In this paper we study the fault diameter of the n-dimensional hypercube (or n-cube for short), Qn, for n ≥ 3. Let F be a set of hybrid node-faults and/or link-faults in Qn such that every node of Qn is still connected to at least one fault-free node by a fault-free link. Then we compute the exact diameter of Qn - F for |F| ≤ 2n - 3. As an immediate consequence, our result improves upon those presented by S. Latifi (1993), in which only node-faults were addressed.
In recent years, many mobile services have been exploited based on the smartphone platform. For example, huge mobile applications (APPs) created for the mobile communication services which are not only for voice services, but also for social networking services. Therefore, the Mobile Chat (MC) services plays a very important role in current social networking. With the increasingly growing reliance on the Mobile Chat System (MCS) in one hand, and the growing number of vulnerabilities and attacks on the other hand, there are lots of increasing demands for their security solutions. In spite of the critical role of MCS in the representative internet mobile user's life, electronic MC services are not secure enough. Thus, both the Secure End-to-End Secure Mobile Chat (SE2E-MC) scheme and Secure Group-based Mobile Chat (SG-MC) scheme are provided the suitable solutions. The SG-MC scheme and its associated requirements are also designed in this paper. The scheme is implemented to provide mutual authentication and prevent the password guessing attack and the undetectable on-line password guessing attack. Finally, the scheme could prevent the password-based authentication, and provide the passwordbased key agreement (AKA) with easily remembered characteristic.
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