Many people may still remember the debates a few years ago about the HMQV protocol, a modification of MQV with the primary aim of provable security. Various attacks were later discovered for the original HMQV. In the subsequent submission to the IEEE P1363 standards, the HMQV protocol has been revised to address the reported weaknesses.
However, the revised HMQV protocol is still vulnerable. In a paper that I presented at Financial Cryptography ‘10, I described two new attacks. The first presents a counterexample to invalidate the basic authentication feature in the protocol. The second is generally applicable to other key exchange protocols, despite that many have formal security proofs.
The first attack is particularly concerning since the formal security proofs failed to detect this basic flaw. The HMQV protocol explicitly specifies that the Certificate Authority (CA) does not need to validate the public key except checking it is not zero. (This is one reason why HMQV claims to be more efficient than MQV). So, the protocol allows the CA to certify a small subgroup element as the user’s “public key”. Then, anyone who knows this “public key” can successfully pass authentication using HMQV (see the paper for details). Note, in this case, a private key doesn’t exit, but the authentication is successful. What is the “authentication” in HMQV based on?
The HMQV author acknowledges this attack, but states it has no bad effects. Although I disagree, this will be up to the reader to decide.