The Canetti–Krawczyk (CK) and extended Canetti–Krawczyk (eCK) security models, are widely used to provide security arguments for key agreement protocols. We discuss security shades in the (e)CK models, and some practical attacks unconsidered in (e)CK–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 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.
Augustin P. Sarr, Philippe Elbaz-Vincent, Jean-Cla