sufficient to consider the system under an adversary completely controlled by the environment [@Canetti], a *dummy adversary* that only forwards the desired channel output from the environment. As is, the systems are trivially distinguishable because of the lack of a tag in the ideal system. We therefore add a *simulator* ${\mathcal{S}}$ to the ideal functionality, that adds a tag $t$ that is generated from $m$ using the appropriate key and hash function to make it indistinguishable from the real case, and strips off any received tag $t'$ after the channel. The name simulator also alludes to simulating the adversary, and is especially simple when simulating the dummy adversary.

We now want to ensure that the environment ${\mathcal{Z}}$ cannot distinguish between the two cases *(a)* it is interacting with ${\mathcal{A}}$ and participants running the WCA scheme or *(b)* it is interacting with ${\mathcal{S}}$ and participants running ${\mathcal{F}}$, except with low probability (see Fig. \[fig:setup1\]). Perhaps we should point out that the description here differs slightly from that of [@Portmann]. The WCA scheme is resolved in somewhat finer detail and is separated from the participants, and the ideal functionality is that of an authentic channel rather than an immutable but blockable channel. 