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How exactly has the wiring for the different rotors been generated? Were those generated totally at random (except that no letter can be mapped to itself), or is there some kind of algorithm to generate a “strong” wiring? Or, in other words, is any “random” wiring as secure as any other “random” wiring, or does the wiring need to have certain properties?
Specifically, is there any reason why they used a small number of rotors, each of which had a “fixed” wiring, instead of generating a unique/fresh wiring for each message (or at least for each day), e.g. by using Fisher–Yates shuffle algorithm with a PRNRG that is seeded with a value derived from a secret password and a message-specific nonce?
I don’t know how the Germans picked the wiring. For the commercial Enigma the manufacturer advertised that they offered different wiring for different companies, making it harder to decrypt another company’s message. Clearly this would not work for the German Army. All the machines had to be the same. The various cryptonets use different published keys, but the same machine.
The rotors, for the reasons above, had to be the same in all machines. The wiring in the rotors was in a core encased in Bakelite and could not be changed in the field. The core had spring pins on one side and flat metal contacts on the other to allow the current to flow from one core to the next. The elements that the operator could change were the rotor order and the plugboard setting.
The Enigma, for the Army, was often in the back of a truck, carried by hand, etc. It had to be set up quickly and easily. The Germans believed Enigma could not be broken, primarily because of the large number of ways to set up the machine. In December 1932 the Polish mathematician Marian Rejewski broke Enigma using permutation methods and recovered the wiring of the cores without ever having seen a military Enigma. The Polish Cypher Bureau regularly read German messages until Germany invaded Poland on September 1, 1939.