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The primary task of secure group communications in wireless sensor networks (WSNs) is to securely transmit various types of data, for example weather data, traffic data, etc. Collected data in WSNs is different from most data transmitted in digital communication applications. Most collected data in WSNs contains only few bits of information. Conventional protocols are not suitable for WSNs since WSNs need more fast and lightweight protocols for secure group communications. User authentication and key establishment are two fundamental security services in secure communications for WSNs. The user authentication allows communication entities to authenticate their communication partners and the key establishment allows a secret session key to be shared among all communication entities. The session key can be used to protect exchange information in the communication. Communication has been moved from traditional one-to-one communications to many-to-many communications, also called group communications. Traditional user authentication which authenticates one user at one time is no longer suitable for a group communication which involves multiple users. In this paper, we propose a protocol which provides both membership authentication and key establishment simultaneously for WSNs. However, all existing solutions can only provide either user authentication or key establishment separately. Furthermore, our proposed membership authentication has complexity O(n), where n is the number of users in a group communication, which is different from all existing user authentication schemes which are one-to-one authentications with complexity O(n<sup>2</sup>).

Fast Multivariate-Polynomial-Based Membership Authentication and Key Establishment for Secure Group Communications in WSN