Given $plaintext$ and its respective authentication $tag$ which is generated from HMAC-MD5 so that $|tag| = 128$ bits.
If the application is constrained and can send only $64$ bits. Is it ok, if we xor the first $8$ bytes and second $8$ bytes of the $tag$ in order to generate a total $64$ bit $tag$?
I believe the strengthen is really in the key size not really the output size for somebody to do a brute force. What worse can happen is two different inputs could have same signature if we are doing the above ?
Or does this weaken the strengthen in any way?