Abstract: Underwater wireless sensor networks(UWSN) is a network composed of dynamic connection nodes. Its characteristics provide a favorable guarantee for the construction of battlefield information network. However, it is necessary that data center in UWSN quickly verifies the received messages, ensures that the message is not tampered, and can protect both identity and location privacies of nodes. The existing aggregate signature schemes can achieve rapid verification of messages and ensure integrity of the messages, but they incur high computation and communication overhead because their constructions rely on complex mathematical operations such as modular exponentiation. In this paper, an effective aggregate signature scheme without modular exponentiation is proposed. This scheme is performed by the trust agency(TA) and key generation center(KGC) to generate a temporary secret key(TSK) according to the identity string submitted by the node. On receiving TSK from the KGC, each node generates a set of pseudonym, private key and public key. Then node signs a message using its pseudonym and private key. The data center aggregates all signed messages received and validates the signature using public key of the node. Under the assumption of calculating the elliptic curve discrete logarithm problem (ECDLP) and the random oracle model, the new scheme is proved to be able to resist the existence forgery under adaptive selection message attack and identity document(ID) attack. Compared with other traditional signature schemes, the proposed scheme can provide fast signature and verification of message, have higher computing efficiency, and protect privacy of identity and location of node