Generating only 720 permutations to illustrate the enormity of Enigma coding.

Enigma Permutations, Encryption Decryption Keys, Code, Software

By Ion Saliu, Enigmatically At-Large

The Enigma machine was betrayed by humans and the dreadful Heil!

If we take 10 digits and 26 letters, Permutations of 36 elements is a monstrous number: 3 followed by 41 digits! You can try to generate such permutations either starting with the keyboard configuration; or indexing the elements starting at digit 0, to digit 9, then to A and all the way to Z. Looking at my keyboard, I can see 10 digits from 0 to 9 and 26 letters from A to Z: 36 elements in total. Permutations (36) = 3.71993326789901E+41.

We can ignore the digits, as the numbers can be expressed as words. In that case, Permutations (26) = 4.03291461126606E+26. If only 40%, even just 1%, of the permutations are totally different from permutation #1 (based on the keyboard layout), 40% of the number above is still an impossible for humans to deal with! The Germans made sure that A was not A, B was not B, C was not C… etc. … in any code. Just one letter as in the original setting could help with decoding.

Thus, one important condition is: NO letter encrypts to itself. The first alphabetical permutation is, for example: