The formation process of Definition 4.

The formation process of Definition 4.

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Graphical password (GPW) is one of various passwords used in information communication. The QR code, which is widely used in the current world, is one of GPWs. Topsnut-GPWs are new-type GPWs made by topological structures (also, called graphs) and number theory, but the existing GPWs use pictures/images almost. We design new Topsnut-GPWs by means o...

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... Complex passwords, while more secure, are often difficult to remember, leading users to compromise security by writing them down or reusing passwords across multiple accounts [12]. In response to these challenges, graphical passwords have been suggested as a replacement form of authentication [13][14][15]. ...
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The rapid advancement of information technology (IT) has given rise to a new era of efficient and fast communication and transactions. However, the increasing adoption of and reliance on IT has led to the exposure of personal and sensitive information online. Safeguarding this information against unauthorized access remains a persistent challenge, necessitating the implementation of improved computer security measures. The core objective of computer security is to ensure the confidentiality, availability, and integrity of data and services. Among the mechanisms developed to counter security threats, authentication stands out as a pivotal defense strategy. Graphical passwords have emerged as a popular authentication approach, yet they face vulnerability to shoulder-surfing attacks, wherein an attacker can clandestinely observe a victim’s actions. Shoulder-surfing attacks present a significant security challenge within the realm of graphical password authentication. These attacks occur when an unauthorized individual covertly observes the authentication process of a legitimate user by shoulder surfing the user or capturing the interaction through a video recording. In response to this challenge, various methods have been proposed to thwart shoulder-surfing attacks, each with distinct advantages and limitations. This study thus centers on reviewing the resilience of existing recognition-based graphical password techniques against shoulder-surfing attacks by conducting a comprehensive examination and evaluation of their benefits, strengths, and weaknesses. The evaluation process entailed accessing pertinent academic resources through renowned search engines, including Web of Science, Science Direct, IEEE Xplore, ProQuest, Scopus, Springer, Wiley Online Library, and EBSCO. The selection criteria were carefully designed to prioritize studies that focused on recognition-based graphical password methods. Through this rigorous approach, 28 studies were identified and subjected to a thorough review. The results show that fourteen of them adopted registered objects as pass-objects, bolstering security through object recognition. Additionally, two methods employed decoy objects as pass-objects, enhancing obfuscation. Notably, one technique harnessed both registered and decoy objects, amplifying the security paradigm. The results also showed that recognition-based graphical password techniques varied in their resistance to different types of shoulder-surfing attacks. Some methods were effective in preventing direct observation attacks, while others were vulnerable to video-recorded and multiple-observation attacks. This vulnerability emerged due to attackers potentially extracting key information by analyzing user interaction patterns in each challenge set. Notably, one method stood out as an exception, demonstrating resilience against all three types of shoulder-surfing attacks. In conclusion, this study contributes to a comprehensive understanding of the efficacy of recognition-based graphical password methods in countering shoulder-surfing attacks by analyzing the diverse strategies employed by these methods and revealing their strengths and weaknesses.
... Wang et al. [9,2] designed a topological coding consisting of topological structure and graph colorings. According to the order of vertex-edge-vertex, Yao et al. [8] arrange the labels or colors of each edge and two end-vertices of a graph H with p vertices and q edges in topological matrix T code = (U, E, V ) T 3×q corresponds a graph H with V (H) = (U V ) * and E(H) = E * , where U = (β(u 1 ), β(u 2 ), . . . ...
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... We show the relationships between labelings on trees by producing several image-labelings from the set-ordered graceful labeling. Such results can be applied to molecular structures [17] and asymmetric cryptosystem [18], therefore, the theoretical research on labeling is meaningful. ...
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