The Canetti–Krawczyk (CK) and extended Canetti–Krawczyk (eCK) security mo-dels, are widely used to provide security arguments for key agreement protocols. We discuss security shades in the (e)CK models, and some practical attacks unconsi-dered in (e)CK–security arguments. We propose a strong security model which en-compasses 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 particularly 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 assumption and the Random Oracle model.