MITM defense in Diffie-Hellman protocol

Question

Let's consider that Alice and Bob both know a shared secret $secret$ and don't know each other DH public keys. They want to authenticate each other and their keys using only $secret$. Let's also forget about an existence of SMP. Can the following scheme be considered secure?

First, Alice and Bob perform Diffie-Hellman KE:

$Alice: send(g^a)$
$Bob: recv(g^a);\ send(g^b)$
$Alice: recv(g^b)$ // Now both Alice and Bob has a shared $dh\_key$

Next, they want to be sure that their companion:
a) Knows a shared secret.
b) Is the owner of the corresponding DH private key.

$Alice: send(HMAC(g^a, secret))$
$Bob: recv\_and\_check(msg, secret); send(HMAC(g^b, secret))$ $Alice: recv\_and\_check(msg, secret)$

If all checks are passed Alice and Bob can start a secure data exchange. They also can save DH-public keys for future conversations.

So:

1. Is the scheme secure?
2. If the answer to the first question is 'yes' what are pros and cons in comparison with SMP (like in OTR SMP)?

Answer 1

Since you tagged the question with "man-in-the-middle" then the answer is that the protocol is not secure after its first use because the eavesdropper can record the exchange and repeat it. Instead, each party should challenge the other party with a random value that will be used by the other party to construct the HMAC.