In wireless sensor networks (WSNs), broadcast authentication is a crucial security mechanism that allows a multitude of legitimate users to join in and disseminate messages into the networks in a dynamic and authenticated way. During the past few years, several public-key based multi-user broadcast authentication schemes have been proposed to achieve immediate authentication and to address the security vulnerability intrinsic to $\mu$TESLA-like schemes. Unfortunately, the relatively slow signature verification in signature-based broadcast authentication has also incurred a series of problems such as high energy consumption and long verification delay. In this contribution, we propose an efficient technique to accelerate the signature verification in WSNs through the cooperation among sensor nodes. By allowing some sensor nodes to release the intermediate computation results to their neighbors during the signature verification, a large number of sensor nodes can accelerate their signature verification process significantly. When applying our faster signature verification technique to the broadcast authentication in a $4 \times 4$ grid-based WSN, a quantitative performance analysis shows that our scheme needs 17.7%~34.5% less energy and runs about 50% faster than the traditional signature verification method.