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I have a question regarding the exchange of the rotors in a enigma machine.

I know that there are 3 slots and that up to 8 rotors can be used in those slots. What I don't understand is, as all the rotors have 26 letters each (they are equal), what is the difference in exchanging the rotors in the slots?

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They may look equal but in fact each rotor defines a different letter substitution. A letter substitution is a function that converts each of the 26 letters into another letter. For example $a\rightarrow z$, $b\rightarrow x$, $c\rightarrow y$ and so on. There are many ways this can done. Therefore, exchanging the rotors changes how each letter is substituted in the cipher.

Furthermore, each letter to be encrypted actually goes through all three rotors one after the other, being substituted each time. Also the rotors rotate so that this substitution function changes every letter. This rotation shifts the letter substitution so if in the initial position $a\rightarrow s$ then one rotation along would substitute $b\rightarrow t$ since $b$ and $t$ are the next letters from $a$ and $s$ respectively.

There is other stuff such as reflectors and custom wiring but that is the basics.

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  • $\begingroup$ I know that 3 rotors A, B and C perform a 26x26x26 shift. But I am still unable to see the point of exchanging them A B C A C B B A C and so on... $\endgroup$ – Marcus Jan 31 '18 at 14:45
  • $\begingroup$ They are not always just a shift, they can perform any substitution. Eg. for the alphabet a, b and c let F map a->b, b->c, c->a and G map a->c, c->a, b->b. Then F . G is a->a, b->c, c->b whereas G . F is a->b, b->a, c->c. So order does matter. $\endgroup$ – Jackoson Jan 31 '18 at 21:54

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