The Canetti–Krawczyk (CK) and extended Canetti–Krawczyk (eCK) security mod- els, are widely used to provide security arguments for key agreement protocols. We dis- cuss security shades in the (e)CK models, which make some practical attacks unconsi- dered in security arguments. We propose a strong security model which encompasses the eCK one. We also propose a new protocol, called Strengthened MQV (SMQV), which in addition to provide the same efficiency as the (H)MQV protocols, is particu- larly suited for distributed implementations wherein a tamper–proof device is used to store long–lived keys, while session keys are used on an untrusted host machine. The SMQV protocol meets our security definition under the Gap Diffie–Hellman assump- tion and the Random Oracle model.