The Enigma Encryption Machine (case study) WW2 Encryption is explored with a focus on the Enigma.
The Enigma Encryption Machine (case study)
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- On August 5th, 1857,
- a 4,300 km 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.
- Please stand by for this announcement.
- Germany has invaded Poland.
- And it has bombed many towns.
- General mobilization has been ordered in Britain and France.
- And consequently this country is at war with Germany.
- Throughout the world, which is the real cause of the war
- that today threatens the freedom of mankind.
- (Italian words)
- (Japanese words)
- The Japanese has attacked Pearl Harbor Hawaii by air.
- President Roosevelt has just announced.
- (German words)
- During World War II, 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 machine 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 the 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.
- 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 of the time
- was called a rotor encryption machine.
- We're 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 3 rotors, each with 26 numbers,
- the length of the sequence before repeating is 26x26x26.
- This is equivalent to having
- a list of shifts 17,576 numbers long.
- Understand that each rotor position
- is equivalent to a location in the 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 6 ways.
- Let's visualize the key space at this point.
- First, we choose from 1 of 6 possible rotor orderings.
- Then we select an initial position from the rotor sequence.
- This gives us a key space with over a 100,000 key settings.
- Remember, every machine configuration
- is a point in this space.
- When we select a key setting,
- we're 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 II,
- one of the most important encryption technologies
- used by the German military was known as the Enigma.
- It was an electromechanical rotor machine
- invented by a German engineer at the end of the World War I.
- Each rotor wheel had electrical contacts
- on either side with a maze of wirings within.
- So at each rotor position, there's 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 into the machine to 60.
- This has 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 German confidence that the allies,
- even if they have the 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 machine,
- 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 reused 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,
- and this lead 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 crypts.
- For a given messaging crypt,
- 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 attempts at automating the one time pad failed.
- If the operators had instead rolled dice
- to decide their initial rotor positions,
- the starting points in the sequence
- could have been uniformly distributed.
- This would have prevented
- the reverse engineering of the rotor wirings,
- and if the Enigma allows the letters to
- be encrypted to themselves,
- the Bombe couldn't have taken advantage of crypts,
- and this would require 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 II
- could have been drastically different.
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