily \"mathematically unclonable\" [21]. It should be very hard and expensive to build a mathematical model that provides the correct answer to the same challenge-response generated by a PUF. As these vision based systems do not have this feature, it is possible to create a mathematical clone (fake image - i.e., print attack) that presents the same result as the one provided by a PUF. As a workaround, it is assumed that this process has to pass a first check to validate the study image. Contrary to other PUFs, the input of an image-based PUF is usually a fixed challenge (e.g., light used to capture the photos) and, as mentioned before, it is possible to create a mathematical clone that presents the same response. The response of an image-based PUF is a real value image so it is necessary that the image processing system is integrated in the extraction process [21]. Recently, [PERSON] et al. presented an authentication mechanism using images of metallic dendrites as an image-based PUF [37]. The recognition framework includes image denoising, skeletonizing, pruning, and feature point extraction. The authentication problem is converted to a graph matching problem, because the obtained skeletons are mapped to tree-based weighted graphs. An image-based PUF using imagery from injection moulded plastic for anti-counterfeiting purposes was introduced by [PERSON] et al. [38]. A database of 200 samples from two different injection moulded materials (100 + 100) was used to demonstrate the effectiveness of using the surface patterns for individual object recognition.