## 1 Introduction  
The advent of the Internet of Things (IoT) has led to a web of connections that provides network infrastructure and shares a massive amount of private information among smart devices [1]. The requirements for trustworthy communication have been one of the biggest concerns [2]. In recent years, it has been demonstrated that hardware-based security systems are more secure than software-based security systems due to innate architectural risks in software [3]. Hardware-based security systems typically store digital keys in non-volatile storage and the keys play an important role in encrypting shared information or in processing access authentication. However, it has been shown that the typical method is vulnerable to invasive attacks on physical systems to reveal their secret information [4; 5; 6]. To defeat such potential threats, physical unclonable functions (PUFs) have been introduced as a promising alternative. PUFs primarily utilize inherent physical variations that naturally occur during hardware device manufacturing [7]. The major advantage of PUFs is that they are easy to build but practically impossible to duplicate since the formation of such physical variations is unpredictable and uncontrollable, even under the same conditions. In general, PUFs implement challenge-response protocols rather than extracting stored keys. When a challenge is applied to a PUF, a corresponding response is generated. Each response depends on the unique features of a PUF instance [8]. Therefore, a set of challenge-response pairs (CRPs) is regarded as the fingerprint of a PUF-integrated device; with unique CRPs, PUFs can be used in security applications such as authentication and identification as well as key generation [9]. However, a PUF generates and transmits a response to a challenge even if the challenge comes from an attacker [10], so eventually, attackers can obtain CRP information from a hardware PUF.  
A Bloom filter (BF) is a simple and efficient bit vector structure that represents the membership information of a set of elements [11; 12; 13; 14; 15]. Bloom filters are used in various lookup systems to improve their performance by avoiding access to unnecessary data [16; 17]. Bloom filters can reduce memory usage according to many studies in the storage field [18; 19] and can remove data duplication [20]. The Bloom filters are also applied to many security fields [21; 22]. A Bloom filter implemented in hardware can accelerate information retrieval and save memory [23; 24; 25]. Bloom filters are used in a wide variety of applications and will increasingly be the subject of various research studies in the future [26; 27; 28].  
This paper describes a security approach that exchanges only the correct CRPs with the authentication server by removing unnecessary challenge access from attackers. The proposed approach is based on a pulsewidth-based memristive PUF (pm-PUF) [29]. To increase the accuracy of the exchange of CRP information between the pm-PUF and its authentication server, we propose to add a small-memory Bloom filter. When the CRPs of authentication server are stored in the Bloom filter and applied to the pm-PUF, its security is improved by removing unnecessary attacker access to CRPs and avoiding duplicate CRP usage.  
The remainder of this paper is organized as follows. Section 2 describes related works including variant PUFs and Bloom filters. Section 3 introduces our proposed structure. Section 4 describes the simulation data set. Section 5 discusses the performance evaluation results, and Section 6 briefly concludes the paper.