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Anonymity of user is an important property in the cryptographic protocol, to protect the privacy of the participants. In this paper, we propose a new primitive, fully anonymous signcryption, which provide anonymity of both sender and receiver along with the advantage of traditional ring signcryption (only provides anonymity of sender) scheme. We also construct a fully anonymous identity-based signcryption scheme in the standard model. The proposed scheme satisfies the semantic security, unforgeability and full anonymity.