Concept Question for Secure Computation I think this should be a simple question and I might be missing something fairly fundamental, but I haven't been able to find the answer.

Basically, suppose there are parties $A$ and $B$. Party $A$ gets a secret input $s$. Party $B$ has no input. They wish to securely compute the function $f(s) = (\bot, \bot)$ so nobody learns any information.

Suppose the protocol they use goes as follows: $A$ sends $s$ to $B$ in the clear. Clearly, this 'should not' be considered secure, as $B$ wasn't supposed to learn anything but she learned $s$. However, by the simulator-based definition of security, I don't understand why we can't efficiently simulate $B$'s view.

I.e. if we generate a simulated transcript just by picking a random $s$ and sending it to $B$, how can he distinguish between that and a real transcript?
As in the linked question, what you are missing is that the simulated view for a given input pair must be indistinguishable from the simulated view for the same input pair.

So if $A$'s input $s$ is $0$, then the real view of $B$ will be $0$ with probability $1$. On the other hand, if your simulator just chooses a uniform bit, the simulated view of $B$ will be $0$ with probability $1/2$. That's distinguishable, so your simulator doesn't work. (Same if $s=1$ of course.)

A slightly more involved argument shows that any simulator will have the same issue, so there is no suitable simulator, and the protocol is not secure.