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It is a significant challenge to find out suitable cryptography for wireless sensor networks owing to limitations of power, computation capability and storage resources. Many schemes based on public or symmetric key cryptography are investigated. This paper proposes a new broadcast encryption scheme, which can be used for key distribution or directly broadcasting message. The scheme is suitable for typical type of networks. We review identity-based encryption and attribute-based encryption first. Then we describe a key agreement and encryption scheme based on them. We discuss the efficiency and security of our scheme by comparing with traditional public key technique and symmetric key technique.