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The focus of this paper is on access security aspects of 3G-WLAN interworking. Firstly, the authentication entities which do not rely on the concrete heterogeneous network are abstracted by analyzing 3G-WLAN multi-kind heterogeneous network model. And then a common authentication model is established and a novel access authentication and key agreement scheme combined elliptic curve cryptographic techniques with public key infrastructure is proposed. In this scheme, encryption data uses the shortest key length ECC with the same security coefficient, and authentication information is signed. In addition, the encryption/decryption and signature algorithm are carefully chosen and improved. Therefore mobile terminal computation overhead is reduced. Finally, the security analysis shows that the proposed scheme satisfies the security properties such as mutual authentication, key control, key confirmation, confidentiality of the sensitive data, non-repudiation, data integrity, resistance to replay attack. And the performance analysis also shows that the proposed scheme is efficient in regard to computation and communication overheads.