Enigma changes its letter substitutions as an operator types. Its design still creates relationships that codebreakers can test without listing every possible complete setting.
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The large setting count
The video uses the German military Enigma as a starting point. For the stated configuration, it has about 159 quintillion combinations. That count assumes three ordered rotors from five, ten plugboard pairs, and fixed ring settings.
At a million complete checks per second, exhausting that count takes about five million years. This is a hypothetical brute-force calculation. It is not the method that historical codebreakers need to use.
The count alone cannot show whether a system has exploitable structure. The rest of the explanation follows the machine's signal path and the constraints it creates.
A fixed substitution and letter frequencies
A simple substitution replaces each letter with a fixed alternative. If A always becomes Q, every appearance of A contributes another Q to the ciphertext. Ciphertext means the encrypted message.
Patterns in the original language therefore remain in changed form. In typical English text, E appears frequently, often near one letter in eight. The exact frequency depends on the sample.
Counting frequent letters can suggest which substitutions occurred. One frequency alone does not solve every short message, but a long sample provides more evidence. Enigma complicates this attack by changing the substitution during typing.
Rotors change the substitution
A rotor has 26 electrical contacts on each side, connected by internal wires. At a fixed position, it maps each incoming contact to an outgoing contact.
Turning the rotor changes how those wires connect with the rest of the machine. The right rotor steps for each key press. The same typed letter can therefore produce different encrypted letters at different positions.
The video's demonstration gives Q, X, and N for three presses of A under its chosen settings. This is an example, not a universal sequence. Repeating a letter does not guarantee that every output differs from the previous output.
Three rotors and their positions
Three rotors connect in sequence. The right rotor advances most often, while turnover notches cause additional stepping. The middle rotor can step on successive key presses at a turnover.
This double-step behaviour makes the mechanism more complex than a simple car odometer. The odometer picture explains linked motion, but does not specify every stepping detail.
Each rotor has 26 visible starting positions. Three such choices give 26 × 26 × 26, or 17,576 starting combinations. This counts initial positions rather than the length of a simple odometer cycle.
The reflector and reciprocal decoding
After the signal passes through the rotors, the reflector sends it through a different contact on the return path. The signal crosses the rotors again and reaches the lamp board.
At the same rotor state, if A maps to G, G maps to A. This property has the name reciprocity. It allows the same electrical arrangement to encrypt and decrypt.
The receiver must use the matching setup and stepping sequence. Resetting to the sender's initial state makes corresponding key presses encounter corresponding rotor states. Typing the ciphertext then recovers the original letters.
The plugboard
The plugboard exchanges pairs of letters before the rotor path and after the return path. Each cable joins two letters. A connection between A and Q therefore acts in both directions.
The example uses ten cables. They connect twenty distinct letters, while six letters remain unconnected. These pair choices add a very large number of possible configurations.
Counting the combinations
Choosing three rotors in order from five gives 5 × 4 × 3, or 60 choices. Multiplying by the 17,576 starting combinations accounts for rotor order and initial position.
Ten plugboard pairs among 26 letters give 150,738,274,937,250 arrangements. The counting formula removes repeated orderings of the pairs and repeated orderings within each pair.
Multiplying all three factors gives 158,962,555,217,826,360,000 combinations. Rounding gives the opening 159 quintillion. Ring settings remain fixed in this calculation, and different Enigma variants require different assumptions.
Why a letter cannot encrypt as itself
The reflector connects different contacts in pairs. It has no contact that returns directly to itself. The reversible path through the rotors and plugboard preserves this absence of self-encryption.
Thus A cannot encrypt as A at any state of this machine. The rule applies to every letter. It is a structural property, rather than an accidental result for one setup.
The video illustrates the rule with 100,000 simulated presses under varied settings. Other output letters occur, while A never appears as the output of A. The approximate 4,000-per-letter picture illustrates a distribution, not a required exact frequency.
A simulation can check examples, but the reversible-path argument explains why the rule always holds for this design. That is the feature codebreakers exploit.
Cribs: likely words in a message
A crib is a guess about part of the original message. Routine weather reports and repeated phrases give codebreakers possible words or sentence fragments.
The guess is not yet a decryption. It may be wrong, or it may belong at a different position. Codebreakers need tests that reject impossible placements.
The video uses WETTERBERICHT, the German word for weather report, in a constructed example. Its demonstration ciphertext comes from a simulation, rather than an intercepted historical message.
Sliding the crib
Place the guessed word beneath one possible stretch of ciphertext. If any original letter matches the encrypted letter directly above it, that alignment contradicts the no-self-encryption rule.
The screen shows examples with E beneath E and T beneath T. Either match rejects the whole alignment. Codebreakers can then move the crib and repeat the test.
In the video's particular example, nine of eleven alignments fail. Two alignments survive. These counts describe that constructed message, rather than a general success rate for Enigma attacks.
Surviving alignments are not surviving complete machine settings. Each still leaves many rotor and plugboard possibilities. This distinction corrects the compressed wording in the related Short.
Poland's earlier breakthrough
In 1932, Marian Rejewski makes a crucial mathematical breakthrough against Enigma. He uses permutations, which describe rearrangements of a set, to reconstruct the machine's internal relationships.
Polish work also benefits from intelligence that France obtains through a German source. Mathematics, documents, and continued analysis work together. The history therefore cannot begin with a lone British inventor.
In July 1939, Poland shares its knowledge with Britain and France. This provides an essential foundation for later wartime work.
Turing's bombe
At Bletchley Park, Alan Turing develops a machine-based way to test crib relationships. The bombe represents the rotor transformations at different message positions.
Its task is to find contradictions efficiently. It does not need to decrypt the entire message under every complete plugboard arrangement. A contradiction can reject many arrangements at once.
The loop test
The example connects E with X at position 7, X with T at position 6, and T with E at position 15. Those relationships form a closed loop.
Start with a possible plugboard partner for E. Pass that possibility through the transformations associated with the loop. Consistency requires the result to return to the same starting possibility.
If it returns somewhere else, the assumption fails. Additional crib relationships add more constraints. Together they can reject a rotor state even though they do not test every possible plugboard.
The logic follows this sequence.
- Select a candidate rotor order and state.
- Assume a possible plugboard partner for a letter.
- Propagate that assumption through the crib relationships.
- Reject assumptions that produce conflicting connections.
- Retain candidates that need further checks.
Checking surviving settings
The demonstration tests 26 possible partners at each rotor starting position. If none survives the consistency checks, that rotor candidate fails. This can reject all complete plugboard arrangements compatible with that failed candidate at once.
Gordon Welchman's diagonal board strengthens the process by using reciprocal plugboard connections. If A connects to Q, Q must connect to A. The machine shares these constraints across the network.
The video's local simulation leaves two of 17,576 starting positions for one selected rotor order. One is the original position used to create the example. These are demonstration results, not universal historical statistics.
The narration gives about twenty minutes for a historical run across one rotor order. A wartime operating report gives a similar time when the run includes several stops. The time depends on the machine and the checks it requires. It also describes roughly two hundred British bombes. Actual work still requires preparation, candidate checking, and recovery of usable settings.
What this means
Enigma's large combination count does not prevent attacks that exploit relationships within the design. The reflector helps operators use the machine in both directions, but also creates a constraint for codebreakers.
The success also depends on cribs, Polish breakthroughs, improved machines, and extensive human work. The no-self-encryption rule is one important part of that larger process.
FAQ
Does a repeated letter always give a new output?
No. Rotor movement changes the substitution, but outputs can repeat.
Do two surviving crib placements mean two possible keys?
No. A placement and a complete key are different things.
Does 159 quintillion include every possible Enigma variant?
No. It uses the stated rotor, plugboard, and fixed-ring assumptions.
Does the bombe automatically prove a complete decryption?
No. Surviving candidates require further checks.