Question

The Enigma machine is a symmetric encryption device used by the German army during WWII. In the machine, there is a “connector” that is a permutation of the 26 letters of the alphabet with two constraints:

(a) there are 14 fixed points (letters that are sent to themselves). For example, if the connector sends c to c, then c is a “fixed point.”

(b) there are 6 pairs of letters that are sent to each other. For example, if the connector sends b to z while z is sent to b, so (b, z) is such a pair.

Note this accounts for 14 + 2 ∗ 6 = 26 letters, so every single letter is either a fixed point or part of a pair of exchanged letters of the second type. One important thing to consider when breaking the Enigma is: how many different settings for a connector are there? Answer this question.

Answer 1

This question is based on permutations and combinations. We deal with permutations on a set of 26 symbols out of which 14 are fixed and rest are 2- cycles.

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