SPEAKER 1: Cryptography.

What is it, and why is it important?

We're going to answer those two questions in exactly that order.

Let's start with what cryptography is.

It's the art and science of obscuring, and ideally protecting, information.

Now it's an art and a science because there's math involved with it.

It's pretty straightforward to manipulate characters in some way

by adding some constant number to them or to change them

in some systematic manner.

But it's an art, because doing so in a way to defend against potential attacks

is not as easy as it might first appear.

There's a lot of guesswork and calculation

that needs to go into play to find a really strong cipher.

Cryptography gives us the opportunity to have

a basic level of security against an adversary who might

do bad things with the information.

We usually contrast, in cipher information,

with information that is presented in the clear, which

is to say there's no protection surrounding it at all.

And it's generally considered better to protect information using cryptography

than to have information just freely available out there.

Now a cipher, we're going to start by talking about cryptography

sort of through history.

We'll lead up to more modern forms of cryptography,

which are derived from more ancient forms of cryptography.

But a cipher is one of the most fundamental forms of cryptography.

And ciphers are algorithms.

And recall that an algorithm is just a step-by-step set of instructions

that we use to complete a task.

And in case, the task is to obscure or encipher information.

And ciphers can also be used in reverse to unobscure, or decipher,

that same information that was previously encoded or enciphered.

Now there are many different ciphers out there

that have varying levels of security potential.

Some of the more ancient ciphers that we're going to start with

should be [INAUDIBLE] be considered to have no security potential at all

considering how easy they are to crack.

But again, this leads into the more modern approach to cryptography,

which is much more secure than some of these basic ones.

And now let's start by imagining that we have possession of this device.

Now if you're looking at this device and it seems somewhat familiar to you,

it may be because you've recently seen the movie A Christmas Story,

where Ralphie, the character there, obtains

one of these, which is a little orphan Annie's secret society decoder pin.

And this decoder pin has a set of numbers going sequentially one

through 26 around the inner edge, and a set

of letters, which is not presented in any particular order,

around the outer edge.

And what would happen is the radio announcer would provide,

set your pins to some combination.

So line up one number with one letter.

And then it would read off some secret message

that, ostensibly, only individuals who possessed this pin,

or many of the duplicate versions of this pin that were distributed

to children around the country, could then decipher

by taking the numbers that were given over the radio

and transforming them back into letters so that it makes sense.

So if you can, if you zoom in on this image,

it might be a little difficult to see, but you

can see that the 3 corresponds to the letter L, and the 4 corresponds to an M

based on this particular setting of this decoder pin.

So this is one potential, what we would call a substitution cipher,

where we're changing, we're substituting a letter in this case for a number,

and that number will henceforth represent that letter

for the rest of this message.

But what is the problem with this cipher?

Or more generally, when we think about issues in computer science

where we have adversaries who are trying to penetrate some system,

or break a code, or break in, or hack into anything,

hack your password, we sometimes frame this in terms of asking the question,

what is the attack vector?

Where is the vulnerability that is potentially

part of this particular cipher?

And in this case, it's that anybody who has access to this pin

is able to break any cipher that is made with this pin.

And again, this pin was distributed pretty extensively in 1930s and 40s

to children who listened to this very popular radio program.

So these pins were in the hands of many people.

And anybody who had access to the pin would

be able to understand the message.

And so that is, how we might frame this attack vector,

is the key, in this case, the pin, which we will call a key for this purpose,

is just very prevalent.

It's pretty well known how to use this key and manipulate this key.

A lot of people have access to that key.

But that's just one example of a substitution cipher.

We have many different examples of substitution ciphers that we could use.

Let's just take another very simple, straightforward one,

which is imagine we have all of the letters of the alphabet

and we're just going to assign the ordinal position of that letter

as its cipher value.

So with the secret society pin, there was this sort of random element

to it, right?

The letters were being skipped.

There wasn't a rhyme or reason to them, although the numbers were sequential.

Here let's just line up both.

Let's use sequential letters and map them to their sequential numbers.

So A becomes 1, B becomes 2, and so on.

Both of these things are increasing linearly.

Now you may recall that as computer scientists,

we ordinarily start counting from zero rather than counting from one.

I'm counting from one here because this mapping of A to 1 and Z to 26

is much more familiar to us intuitively as humans,

and I want to keep us grounded in this discussion of cryptography right now.

But ordinarily, you might actually instead see this as 0 to 25, 0 being A,

through Z being 25 as opposed to 1 through 26.

But this cipher would work exactly the same

and has roughly the same security potential

as Annie's secret society cipher does.

And we can actually make this a little bit better because we are consistently

increasing the letters, A through Z, and consistently increasing

the numbers, 1 through 26.

We could also, instead of just doing this direct mapping,

we could rotate around.

We could start the 1 somewhere else as opposed to being A.

And now instead of having just one cipher where A maps to 1, B maps to 2,

we have a variety of different ciphers, depending

on where we decide we want to have our starting point.

So for example, we might instead add two to every number.

So instead of going from 1 to 26, we go from 3 to 28.

Now think about it.

If you're trying to break this cipher and you see patterns

like this with all these numbers in them, what might jump out at you?

Well, if you're used to seeing ciphers that are 1 through 26, for example,

something where you don't see any 1s or 2s

and suddenly you're seeing 27s and 28s potentially in the message that might

be long enough to have, in this case, Ys or Zs in it

might seem to you that this is slightly off.

Like this cipher must be shifted in some way.

Instead of being this straightforward line,

there's some modification that's been made to it.

That's kind of a tip off if you're trying to defend

against somebody figuring that out.

And so instead of going 27, 28 at the end,

we might instead wrap around the alphabet.

Once we have exhausted the 26 possible values that we started with,

the 26 letters of the alphabet, we might instead, once we have X is 26,

say, well, instead of Y being 27, Y is 1 and Z is 2.

And this is not a massive improvement on the security of this cipher.

Like I said, it's still quite fragile and quite easy to break.

But it doesn't give quite as much of a clue to a potential adversary

as to how to crack it, how to decipher the message.

And this can be done for any different value

to obtain any number of different ciphers.

Instead of going forward by two positions,

we could add 20 to every letter's value, again,

wrapping around the alphabet when we exhaust,

when we get to 26, instead of having 27, 28, we would just reset at 1

and continue on.

But we can also add 26 to it.

But that doesn't look very different than what we had before.

And that's where this cipher's vulnerability comes into play.

There's only 26 possible ways to rotate the alphabet

while keeping the order of the letters preserved, right?

Unless we start skipping A, D, G, and then,

you know, rearranging the other letters in some other way.

If we want to keep everything straightforward in a line,

again, wrapping around 26 when necessary, there's

only 26 ways to do it.

That is to say that shifting the alphabet forward by 26

is exactly the same as shifting the alphabet forward by 0.

And so that's our limitation.

We have a very small number of, again, this word keys that can

be used to decipher using this cipher.

Now this is an example of something called a rotational cipher,

and it's actually a rather famous rotational cipher

known as the Caesar Cipher.

It's attributed to Julius Caesar and was apparently used

more than two millennia ago for him to encode messages to his troops