Wireless Sensor Networks (WSNs) are one of the core techniques for the upcoming ubiquitous environment. A WSN is an $\It{ad-hoc}$ network which consists of hundreds to thousands of tiny resource-constrained sensor nodes and several powerful Base Stations (BSs). WSNs will be widely used for autonomous remote data acquisitions in many different applications from battle field surveillance to building maintenance [7].
Even though, WSNs have many similarities with existing $\It{ad-hoc}$ networks, there are many differences; more constrained resources, large scale deployment, and node compromise. These differences make existing security protocols for ad-hoc networks impractical in WSNs [9].
In WSNs, Broadcast authentication allows sensor nodes to verify the authenticity of broadcasted messages including commands and queries. Due to above mentioned differences, existing broadcast authentication protocols for $\It{ad-hoc}$ networks or Internet are impractical as they require computation intensive public key operations. To conserve the energy of sensor nodes, most protocols for WSNs utilized delayed key disclosure. The problem of these protocols is not only legitimate senders could broadcast messages but also adversaries easily flood malicious messages into a network by which they could easily destruct the operations of the network by overflowing the buffer of sensor nodes.
Recently, some researchers have proposed several multi-user broadcast authentication protocols which allow legitimate mobile users to directly disseminate their messages into the network in an authenticated manner. However, most of them are based on public key cryptography (PKC) which consumes a lot of energy of sensor nodes to verify the messages. Although, PKC can provide immediate authentication of messages (thus, it can prevent the network from flooding attacks), it could not prevent the network from careless and excessive message dissemination by legitimate users. Therefore, we strongly be...