A security proof for key exchange protocols

We present a technique of modular security proofs for key exchange protocols in the modified Bellare–Rogaway (mBR) model introduced by C. Kudla and K. G. Paterson. We have applied this technique to modify Protocol 1 in their paper to Protocol 2 and analyze its security in this model. These two protocols differ only in the combination of the ephemeral and long-term private keys in the computation of the session key. Our method for proving strong partnering of Protocol may be applied to prove a same result (stated without proof) by C. Kudla and K. G. Paterson.