Okay, folks. So now, what we're going to do in this video is crazy fun. Some of you watching this are going to get turned on by this and like theoretical computer science and some of you are going to say, "Forget it, it's for the birds." But, I want to expose all of you to this a little bit, because again, from a cyber security perspective, you should see some different angles. Now you recall, we talked a minute ago in one of our previous videos about the idea of an overt and covert channel being different, right? That overt is something you intend, covert is the shared thing where I can signal someone. Now, I'm going to posit some systems that are create- that are kind of theoretical. It's due to some work by a guy named Daryl McCullough, in the 1990s, very interesting researcher, who's trying to come up with alternate ways to think about disclosure of integrity properties in computer system for cyber security. Here's what he came up with. Now, I'm going to pop up a chart here, you'll see something we're calling system Y. And on the left, we've got a user, User A. And on the right, we've got a user, User B. And the way, this dopey little system works, is that A sends a bunch of messages to this system, system Y. And then, at the end of sending a bunch of these messages, the parity or odd or even this, in the number of messages that were sent is sent to the user B, got it? So, I go, boom, boom, boom, boom, boom, boom, boom. And then, we add up how many of those there were. If it was odd, I send odd. If it's even, I send even. And I think you would agree, A can certainly signal B, [inaudible] I want to do an even number stuff, I do that, I send you even. If I want to do an odd number stuff, I do odd, I send you odd. And you're getting odder even, we can come up with an X bit per second covert channel or microsecond or millisecond or whatever it is, do you follow? But, now if we look at our chart up here, that's going to show you the system itself, introducing randomly generated messages, I have it shown as a zero popping out from the system. So, we're going to make the zeros and ones be the inputs that are coming in, and then some random thing the system does. And then the parity, that B, user B sees is going to add up everything, not just what user A does, but what randomly the system does as well, it's noise. So, I want to send even but the system generates a noise. Let's say, it's odd, user B is going to see odd. Let's say, I want to send odd and the system generates odd as well, odd plus odd is even. User B is going to see if I close the channel, do you see what I mean? Another example, I send one message, I send one. The system sends one output randomly, a zero. One and one, that's two, things that were sent, it's even. I'm not adding the ones and zeros, I'm adding the number of messages that are being sent, do you follow? I would claim that this system Y prime, we changed Y to Y prime when we added the noise is called Deducibility Secure. That's the definition that was introduced, meaning, A can't signal B, in this example and that's a property that we look for. It's something called Information Flow Theory. So, instead of [inaudible] who can read, who can write, we say, "Is it possible for A to somehow signal B? Can I have information flowing from A to B? Don't worry about whether you've got TCP packets going this way or that, forget all that. I'm really interested in information and I think it's a better model. So, we can see this system Y is clearly deducibility secure. Let's look at another example. In this one, I've drawn a little funny. I put the user down in the bottom and say, the user A can't even signal the system Z or Z'ed, I will say system Z'ed. User A can't do it. There's no way of signaling the system. But then, randomly from somewhere, inputs and outputs are hitting the system randomly, no input from A. And then, B just sees the parity of the random stuff that's hitting its system. Clearly, when I show you in the next diagram here, you can see that system Z clearly deducibility secure right? But it's sort of obvious, given the fact that A can't signal B. Do you follow? These are two examples of systems that respect the property that's focused on closing covert channels. And we did it in both cases by introducing sort of, crazy noise property. Daryl McCullough did it and you get to see in the subsequent video, we're going to put these things together to see what happens. You're probably wondering, "Why is Ed showing me these weird systems?" But once we hook them up, you're going to see an interesting property will come up. Now, just to make sure we're all together, let's do a little quiz here, as we do on many of our video. And the answer is obviously C, C is the definition of an overt channel. So, I think you probably have a pretty good understanding at this point of these things. Now, in a subsequent video, the next one, we're going to hook these things up and I'm really going to knock your socks off with that. So, we'll see you in the next video.
