# Quantum Key Distribution with Post-Processing Driven by Physical Unclonable Functions
## 1 Introduction
The complications caused by the necessity for authentication and the management of pre-shared secret keys have not gone unnoticed by the community. When a pre-shared key is stored or distributed in plaintext, one cannot guarantee that a malicious third party will not obtain access to it and launch a successful man-in-the-middle attack in the first QKD session, which will compromise the security of the next sessions as well. The problem is not solved by encrypting the pre-shared key or by storing it in a password-protected electronic device, but rather it is transferred to the management and the distribution of an additional key (or password), which is needed in order to ensure the secrecy of the pre-shared key. There have been efforts in the past to decrease the length of the pre-shared key in existing QKD protocols, as well as to facilitate the distribution and management of pre-shared keys. [PERSON] et al. [19] proposed an authentication scheme which relies on a two-step hash function evaluation and involves two-step non-ITS hashing, resulting in low key consumption. Later, it was shown that the proposed scheme is not secure [20; 21]. More recently, [PERSON] and co-workers [22; 23] experimentally studied the performance of QKD when the authentication relied on a post-quantum cryptographic (PQC) protocol [24]. Although this hybrid protocol has efficient key management and new users can be easily added to the QKD network, it is not ITS, because the adopted PQC is computationally and not information-theoretically secure. In fact, the key that is distributed by means of the hybrid protocol is secure provided that the underlying PQC has not been broken during the execution of the protocol, which can be guaranteed only in the framework of computational security. Unless the adversary is present during the execution, they cannot later obtain the distributed key, even if they have unlimited resources. In the present work, our aim is to propose a scheme for the generation, distribution, and management of pre-shared keys that relies on physical unclonable functions (PUFs). In contrast to post-quantum public-key cryptosystems, the judicious integration of PUFs in existing QKD systems promises ITS QKD under limited assumptions pertaining mainly to the performance of the PUF under consideration. Furthermore, our scheme allows for the real-time authentication of the QKD devices that are connected to the network. PUFs were proposed by [PERSON] et al. [25] as a means to generate random numerical keys from the laser speckle that is produced from a multiple-scattering optical medium. The optical medium plays the role of a token, which is technologically hard to clone and it can produce a large number of independent, almost truly random keys, each one associated with different parameters of the input laser light (e.g., wavelength, power, wavefront, angle of incidence, etc.). Following the work of [PERSON] et al., PUFs have attracted considerable attention over the last two decades or so, and the related literature is rather rich [26; 27; 28; 29; 30; 31; 32; 33]. Currently, there are different types of PUFs, including optical (non-silicon) PUFs, time-delay-based silicon PUFs, intrinsic silicon PUFs, magnetic PUFs, etc. Their main applications are in entity authentication, and in the development of anti-counterfeiting methods, and there is also a number of companies commercializing PUF products [27]. For our purposes, it is sufficient to know the basic operation of a PUF, which is the generation of random keys, leaving aside details that go beyond the scope of the present work. An interested reader may refer to the related review articles [26; 27; 28; 29; 30; 31; 32; 33], and the references therein. In a nutshell, as shown in Figure 3, a PUF is a mathematical function that refers to the behaviour of a physical object or device (to be referred to hereafter as the PUF token or tag). The PUF tag is characterized by internal random disorder, which plays the role of a fingerprint, and it is technologically hard to clone.