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ÖgeGroup authentication and its application(Graduate School, 2023-03-17)This Thesis is about Group Authentication and Its Application. One of the most important subjects of secure communication is authentication. The data exchange process among communicating parties starts only after handling identification of each party. By increasing the usage of digital communication and private data transmission, authenticating a big amount of parties at the same time has an important role to have a secure and confident connection. The development of new technology in several fields forces various new devices to use public Internet. For example, autonomous vehicles are expected to compromise large part of communication system in the near future. The unmanned drones are already a part of surveillance and delivery systems. Most importantly, the internet service providers exploit the satellite technology to provide infrastructure for its users to access Internet while absence of base stations. In all these examples, the communicating parties do not necessarily perform identity confirmation. Group authentication provides this opportunity to authenticate a big part of a group at the same time. In this thesis it has been analyzed and evaluated the previous researches in group authentication field and the methods used for this purpose. Group membership authentication is one of the common method in group authentication which confirms the membership of a subset of a predetermined group by a single operation at the same time to figure out if all are members of the group or there is any nonmember. During the group authentication all legal members are allowed to establish a common key which is secret to the group. A trusted authority called group manager is responsible to generate tokens and distribute to each user. In computational side of these researches mathematical theorems and methods has been used; The basic theorem is Newton interpolation theorem which has brought many theorems and corollaries behind like Lagrange interpolation theorem. In addition, Elliptic curves method has been used in order to make the key transferring between the users secure. Even though the first group authentication method appeared in 2014, some other applications have been implicitly employed group authentication like methods as their security measurements. For example, a group like authentication scheme in autonomous vehicle realm is being called a batch authentication and in federated learning applications some researchers call it secure multi-party computation and it is called group authentication in wireless networks in order to authenticate the group users at the same time, but finally all mentioned terms are discussed as group authentication in this thesis. As an improving technologies and increasing the users, malicious usage of these technologies are growing as well. impersonating or fake data transferring through a large group of users may cause several serious problems in peoples life and also in the system which is used; On the other hand, authenticating a large group of users one by one is practically useless. Group authentication is going to become a necessary method for systems with large membership because of the ability of authenticating a group at the same time and using much more less storage, energy and time than the previous methods.