Seizing the Enigma (8 page)

Suppose a plaintext consists solely of the letter
a
. The first 26
a
’s will all have different ciphertext replacements as the rotor revolves. But the 27th will have the same ciphertext as the first because the rotor will have returned to its first position. So short a period—26 letters—is a cryptographic weakness. However, the period can be lengthened, and the cipher simultaneously made more complex, by placing a second rotor, with wiring different from the first, next to the first and having it turn one space each time the first wheel completes a revolution. The continually varying positions of the two rotors will create different internal combined wiring until the first wheel has revolved 26 times, when the second rotor returns to its original position. The first wheel’s 26 revolutions of 26 letters each means that 26 × 26, or 676 letters, will be enciphered through a different wiring maze. Only at the 677th will the internal maze be the same as for the first letter. (The alphabet, of course, has only 26 letters, and many of these will repeat in the ciphertext. But if the plaintext consisted only of
a
’s, the sequence of ciphertext letters would start to repeat only at the 677th
a
.)

Using the same principle, more rotors can be added, each one lengthening the period by a factor of 26. Four rotors produce a period of 456,976 letters; five rotors, a period of 11,881,376.

To decipher a message in such a machine, the cipher clerk obviously needs to know the starting positions of the rotors. This crucial information, called the key, must be agreed upon by sender and receiver in advance of any communication between them. Often a key takes the form of a list of starting positions for each day in a month; the sheets of paper bearing this list are distributed by couriers to all the radio or telegraph stations that will encipher or decipher their communications with the same machine. A key can encompass other elements as well. If, for example, the rotors are removable, so that they can be inserted into the machine in varying orders, the key
will specify the order of the rotors from left to right. Without the key the decipherer would not be able to read the message except by playing codebreaker.

The mechanism that Scherbius offered the navy in the spring of 1918 was a sample multirotor machine. His memorandum explained the rotor principle and then his chief point: the impracticability of the enemy’s solving a message even if he had the machine:

The key variation is so great that, without knowledge of the key, even with an available plaintext and ciphertext and with the possession of a machine, the key cannot be found, since it is impossible to run through 6 billion (seven rotors) or 100 trillion (thirteen rotors) keys [rotor starting positions]. If the examination of each telegram takes half a minute in a 24-hour workday, this would require 5.8 years with a simultaneous employment of 100 machines of seven rotors and 14.5 years for 1,000 machines of eight rotors.

He noted, correctly, that “it would only make sense to search for a key in this way when it is known that unknown cryptograms have the same key. And when the same key is maintained for a long time.”

The naval staff examined Scherbius’s machine and found that it afforded “good security, even if compromised.” But it decided not to buy it “because with the present kind of naval cipher traffic, the use of machines is not worthwhile.” Instead it recommended that the Foreign Office examine the machine to see if it were suitable for diplomatic correspondence. The price of a ten-rotor machine, measuring 12 by 5½ by 4¾ inches, with an attached typewriter to print the output, was 4,000 to 5,000 marks, or $1,600 to $2,000 (about $14,400 to $18,000 in 1991 dollars), and delivery time was eight weeks. This price, Scherbius said, could be reduced to 1,400 to 1,800 marks, or $560 to $720 ($5,000 to $6,500 in 1991 dollars), if a thousand machines were bought.

But the Foreign Office was not interested either. This may have discouraged Scherbius, but it did not defeat him. The cryptography bug had bitten him.

Scherbius was born on October 20, 1878, in Frankfurt-am-Main, the son of a small businessman. He graduated from that city’s
Ober-realschule
, a type of secondary school that emphasized mathematics, natural sciences, and modern languages; most of its graduates went into engineering. After studying electricity for the 1901–02 winter semester at the Technical College in Munich, Scherbius matriculated May 13, 1902, at the Technical College in Hanover. He studied one or two courses at a time for several months, among them Electrical Installations and Factory Installations, and completed his studies in March 1903. The following year he finished his dissertation, “Proposal for the Construction of an Indirect Water Turbine Governor,” which was accepted. At the age of twenty-five, he was granted a doctorate in engineering.

Scherbius worked for several of Germany’s major electrical firms and for a large Swiss electrical firm. He made his first invention, a high-voltage drive motor designed to handle sudden changes of stress, for the Swiss company. In 1918, he and E. Richard Ritter, the certified engineer mentioned in his first letter to the navy, founded the firm of Scherbius & Ritter. As a partner in it, he continued to invent (electric pillows, ceramic heating parts, and asynchronous motors, among others), research (problems of high-tension direct current and temperature control), and publish. He wrote articles on such subjects as a shunt phase compensator and a ninety-one-page pamphlet on magnetic induction in closed coils. His name became enshrined in the field with the Scherbius principle for asynchronous motors.

It was probably World War I that made Scherbius succumb to the bacillus of cryptography. Yet that science was underdeveloped in German-speaking lands. The most recent comprehensive text in German dated from 1881, more than forty years before, and the author had had to publish it himself. The German and Austrian literature after that time consisted of a handful of scholarly historical articles and books, a few survey articles in scattered magazines, pamphlets telling how to shield love letters and telephone conversations
from pryers, a booklet overview of elementary ciphers intended for businessmen, and studies of cable secrecy and codes. A few dozen cipher devices had been patented in Germany, Austria, and Switzerland, but they had merely mechanized systems that were hundreds of years old.

Perhaps the greatest activity, and that not very intense, was manifest in the publication in German of commercial codes. These thick books, sometimes produced privately for a firm, sometimes published for general sale, replaced business and personal phrases with codewords. “Do not exceed limit,” for example, might become JIWUL. Their chief purpose was to economize on cable tolls. But they did provide some secrecy, they were constructed in the same way as many secret governmental codes, and they had the word “code” in their titles, all of which brought them into the purview of cryptology. The codewords, sometimes taken from real languages, sometimes made up, were always “pronounceable,” because international telegraph regulations set lower rates for pronounceable codewords than for unpronounceable ones or for codenumbers.

Scherbius’s first cryptographic device sought to maintain this economy while making these mostly nonsecret messages secret. It enciphered codenumbers into pronounceable codewords by replacing the successive digits alternately with vowels and consonants. One of the first cipher mechanisms to employ electricity, it passed the input impulses through “multiple switch boards which connect each arriving lead with one of the outgoing leads and which are adapted to interchange this connection with great facility of variation.”

These switchboards formed the germ of the rotor. That concept may have come to Scherbius while he was at a concert, as his best ideas often did. He was said to be very musical, but his mind apparently wandered frequently from the melody, for he often jotted ideas and made calculations on his cuffs while the orchestra played. His first rotor enciphered numbers, presumably codenumbers, gaining security but losing pronounceability.

A rotor for letters followed, and it was this device that Scherbius submitted to the navy and the Foreign Office in the spring of 1918. That both rejected his machine did not diminish his confidence in it. He turned to the commercial market.

Scherbius & Ritter transferred the cipher patent rights to the Gewerkschaft Securitas. Though a
Gewerkschaft
was, in the German law of the time, a corporation for mining (and this one was indeed headed by a mining director), this one’s name, Securitas, and the fact that it had also been granted the rights to the Dutch rotor patent suggests that it may have been established to funnel risk capital into cipher machines. On July 9, 1923, Securitas founded the Chiffriermaschinen Aktien-Gesellschaft (Cipher Machines Stock Corporation), which began operating in August 1923 at Steglitzerstrasse 2, in central Berlin. Scherbius and Ritter sat on its board of directors.

The firm publicized its cipher machine—by now named the Enigma—as much as it could. It printed flyers and exhibited the Enigma at the 1923 congress of the International Postal Union. A number of articles about the machine appeared in German and foreign electrical and business publications. Many were illustrated with diagrams of rotors and photographs of the firm’s ponderous printing version of the Enigma—a 15-inch-high monster with knobs and handles on its right side that weighed more than 100 pounds. This was being tested by the
Deutsche Reichspost
. Another version worked directly from and to punched teletypewriter tape.

Gradually the simpler version that indicated its output by illuminating letters, the “Glow Lamp” Enigma, became the most widely known and, eventually, the only one produced by the firm. It was much more compact than the printing version, standing only 4½ inches high, 10 inches wide, and 10¾ inches deep, and it weighed only 15 pounds. At the front stood three rows of typewriter keys. Behind them lay the three rows of circular windows for the output letters. In back of these and to the right was a switch allowing the operator to choose battery or house current. On the left, the tops of
four rotors and four toothed thumbwheels for setting them poked up through the closed lid of the machine. The lid also had little windows through which showed the letters on the rims of the rotors.

The mechanism incorporated three significant improvements by other people over the straightforward system described by Scherbius in his letter of 1918. Two came from Willi Korn, an engineer in Scherbius’s employ, and one from Paul Bernstein, a Berliner.

Korn designed rotors that were removable. Previously their order left to right was fixed, but now the operator could put them into the machine in any order. This made possible Bernstein’s improvement: a movable ring with indicator letters on it on each rotor. The ring rode the circumference of the rotor like a tire on a wheel; the ring could be turned to any position and locked in place with a pin. Previously, a particular indicator letter meant that the rotor was in a particular position; now the indicator letters bore no relation to the position of the rotor. The position of the alphabet ring on the rotor had to be known to the decipherer, so it became part of the key. In addition, Bernstein shifted from the rotor to the ring the notch or notches that caused the rotor to the left to move one space at a certain point or points in the rotor’s revolution. This disjoined the rotor moves from the rotor encipherment, throwing up a further obstacle to solution.

Finally, Korn converted the leftmost of the four rotors into a reflector. Although it was called a rotor, it did not turn. It had contacts only on one face, and it sent the current that had come from the three normal rotors back through them along a different path before it illuminated an output letter. The reflector was sometimes called a half rotor because its wiring went from one contact on the side facing the three main rotors to another contact on the same side; it consequently had only thirteen connections instead of the twenty-six of the main rotors. The current’s double traversing of the rotors meant that encipherment was like decipherment: if plaintext
a
became ciphertext X, plaintext
x
became ciphertext A. This reciprocity had the advantage
of eliminating the need for any switch to shift from enciphering mode to deciphering and vice versa, thus precluding the error of enciphering a message in the deciphering mode. But it had the crypt-analytic disadvantage of yielding the knowledge of a second plaintext letter whenever a first was found. The double passage brought another advantage and disadvantage: it complicated the cryptosystem, but it meant that no letter could ever represent itself, a fact that might speed solutions by showing which possibilities could be rejected.

In 1924, the firm got the German post office to exchange Enigmaenciphered greetings with that year’s congress of the International Postal Union. Later a book on cipher machines by an Austrian criminologist, Dr. Siegfried Türkel, gave the Enigma extensive coverage, including a detailed description of the various models, many photographs, and praise from the Austrian cryptanalyst and author Colonel Andreas Figl. But, no more than any other cipher-machine inventor of the time who had dreamed of getting rich by selling protection for businessmen’s messages, no more than Alexander von Kryha or Edward H. Hebern or Arvid Damm, did Arthur Scherbius make money. By the end of 1924, his firm still had not paid dividends.

The situation, however, was changing. Behind the sandstone walls of the four-story headquarters of the Naval Command at Tirpitzufer 72–76, facing Berlin’s tree-lined Landwehr Canal, the cryptologic branch that had turned Scherbius down in 1918 was reconsidering the security of German naval communications. The reason was the shocking discovery that the British had been reading coded German naval messages for much of World War I.

The first clue came from the fiery builder of Britain’s Dreadnought navy, the retired first sea lord, Admiral of the Fleet Sir John Fisher. In his
Memories
, published in 1919, he wrote: