I love Faisal Networks.

They're brilliant.

I one of those things in cryptography where you just think, Wow, that's very clever.

That's really elegant and it's not even that complicated.

And yet you just think that's that's great.

The faster network was designed roughly around the seventies when Horst Faisal, who worked for IBM it was a German physicist with the NSA.

He helped develop the data encryption standard Death nowadays was, as we know from previous video replaced by A S eventually, mostly because of its short key links.

But days, the structure of desert something called a fire still cipher or Faisal network on There are a few of these around to fish, for example, is a FISA cipher five society see use in patting schemes like the pattern scheme used for digital signatures on certificates, fire societies.

They're used for key schedules.

They used to in all over cryptography on their very, very cool.

So I was what I wanted to talk about.

Today S O.

A FISA cipher is no, actually a cycle in and of itself, it's essentially a kind of framework for building encryption algorithms.

It's a structure.

And then you put in some encryption rounds on a key and things like this, and then it turns it into a cipher for you.

I'm and it has some really neat properties, so I'm gonna draw it out, and then we'll talk about the interesting properties that it has.

So you start of a block on.

We're gonna split that block in two, and then we're gonna take This is the right hand side of the left hand side were tailored right hand side down.

We're going to put it through some kind off function, which is gonna be some kind of pseudo random function, like a hash or an encryption round or something like this.

We'll take out here, we're gonna excellent with the left, and then we're gonna bring the left down, and we're gonna bring the right down here, and this is your next block.

So when you say left, you mean the left inside of that lot on the right ones didn't have to be exactly half a very good question.

So in this case, yes, but in general no, you have unbalanced vitals.

Life is where the left on the right are different sizes for this demonstration there going to be the same size.

A sneer is I can draw it.

I'm not very good at drawing, so the next round is exactly the same.

We take whatever his new writers, we bring it round.

We go through f we ex saw it with the left and we come down here like this and so on.

And you could repeat this process as many times you like for however many rounds and then at the very end after the last round, you flip the output like this thing is a structure for encryption in the sense that you can put in any f here on dhe, you talk about yourself A siphon.

Every safe obviously needs to be somewhat reasonable.

But what's so incredibly clever about this encryption algorithm is how you decrypt it to decrypt using the same facets of you encrypt by putting your blocking here, it goes through here, go through here.

It goes through here and it goes with many rounds you want and you get some output to decrypt it.

You pick that up and you put it in the top and you run it again on.

Even if this f is a one way hash function that can't be reversed, that's still decrypt it.

What e basic basis.

While of farce of siphons.

So we're gonna do it.

We're gonna start with L R.

And we're gonna work through, and we'll see that it does actually reverse itself.

Right, Which is just amazing.

I mean, maybe you seen a fight inside for maybe?

No, This happens.

I think when The first time I learned about this, I thought that is That is awesome.

So let's do this.

This is the left.

This is the right.

Now for the sake of argument, they're the same size in this one.

The light's gonna come down here, and it's going to go through this function.

So we're gonna put in a key into bit F on dhe with a lot more secure to make these sub key.

So lots of different Keith reach around, so it's going to be key one.

This is going to be key to, but this stuff is around function that combines whatever comes in with the key and mixes it up and sends out here.

This are comes through this f on his ex sword with this l on this comes down to here.

So this element is L X or F with our on K one.

So I mean, that's gonna look like gibberish.

If I'd like to send this side is fairly straightforward.

The I just comes straight down and turns into are like that.

So let's do the next round.

This is going to come down here and go through here.

It's gonna be ex sword with this are so this out.

But here is our X or f off this, which is l.

I'm gonna run out space.

L excell f of r k one off que tu like that.

Is that right?

I think it's what?

Maybe it's a good thing that we didn't do three rounds or four rounds of this because this could take me quite a while by hand.

This one is going to get copied down.

So this is going to be l excell f off are on a K one now.

Both of these will look like gibberish.

We're gonna switch around here.

I won't draw them in quite yet.

Right.

But this one comes down here and this one comes down here.

Feel free to animated.

So now we're gonna see how we can decrypt this back to El Ahmar.

But all we have to do is take this, put it in the top, and we have to swap our sub keys around.

Because, of course, the rounds are happening in a different order.

So I'm gonna draw this exact same structure again on the next piece of paper so that we have something new to work on it.

I'm gonna get very confused.

So this could be a competition.

How fast can you draw Faisal Cipher from memory s o go that I mean, they're not nearly wide enough for me to fit my stuff.

Let's go again.

That's what you said.

The keys need to be in a different order.

So this is going to be K two coming in here.

And this is going to be K one coming in here reversing these keys.

You know, I wouldn't be not too much important.

That will be a list of data or something like that.

Very straightforward.

All right, so let's put let's copy our data.

Our cipher text in, We're gonna do t that.

Plug them in like this, so I'm gonna draw them in.

Um so bear with me.

This one is gonna be over here are ex or f off L a X or F R K one k two and we'll just pretend that green eyes a little bit further along right on this one is just l excell f off r k one and then we're going to see what happens.

Can you remember what itwas that's really interesting about X or if you do it again a second time, It's the reversible thing, right?

It's irreversible thing.

That's the key to this whole thing when you x or something with the same thing again, does it?

So what happens here?

It's l f r K one is gonna come through here and turn into F off L f of r K one K two, which is this bit so that's gonna come in exile with this and we're just going to get our out again here.

This gets copied down here, so l x or F r k want.

So let's go again.

Our comes in here.

It becomes f of r k.

One.

Excel with this.

This becomes L R.

Gets passed down here.

L goes to hear our goes to here on this will work for any number of rounds and for any round function, which is super cool.

And it's going to be a combination of all of these.

So this one time, this one process, one times it's one plus this one time this one plus it sometimes this one.

Then we repeat this process for each of the values.

So we're taking bits and bytes from all of these in this column, jumbling them up, moving them around.

Chippenham on.

There was a reverse inverse matrix.