TMQV: A Strongly eCK-secure Diffie-Hellman Protocol without Gap Assumption

In this paper, we propose an authenticated key exchange (AKE) protocol under the computational Diffie-Hellman (CDH) assumption with respect to the strengthened eCK-security (seCK-security) of Sarr et al.. To date, many AKE protocols either are provably secure under a rather strong and nonstandard assumption named as the gap Diffie-Hellman (GDH) assumption, or fall to practical attacks on the intermediate result leakage which can be captured by the seCK model. In order to remove the gap assumption and to achieve stronger security requirements, we present the TMQV protocol using the twinning technique and the MQV key derivation method. With the help of trapdoor test theorem, TMQV is provably seCK-secure under the standard CDH assumption in the random oracle model. Compared with the related works, TMQV achieves not only stronger security but also higher implementation efficiency with weaker cryptographic assumptions.