Broadcast authentication is a critical security service in wireless sensor networks (WSNs), as it allows the mobile users of WSNs to broadcast messages to multiple sensor nodes in a secure way. Although symmetric-key-based solutions such as μTESLA and multilevel μTESLA have been proposed, they all suffer from severe energy-depletion attacks resulted from the nature of delayed message authentication. This paper presents several efficient public-key-based schemes to achieve immediate broadcast authentication and thus avoid the security vulnerability intrinsic to μTESLA-like schemes. Our schemes are built upon the unique integration of several cryptographic techniques, including the Bloom filter, the partial message recovery signature scheme and the Merkle hash tree. We prove the effectiveness and efficiency of the proposed schemes by a comprehensive quantitative analysis of their energy consumption in both computation and communication.