How to Formalize Noise Protocol Messages I try to understand the messages of the Noise Protocol Framework. The handshakes are based on Diffie-Hellmann key exchange.
This is an example for a handshake pattern:

-&gt; e
&lt;- e, ee, s, es


I try to formalize the handshake with mathematical descriptions.
For example the mathematical description of the first message is:
. Where  is a generator and  is the private ephemeral key of the sender.
But I don't understand how the values ee and es are calculated.
How can these patterns be descriebed mathematically?
ee and es aren't values, they're function invocations. 

ee denotes the use of a Diffie-Hellman key exchange using two ephemeral keys, es denotes the use of a Diffie-Hellman key exchange using an ephemeral key and a static key. The first letter is the initiator, the second is the responder. 

So it's just $ee = DH(e, re)$, $es=DH(e,rs)$, $se = DH(s, re)$, $ss = DH(s, rs)$, where $DH(i,r)$ is the Diffie-Hellman exchange function applied to the $i$nitiator's key and the $r$espoder's key.