Cryptography, Information Theory, and Error-Correction. Aiden A. Bruen
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The initial settings are defined with
For the signal traveling toward the reflector plate, the substitutions through the rotors are represented mathematically as follows:
where raising a term to the exponent
Since the reflector has contacts which are only connected in pairs, we get
Once
After the successful completion of the cipher text substitution, we need to update the rotor settings to take into account the rotation(s) that may have taken place:
Similarly, if
Let us see what happens when we encode the letter “k,” which has numerical value 10.
Reaching the reflector, we get
Therefore, the first cipher text character corresponds to 7, and is thus is “H.”
Now, we must update the rotor settings:
If the settings were such that
As mentioned above, an interesting aspect about the Enigma enciphering scheme is the fact that deciphering a message follows the exact same process.
2.8 Modern Enciphering Systems