Secret Science

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radio4.

Hello, welcome to Infinite Monkey Cage.

On my left, the sort of man who is lent a £100,000 diamond to illustrate Pauli's exclusion principle.

Yep, he's just into particle physics for the bling.

It is indeed Professor Brian Cox.

I have to ask you this, by the way.

I looked on YouTube the other day, and as I went through all of the wonderful different images of you, I found one that was titled, Brian Cox Got It Wrong.

Is it correct that you got something wrong about Pauli's exclusion principle?

It is an interesting question, actually.

It's possible that I got it wrong.

It's also possible that I didn't get it wrong.

And that is the uncertainty principle.

And that answer applies to every single question any of you have about contemporary physics.

So

and on my right, Amanda has never said anything wrong about Paoli's exclusion principle, but also hasn't said anything right about it either, because he never said anything about it at all.

It's Robinins.

So today, in a bid to piggyback on the popularity of Downton Abbey, we look at another flamboyant English estate.

But rather than perpetuating the myth that all old Dowager duchesses are catty, witting, and brimming full of bon mots, our estate is one where mathematical geniuses poured over seemingly impenetrable codes and somehow revealed their meanings.

We are, of course, talking about Bletchley Park and the breaking of the Enigma Code.

We'll be talking about the mathematics of codes and exploring how the challenges of wartime led to the modern computer age, a new age of enlightenment that has opened the world's eyes to, I suppose, pornography and arguments in cat's lock.

So, today's code-breaking guests are.

Did anybody work that out?

I just thought that dolphin was chatty.

Or, for those of you who are not au fai with Morse code, our first guest is the author of Fermat's Last Theorem and the Code Book, and he's also the owner of his very own Enigma machine.

Also, a popular pedant when it comes to scientifically inaccurate pop lyrics.

Most famously, he changed Katie Millure's lyric of We Are 12 billion light years from the edge, and that's a guess, to We Are 13.7 billion years from the edge of the observable universe.

That's a good guess with well-defined error bars.

Please welcome lyric corrector and owner of an Enigma Machine, Simon Singh.

Our next guest is a senior research associate in computer science at University College London.

She spearheaded the Save Blexley Park campaign, and now that it's been saved, she's currently working on a book about Bletley Park, Dr.

Sue Black.

And like other comedy guests we've had on the show, this man started out in the world of science, but before he'd get to the end of his degree, he found standing up and telling jokes was much easier than trying to find a solution to fifth-degree polynomial equations.

Though, he did still find time for his TV series, Dave Gorman's Important Astrological Experiment.

And as Brian knows, astrology, the jury, is still out.

But that's because they're Sagittarians and they don't make a good jury.

It is, of course, Dave Gorman, and this is our panel.

Now, Simon, the Enigma code is obviously probably the best-known code of all time, but when do we first start seeing codes used?

I think as soon as people start writing down important information, people want to start encrypting it and hiding it, whether it's military plans or personal diaries, or I think in cuneiform, there's a glaze recipe for pottery, which is encrypted because whoever came up with that glaze recipe didn't want anybody else to find it.

The Romans used ciphers, everybody's used ciphers.

There's another way you can encrypt information.

We're talking about encryption in terms of scrambling up a message so it looks like gobbledygook.

The other thing you can do is hide the very existence of the message.

That's called steganography.

So, we're looking at things like invisible inks.

Or, my favorite example of steganography was recorded by Herodotus, and he talked about a military general who wanted to send a message.

And so, the way he did it was he shaved the messenger's head, tattooed the message on the scalp, waited for the hair to regrow,

and sent the messenger across the border.

Nothing suspicious, the messenger's allowed through at the other end.

You shave the head and reveal the message.

And so, quite a sweet approach to steganography.

Although I once told this story, and somebody pointed out that it was very low bandwidth, but otherwise,

fairly effective.

Dave, you were obviously very excited by the world of mathematics as a child.

Now, I remember we were of a similar age.

Codes seemed to be everywhere, and all the kind of comic books and things like that.

Did you have any interest or obsession with the nature of codes when you were a child?

I think there was like comic books used to sell not just codes, but all those kind of glasses with mirrors in that would help you look behind corners, and the idea of a spy and being able to lip read and all those sort of things.

You used to think you'd buy them for one pound or something with your postal order.

But I guess, like, secret ink, invisible ink, that kind of stuff.

We used to definitely, we loved all that.

It was just lemon juice and you could hold it up to the window and see it anyway.

But we we sort of it's definitely experimented with all those things.

If you don't want to waste your pound on invisible ink, um what you can do is make your own invisible ink because urine is in fact a very good invisible ink because what what's happening is with with the lemon juice is it dries, it's kind of pretty invisible.

When you heat it, the carbon in the lemon juice carbonizes and goes brown, turns into soot.

But any organic fluid from milk or urine can be used as an invisible ink.

A little tip there for the listeners at home.

That also explains why my bathroom mat's got some Morse code on it.

Sue,

if you say the word code, I think now many people would say Enigma code Bletchley Park, which is a tribute in a sense to

the work that was done at Bletchley Park.

But can you give us a summary of how important Bletchley Park was?

I guess for me it's so important because it brings together the amazing code-breaking achievements, which the work done at Bletchley Park was said to have shortened the war by two years.

And at the time, eleven million people a year were dying, so potentially saving twenty-two million lives.

And at the same time, it was also the birthplace of the computer, so the world's first programmable digital computer.

I have to get that right because there's lots of firsts in computing.

It's the birthplace of Colossus, which is the first computer as well.

So it kind of brings together those kind of the science side and the history side and saving all those lives.

So which place could be more important than that?

Can you give us some sense of the intellectual effort and the intellectual achievement that

to break these codes?

That at least two codes I think were broken there: the Enigma code being the most famous and the Tunney code as well, the Rent Code.

So, how difficult was it?

How many people were working there?

Well, there were actually one of the things I was amazed to find out when I first went there was that more than 10,000 people worked there, because I kind of had this idea that it was about 50 guys, kind of old guys, sitting around in tweed jackets, smoking pipes, doing the Times crosswords, and doing a bit of code breaking.

So when I went there and found out that more than 10,000 people worked there, and more than half of them were women, I was absolutely amazed.

You were saying about, I know I normally ask a question, but you said that you spoke to someone who said the job interview was what they just kind of sat there and they went, Do you play chess?

Yes, I do.

Do you do the Times crosswords?

Yes, I do.

You're in.

It was actually Captain Jerry Roberts, remarkable man.

He's 90 now, I think.

He was 92 yesterday, an incredible guy, code breaker, fantastic guy.

And he said that the job was to

these codes came in overnight.

And in this particular code, which is the Tunney code, was the German command code.

And so they used to come in, and in the morning, they'd get there at six or seven o'clock.

And by lunchtime, usually they'd cracked the positions on the machines.

And he said to me that usually these German command codes would be on Churchill's desk before they were on Hitler's desk.

So they'd crack the code more quickly than the Germans could get it.

And Jerry actually

talks about reading this message where he kind of read through the whole message, and at the end, it was signed by Hitler Führer.

So, like, he was reading a message that had just come straight from Hitler.

It just makes me go, oh my goodness, it's just amazing stuff.

The way you did that, though, suggested Moy went, it was from Hitler.

So, just

I can't believe you're reading out Hitler's letters.

What did he say?

He said he's trying to, he's going to have the parting on the other side.

Before we move on too far into the tiny code and other codes, we should say, Simon, you actually have on the desk in front of you, you have have your own Enigma machine.

So, let's can we just have a little kind of you take us through how the Enigma code, how it was actually used and how it was eventually broken?

Yeah, just one step before that, just to explain what people, the sort of things people were using before the Enigma.

It gives a motivation for the Enigma, really.

The basic code is: I'm going to swap every letter for a different symbol.

So, I'm going to swap A with a diamond, B with a circle, C with a star, and so on.

Now, that code was unbreakable for a thousand years until an Arab philosopher called Al-Kindi in around the 9th century came along and he said

every letter's got a personality.

So in English E, part of its personality is that it's very common.

13% of all letters are E.

So if I've replaced E with a zigzag, well, the zigzag will be the most common symbol in the gobbledygook.

So you can backtrack that the zigzag must be E.

It's called frequency analysis.

And when he came up with that in the 9th century, it destroyed what we call the simple substitution cipher, which is weak because every letter is replaced by the same symbol every time.

Now, this is what the Enigma gets around.

It sits inside a nice wooden box, and you open it up, it looks just like a typewriter.

And it's got a keyboard just like a typewriter.

Now, I'm going to type E.

Where's E?

Here it is.

I'm going to type E,

and above the keyboard is a lamp board.

And what's lit up is the letter Y.

So E is encrypted as Y.

Now, if I hit E again,

W comes up, then F,

and then W again,

and then W again,

and then Q.

We've got three W's, but that's kind of.

The World Wide Web.

It's trying to connect to the internet.

I suppose that's kind of typical of a pseudo-random output.

You keep typing the same thing and a pseudo-random series of letters come out.

So you can't backtrack from a pseudo-random output back to the E.

And the reason why the output keeps changing, even though the input is the same, is that the keyboard is connected to 26 wires.

The 26 wires go into a drum of cabling.

And outside the other end of the drum of cabling are the lamps, so the lamps light up.

But the cabling inside the drums is consistently changing.

Every time I type a key, the electrical connections change.

So if I type the same key again, I get a different output because the electrical connections are changing all the time.

So it's not just scrambling, it's not just electrical, but it's dynamic.

It's that changing of the encryption system after each letter that makes the Enigma so notorious.

So what happens is I type in my message, gobbledygook comes out, I send the gobbledygook across the battlefield to somebody else, they type in the gobbledygook, and if their machine is set up the same way as my machine, they'll get back the original message.

Okay, so there are two things you need to have here.

If I'm going to send you a message, you've got to have an Enigma machine.

That's kind of fairly obvious.

But your Enigma machine has to be set up the same way as my Enigma machine.

And that's where the real security of the machine comes in.

If I open up this lid, I talked about these rotating drums full of scrambled wiring.

Here's one.

It's got 26 settings.

That's got 26 settings.

That's got 26 settings.

That's 26 cubed permutations, which I guess is around 17,000 settings.

And then there are many more things that I can set and change.

I think in total, there's something like 150 million, million, million settings.

So if you're going to crack my code, one, you've got to get the machine, and two, you've got to work out which of the 150 million, million, million settings I've used.

That's why everyone was terrified of the Enigma cipher.

So who's got the other machine that matches up with yours?

Who do you use that to communicate with?

I mean, the Germans built thousands of these.

There was one in every railway station, one on every airbase, one on every U-boat.

The entire communication system of the German military depended on having these machines.

With something like the Enigma Code, is it actually crackable without human fallibility?

Or does it always rely on the fact that one person communicating at some point is going to make an error?

I think there are different ways you can crack it.

One way to crack it is if I'm sending you messages, your machine's got to be set up the same as my machine.

that means I must have sent you a bit of information, a bit of paper or something.

So, if the British could get hold of that bit of paper, they would steal all of the settings for the machine for that whole month.

So, you might steal it by boarding a U-boat, that was typically the way it was done.

And if you did that, you wanted to steal it at the beginning of the month, so you had the rest of the month's settings.

But if you can't steal the information, then there's something else you can do.

The way I look at it is you've got an input, which is the message,

you've got the Enigma setting, and then you've you've got the output.

So that's like an equation.

Input plus Enigma settings gives you output.

It's an equation with three elements.

Now, normally you know the output, you have that in your hand, that's what you've intercepted.

But you still don't know the input or the enigma settings.

So you've got an equation with still two unknowns, that's too hard to solve.

But if you can guess anything that was in the input,

then immediately that becomes a much simpler equation to solve because you've then got only one unknown.

So you have to just guess something that was in the input.

If I know the message came from that direction over there, and I know the Germans have got a weather ship over there, and I've got a weather ship nearby, I know that that message may contain words like fog, rising pressure.

If it was sent at exactly 0, 100 hours, it will have 0, 100 hours in.

And this is called a crib.

If I can get a little bit of a crib on the input, I know the output, I can pin down the settings, and then I can, once I know the settings for that day, I can decipher lots of other stuff, more interesting information that was sent that day.

Yeah, Captain Roberts said to me actually that one of the things they use a lot, that there was a particular operator somewhere in the desert, I think working for Rommel, and he was in some outpost and that nothing was happening at all.

And he kept sending every day nothing to report.

Exactly the same message.

That's how they found one of them.

They found it because they just sent nothing to report.

It was, you know, such a common.

So they always knew that that was, you know, if it was a short message, that's what it was.

Yeah, over and over and over again.

Dave, hearing about the process that this involved, I see you as quite a patient man.

I could never be a code breaker.

The idea of staring, you know, I would be kicking a box after two minutes going, well, I don't know, give it to the professor.

And you are someone who I think does have an element of patience.

Again, you're kind of.

I sort of think, I'd like to think that had I been around at that time, I would have been a code breaker.

Because as a kid, it used to really annoy me.

Anything I don't understand annoys me.

And so I taught myself to do cryptic crosswords when I was sort of 12.

And no one in my family did them.

And so I was keeping the day's paper from before and then going through the answers and working out how that made sense.

And cryptic crosswords actually contain sort of codes.

They have ciphers.

If it says sailor, it might mean ab or tar.

And you sort of learn these things.

And I taught myself that when I was sort of a kid, because it really annoyed me that there was a thing that nobody told me how it worked.

I'd sort of take it apart and put it back together again.

That was always my methodology.

So this kind of this method of thinking, you can actually understand, because I do find it as someone you know non-mathematical, the idea of when we read about people like, you know, when you're talking about capture models, when you're talking about people like you know, Alan Turing, obviously, this being the 100th anniversary of his birth, we should really go back to talking about the idea of actually building a computer built after cracking two codes.

Are you talking about Colossus?

Yes, yes, yes, no.

So, an amazing guy called Tommy Flowers, who was a post office engineer,

realized that he could produce a machine that would help with the code-breaking effort, and so he built that at Dollis Hill.

And I think most people just didn't believe he could do it and didn't give him any money to do it, so he paid for it out of his own pocket.

And I think it was a thousand pounds, which is quite a lot of money then.

Actually, it's quite a lot of money now.

And

yeah, and so he built it with a team of people at Dollis Hill, and then they took it up to Bletchley Park, I think, in January 1944.

And so, towards the end of the war, and that helped amazingly with the code-breaking effort and kind of mechanizing everything, just getting the answers to the messages out more quickly.

And so, that was Colossus, and that was the first programmable digital computer.

And because everything was kept quiet, so he didn't really get very much recognition for what he did, but he did something really incredible.

And so, you know, some people who've worked at Beltrampark have become famous, but others haven't.

So, Tommy Flowers is just starting to become reasonably well known now.

People that did just absolutely amazing things, but in their lifetime, no one really spoke about it.

What's interesting, Sue, and I know you've also spoken to Jerry Roberts about this, that he didn't tell anyone until it was declassified in something like 2000 or 2001.

So to keep quiet for that time is

the thing I find amazing is that 10,000 people worked there.

You know, I mean, there were 10,000 people in on this big secret, and apparently only six people in the world actually knew what was, you know, like the whole story of what was going on there.

And there's amazing stories of,

you know, so the news goes out that it's now been declassified.

You're now allowed to talk about what you did at Bletchley Park if you were there.

And there's stories of, you know, like a husband says to a wife, oh, you know, I've got something to tell you.

I worked at Bletchley Park during the war.

And then the wife says, Did you?

So did I.

So, you know, after 30 years of marriage, they find out that, you know, which hut were you in?

You know, and then they find out that, you know, they were actually working there at the same time because there's so many people of a certain mindset.

Of course, some of them are going to get together, aren't they?

And not necessarily there, but afterwards.

Even the very existence of Bletchley was kept kept secret, or what happened at Bletchley was kept secret to the mid-70s, and the cracking of the Enigma was kept secret to the mid-70s.

And the reason why that happened was that at the end of the war, the Allies swept through Europe and the British troops captured literally hundreds of these machines and brought them back to London, brought them back to Whitehall.

And of course, only the British knew that the Enigma code had been broken.

Only a very few people in the cabinet knew that the Enigma had been broken.

And the people in Whitehall were told to ring up other countries, people in Canada and Australia and New Zealand.

And they'd ring up these other governments and they would say, Look, we've got some of these Enigma machines.

The Germans swear by them.

Why don't you have some?

The British gave away these machines to friendly countries and spied on them through the 50s and the 60s.

These kinds of machines and their descendants were routinely used for decades after the war, and nobody really, except the British, appreciated their vulnerability, so to speak.

We are brilliant.

You've got to admire us.

You've got to have Maris.

Dave, you're someone who is obviously a regular computer user, as again, we know from some of your other work.

I mean, are you now aware of the fact that...

You don't just know it from my other work.

You know it from the fact that I'm alive in 2012.

Yeah.

And I've sat around your house watching the curve regular computer computers.

This is the case.

But I mean, you know, it is something that's been in your work as well.

And do you get an awareness, of course, that we now have in the 21st century codes are being used all the time in our own lives, that we are are constantly you know when you are for instance making transactions etc on the internet many of the different things that are going on there and indeed the very workings of what you're doing we are now constantly around codes and yet we're probably very unaware of that well like the like the password thing is getting i think quite frightening because in the first sort of flourish of the internet you'd have a password which was secure an account which didn't really have anything very damaging on it anyway and now you're banking and everything but not only that every website wants to connect with every other website so if you find one chink in the armour and they break one password, they can get to loads of other information.

I had to contact an organization that I deal with, I'm not going to say which one, to tell them that their ten password questions they were offering me were no use to me because every single one of the answers was in the public domain.

At some point, you will probably have played the porn name game where you take your pet's name and your mother's maiden name, and that's meant to be your porn name, and everyone in offices would be sharing that with one another.

And what they were really doing was often sharing the answers to password questions for your email account.

Now, if they can get your Facebook, they can also get into your Twitter and your thing, and then they will find your bank.

And then, and it all the interconnectedness of it makes it weaker rather than stronger.

It ties back to the Enigma in that, in theory, these systems are very, very good, but the way they're used, the way they're implemented, or the selections that people use for their own passwords, is what undermines the security in the same way that the way the Enigma was being used, as opposed to the Enigma itself, is what allowed people at Blexy to crack the code.

So, how do the codes work on the internet today?

So, what's the general description of

say you use an encrypted website, like your banking, for example?

The massive breakthrough today, as opposed to Enigma or Colossus, or any of the other codes we've talked about, the massive difference is that if I want to send you a message, and if we've never met before, you may be on the other side of the world, in the past, if I'm scrambling up my message, I've got to send you the unscrambling recipe.

Because if you don't have the unscrambling recipe, you can't read my message.

And that transfer of other information is a big problem.

With Enigma, it was a sheet of paper that was distributed around all these battlefields.

How can you avoid that distribution of the key, the distribution of the unscrambling recipe?

And in the mid-70s, people found a way around this.

And it sounds impossible.

How do you send a message to somebody you've not previously communicated with before?

It sounds impossible, but that's what mathematicians like to do.

They like to take on the impossible.

And this is one way to think about how you solve the problem.

I'm going to send you a precious object.

I put it in a box.

I close the box and I padlock it.

And I send it to you.

Now, you can't open the box because I've got the key, and I don't want to send you the key because that's going to be a real pain.

What you do is you put your own padlock on the box.

So it's now doubly padlocked, and you send it back to me.

I now take my padlock off because I've got the key to that padlock.

There's one padlock left on the box, it's your padlock.

I send it back to you, and you can undo your padlock because it's your padlock.

You can open the box and get the precious object.

At no time in transport was the box not locked.

At no time did I send you the key, but at the end of the day, you were able to open the box and get the precious object.

And so, in terms of cryptography, we can think of that in terms of I encrypt the message, send it to you, you doubly encrypt it, send it back to me, I undo my bit of the encryption, send it back to you, you undo your bit of the encryption.

So you somehow have to turn these padlocks into mathematical algorithms.

And that's really what we use today on the internet.

The information revolution wouldn't be possible without public key cryptography.

And we've talked about the Second World War and Bletchley Park and using computers, sophisticated at the time, to crack codes.

So the question must be: in principle, are these codes crackable?

If people want to crack them, let's say the CIA or the MI6 wants to, they've got unlimited computing resources.

Are they crackable now?

No.

I think the crucial word you used was practical, for all practical purposes.

All of the world's secret services using all of the world's computing power and running it for a billion years would not be able to crack that code.

But the extraordinary thing is that these codes, public key cryptography, were actually invented here in Britain in 1973 by a group of people.

One of them was a chap called Cliff Cox.

And in 1973, he worked out all of the mathematical architecture to do this.

And he was only 23 and he was at GCHQ.

And

he'd been in the job a few weeks, and somebody said to him, Well, we'd like to invent this thing called public key cryptography, but nobody really came up with that term yet.

So we'd like to come up with this, but nobody in the world thinks it's even possible.

He went home that night and in three hours created the entire mathematical architecture for public key cryptography.

And he did it all in his head.

Because when you leave GCHQ and go home, you cannot write down anything on paper that relates to your work.

So he had to come up with it all in his head, and then he had to go to bed that night praying that he wouldn't forget about it before.

And then he kept it secret for 25 years.

It was classified for 25 years.

So this notion of people who work in cryptography, it's just part of the business.

It was true in the 40s and the 50s, and for Cheering and his colleagues, and it's probably still true today.

People are doing things at GCHQ and at the National Security Agency in America, and we may not know for generations what they're able to do.

This idea that people

doing these amazing things live their entire lives keeping these secrets, and I say,

and I think that is still happening today because last week I

no, no, I won't.

It's all right.

This is, we asked the audience, what top secret would you most like to know?

And we have about 50 answers here.

Oh, Timmy, here we go.

What Brian is looking for when he gazes into the distance.

Professor Brian, these are mainly the secrets you want to know about your life.

Professor Brian Cox, what is your secret for looking so young?

And the answer is mutation, heredity, and natural selection.

The.

Is Luke really my son?

That's from.

That is from Darth Vader.

This I know.

This is from KTM.

Why are banana skins the easiest surface to write on with Barrow?

Can I just say you're wrong about the banana?

It is the soul of a slipper.

A tangerine skin is dimpled, but the inside of a tangerine skin, not bad.

This has now turned into a...

Hello, it's 1943.

Make do and mend.

Many of us are running out of paper, but don't worry.

It's that Tumba skin.

Maybe a banana skin.

All of them.

So, there was thank you very much for your

questions.

To our question, thank you to our guests, Dr.

Sue Black, Dr.

Simon Singh, and Dave Gorman.

And next week, we are going to investigate the human mind with Joe Brand, amongst others.

So, we actually are going to set up an experiment into the power of the human mind.

As obviously, people here will know the human mind is full of mystery.

And we want to do something about the power of concentration and possibilities.

So, we would like you at home to look around your house.

Have you got an old broken Uri Geller?

If you have,

put it next to the radio now and start rubbing it.

And if it starts working, just email us and we'll tell you the results.

Goodbye.

If you've enjoyed this program, you might like to try other Radio 4 podcasts, including Start the Week, Lively Discussions chaired by Andrew Marr, and a weekly highlight from Radio 4's evening arts program Front Row.

To find out more, visit bbc.co.uk slash radio4.

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