WW2 Enigma Machine

- [Voiceover] On August 5th, 1857,

a 4,300 kilometer-long cable was laid

across the Atlantic Ocean.

It provided a link between
Britain and the Americas,

further strengthening their
social and economic alliances.

Now information could be represented as

a pattern of electrical
pulses and sent across

the world almost instantaneously.

Stock tickers and money transfers -

these were commercial applications
invented by Western Union

which ushered in a new era
of global communication.

- [Radio] Stand by for this announcement.

Germany has invaded Poland
and has bombed many times.

General mobilization has been ordered

in Britain and in France.

- [Voiceover] And
consequently, this country

is at war with Germany.

- [Voiceover] ...which is
the real cause of the war

that today threatens
the freedom of mankind.

(shouting in Italian)

(speaking in Japanese)

- [Voiceover] The Japanese have attacked

Pearl Harbor, Hawaii by air,

President Roosevelt has just announced.

(shouting in German)

- [Voiceover] During
World War Two, Germany,

Italy, and Japan were far
outnumbered by the allies.

Their only conceivable path to victory

was the ability to launch
widespread surprise attacks.

So the goal of encryption
technology was to

automate the one-time pad
using an encryption machine.

Ideally, this machine would
accept an input letter,

apply a random shift, and
output the encrypted letter.

However, all machines
follow the same principle.

They begin in some initial
configuration known as a state,

they accept some input,
they do an operation

with the input, and then
they produce an output.

The operation from initial
state to final state

is always predictable and repeatable.

So the goal was to
produce identical machines

that output a scrambled
sequence of shifts,

which took a long time to repeat.

(mechanical ticking)

Therefore, Alice and Bob could generate

an identical shift sequence as follows:

First they need to
share identical machines

and agree on an initial position,

which is defined as the key setting.

Then they align their
machines to the same position,

and finally cycle through
the identical operations

to achieve identical sequences.

Now the state-of-the-art
technology at the time

was called a rotor encryption machine.

We are all familiar with
the mechanical process

of an odometer, which takes a long time

to finally repeat its cycle.

Now imagine we scramble the numbers

on the wheels of the odometer.

When it ticks forward, a
new shift could be generated

by adding up each number on the rotors.

This is the rough idea behind
rotor encryption machines.

For example, the message,
"Attack Northwest"

would be encrypted as follows.

Notice how a new shift is used

at each position in the message.

With three rotors, each with 26 numbers,

the length of the
sequence before repeating

is 26 times 26 times 26.

This is equivalent to
having a list of shifts

17,576 numbers long.

Understand that each rotor position

is equivalent to a
location in this sequence.

The initial machine state
is known as the key setting,

and the collection of
all possible key settings

defines the key space.

This key space increases
if the number of ways

to initially configure
the machine increases.

For example, if the
rotors can be rearranged

then the order can be
selected in six ways.

Let's visualize the key
space at this point.

First we choose from one of
six possible rotor orderings,

then we select an initial
position from the rotor sequence.

This give us a key space with
over 100,000 key settings.

Remember, every machine configuration

is a point in this space.

When we select a key
setting, we are selecting

a starting point in this space,

which then determines the
rest of the shift sequence.

Give away the key setting

and you give away the entire sequence.

The security of rotor machines depends on

both the size of this key space

and the randomness of the key setting.

During World War Two,
one of the most important

encryption technologies used by the

German military was known as the Enigma.

It was an eletro-mechanical rotor machine

invented by a German engineer at

the end of World War One.

Each rotor wheel had electrical
contacts on either side

with a maze of wirings within.

So at each rotor position,

there was an electrical
path from every input letter

to every output letter.

When the rotor advanced,
an entirely new path

was defined for each letter.

During the war, they continually tried to

increase the key space of the Enigma

in order to make it stronger.

For example, some changes
they made were to add

a fourth rotor wheel and
increase the number of

possible rotors you could
put in the machine to 60.

This had the effect of massively
increasing the key space.

Near the end of the war,

the Enigma could be set up in over

150 million, million, million ways.

Guessing the key setting which
was used for a given message

was about as likely as
guessing the outcome

of 26 dice rolls.

This gave the Germans
confidence that the Allies,

even if they had a copy of the Enigma,

could never check all
possible key settings.

For two parties to
communicate using the Enigma,

it required that they first
shared the daily key settings.

This allowed them to align their machines

to the same position.

This protocol changed over
and over during the war,

but generally involved
distributing key sheets

in advance to all operators.

Each day, the operator would
cut off the daily settings

and this would tell them
the daily configuration

of their machines, such
as what rotors to use

and the order of the rotors.

This key setting was then
to be destroyed after use.

However, one vital step
was left to the operator.

They were to select a
random initial position

of each rotor before communication began.

And a very simple mistake was made

by some fatigued operators.

We make this exact same mistake every time

we set a bike lock combination,

because we tend to rotate the cylinders

only a few clicks from the initial state,

or we reuse a common password.

This destroyed the uniform distribution

of the initial rotor position,

and after repeated observations,

it allowed the Allies to reverse engineer

the rotor wirings completely.

The second major error was a design error,

not a procedural one.

The Enigma was designed
so that an input letter

would never encrypt to itself.

So given an encrypted letter, such as L,

You can now eliminate
the possibility that L

was the original letter.

What they thought was a strength

was actually a weakness in design.

(water dripping)

And this led to a code breaking machine,

initially designed by the Poles

and later improved by the
British-American effort.

The Bombe was multiple Enigma
rotors chained together,

allowing it to rapidly test
different key settings.

It took advantage of the
fact that common words

were known to be in the original message,

such as weather.

And these came to be known as cribs.

For a given message in crib,

the Bombe could scan through all possible

rotor positions and
orders in order to find

possible key settings
in a matter of minutes.

This machine allowed the Allies to read

German commands within
hours of them being issued.

It was a fatal blow to
their combat strategy,

as the Allies could
anticipate their next move.

One fact remains:

This initial attempt at automating

the one-time pad failed.

If the operators had instead rolled dice

to decide their initial rotor positions,

the starting point in the sequence

could have been uniformly distributed.

This would have prevented
the reverse engineering

of the rotor wirings.

And if the Enigma allowed
letters to be encrypted

to themselves, the bombe could not

have taken advantage of cribs.

And this would've required the Allies to

check the entire key space,

which was impossible even
with the fastest computer.

Repetition reduced the key space.

Otherwise, the outcome of World War Two

could've been drastically different.