It was to be supplied by a German inventor, Arthur Scherbius, who in 1918 set up a small engineering business to produce and market inventions. One of the ideas he took up was for a machine that would encipher—but also decipher—automatically. Cipher machines were not a new idea; simple versions had long existed. One, indeed, had been invented by Thomas Jefferson, polymath and third president of the United States. It consisted of thirty-six discs, separately rotatable about an axle, on the rims of each one of which were engraved the letters of the alphabet in random sequence. The sender enciphered by turning the discs to produce a plain text (which could not, of course, be of more than thirty-six letters, though it might be of fewer). He then sent another row of letters to the intended recipient. The recipient turned his discs to replicate the message, which was a garble, and then examined all the other rows of letters. One was the plain text. Security was provided by arranging the discs in a different sequence on the axle, the change of order being preordained and known only to sender and recipient. Had the order of discs not been variable, messages would have succumbed quite quickly to frequency analysis; as it was variable, giving thirty-six possible orders, a number having forty-eight digits (36 3 35 3 34 3 33 . . .), messages were effectively irretrievable in the pre-computer age.10 In the period 1910–20, several attempts were made to mechanise the rotating disc principle though none achieved commercial success. Nor, at first, did the Scherbius disc machine, when offered for sale under the trade name Enigma in 1923. In the later twenties, however, Scherbius managed to interest the German armed forces in Enigma. Models were bought and adapted and in 1928 the German army began to use it for all secret communication susceptible to interception, which effectively meant radio messages. It was also taken into service by the German navy.
What particularly attracted the German forces to Enigma was a feature unique to the Scherbius system, the “reflector” disc, which equipped the machine to work both to encrypt and decrypt; a message encrypted on one Enigma machine would, when entered in encrypted form on another Enigma machine set up in the same way, yield the plain text automatically. That feature eliminated the need to decrypt by separate process, a tedious and time-consuming business. In that sense, the Enigma was an early example of the “on line” machine (though it was emphatically not a computer, but an electromechanical switching system).
Enigma had other characteristics making it attractive to military signal services: compactness and portability. Outwardly it resembled a portable typewriter of the period, with a typewriter keyboard, in the military version originally arranged alphabetically rather than in the QWERTY order, and a strong carrying case; there were no numerals, all numbers having to be spelled out. It was normally powered by dry-cell batteries.
The chief virtue of Enigma, however, lay in its ability to multiply possible encryptions by an order of magnitude so large as to defy decryption by an outsider in any practical dimension of time; estimates of how long it would take mathematicians to break an Enigma encryption by brute calculation vary, but the Germans themselves believed that the lifetimes of thousands, perhaps millions of mathematicians, working without sleep, would not suffice to decrypt a single message. Enigma was supposed to have complicated the making of the “key,” which is the heart of the cipher system of secret writing, to a degree lying beyond the power of human intelligence to produce a solution.
The purpose of the key is to disguise letter frequency and to multiply, to as near infinity as possible, the number of mathematical attempts necessary to establish a frequency table. The Vigenère square was one method of lengthening a key; there are many others, including the use of a common text, such as a word possessed by both users. The principle, however, remains constant: to make the key so long, consistent with convenient decipherment, as to defy mathematical process. Total mystification, unless by the one-time pad, is never to be achieved; the key has a logic and is therefore retrievable by reason; the object is so to overload the powers of reason as to defeat it in real time, indeed in any sort of human time at all.
Enigma appeared to do exactly that. Its electromechanical switching process was entirely logical; but unless the steps by which it worked were understood, and unless the basis on which the switching was started was known, then indeed the mathematics of its decryption became insurmountable.
The steps and the starting were separate from each other: the first was intrinsic to the machine, though variable within definable limits, the second was illimitable, in theory at least, being chosen by human decision.
The intrinsic characteristics of Enigma could produce five variables, most dependent on its discs: (1) the internal wiring of the discs, (2) the choice of discs, (3) the arrangement in order, from right to left, of the chosen discs, (4) the alteration of the disc rims, (5) the “plugging” (steckerung) of the discs from one to another.
Each Enigma disc, which was removable, had two faces, with fifty-two contact points for the letters of the alphabet; the right-hand face had twenty-six transmitter points, the left-hand face twenty-six receptor points; the interior of the disc wired the transmitter and receptor points together in a secret way.
When the key on the typewriter keyboard was depressed it sent an electric pulse through the right-hand (fixed) disc to the right-hand face of the first rotor. By internal wiring, that rotor transformed the impulse from, say, A to B on the disc’s left-hand face (in fact, the course of the wiring; something much more complex was expected by Germany’s enemies). The right-hand face of the second disc picked up the pulse and transmitted it by internal wiring to its left-hand face; the third rotor then worked similarly. When the pulse left the third rotor it was picked up by the fourth (fixed) reflector disc and sent back again along the same route as it had been received. With this difference: because each rotor was notched to turn over when it had received twenty-six pulses, the returning signal would find the right-hand rotor in a different position, by one letter, on its first journey, the second letter in a different position (by one letter) on its twenty-sixth journey and the third letter again in a different position, by one letter, on its six hundred and sixty-sixth (26 3 26) journey.
The eventual destination of the pulse was an electric bulb, each representing a different letter of the alphabet; as each lit up, in sequence, on the receiving machine, the bulbs would reveal the plain-text message. Before the pulse reached a bulb, however, it went through another multiplying process; at the end of the return journey, it moved to a “plug” board, resembling that of a manual telephone exchange, on which six letters were plugged to another six (the number of plugs was later increased): A to E, for example, and G to T and so on; the pluggings were altered according to instructions for monthly, weekly, daily and eventually twice-daily use.
Thus the intrinsic complexity of Enigma. It was enlarged by human alterations. In the original version there were only three rotors.11 Part of the procedure laid down for Enigma’s use, in frequently changed instructions, was to alter the order in which the rotors were arranged in their slots. Finally, each of the rotors had on its outer rim a rotatable ring, often described as the “tyre on the wheel,” which would be moved to any one of twenty-six alphabetical positions. When setting up the machine for use, the operator moved the rim to a position laid down in instructions. The number of variables with which a cryptanalyst was confronted was therefore as follows:
Disc positions (three discs): 26 3 26 3 26 = 17,576
Disc sequence (ABC, ACB, BCA, BAC, CAB, CBA) = 6
Plugboard connections = over 100 billion
Total = 10,000 billion.12
That number does not allow for rotating the outer rims on the three discs, which multiplies it by 17,576.
The task faced by an interceptor of an Enigma-encrypted text may be represented in this way. If he were able to check “one setting every minute [he] would need longer than the age of the universe to check every setting.”13 Even if he had got possession of an Enigma machine, and so had only to proceed through the initial settings of the discs (17,576) to see if the encrypt rendered a plain text, he would still, working day and night, need two weeks to check all the settings, allowing one minute for each.14 No wonder Scherbius advertised his machine as generating “unbreakable” ciphers and that the Germans believed theirs to be so.