Darwin Among the Machines (13 page)

The heart of the Enigma was a series of flat, wheel-shaped rotors, with twenty-six electrical contacts, one for each letter of the alphabet, arranged in a circle on each face. The contacts were connected in unpredictable order so that a signal going in one side of the rotor as a given letter emerged on the other side as something else. There were thus 26! (or 403,291,461,126,605,635,584,000,000) possible wirings for each rotor. Each station in a particular banking or communication network had an assortment of different rotors in matching sets. The Enigma also had a keyboard like a typewriter. Each key closed a circuit that sent a battery current through a stack of three adjacent
rotors; the signal returned via a fourth, reflecting rotor (capable of only 7,905,853,580,025 states) that continued the circuit back through the first three rotors in reverse, ending at one of twenty-six light bulbs, which indicated the letter to be used for the enciphered text. The rotors were mechanically coupled to the keyboard like the wheels of an odometer, so that the machine's state of mind changed with every step. But if the recipient had an identical machine, with the same rotors placed in the same positions, the function could be executed in reverse, producing deciphered text.

In September 1939, at the outbreak of World War II, Alan Turing found himself face-to-face with the Enigma, and later encountered its digital successors, known to the British code breakers as Fish. Turing and a rapidly expanding circle of mathematicians, linguists, engineers, technicians, clerks, and chess players, assisted by an indispensable corps of Wrens (Women's Royal Navy Service), were sequestered at a Buckinghamshire estate known as Bletchley Park for the duration of World War II. As guests of the Foreign Office's Government Code and Cypher School the cryptanalysts kept a low profile, although it was difficult to conceal that so many gifted mathematicians (especially chess players) had suddenly dropped out of sight. Suspicious, but not suspicious enough, the German authorities modified the commercial Enigma machine and frequently changed the keys, suspecting internal spies whenever there was evidence of a leak. For more secure communications, especially with the U-boat fleet, an additional rotor position was added as well as an auxiliary plugboard that further scrambled ten pairs of letters, leaving only six letters unchanged. “Thus, the number of possible initial states of the machine at the beginning of the message was about 9 × 10
²⁰
. For the U-boats it was about 10
²³
,” recalled Irving J. (Jack) Good, who signed on as Turing's statistical assistant, at the age of twenty-five, in May 1941.
²³

For the three-rotor Enigma a brute-force trial-and-error approach would have to test about a thousand states per second to run through all possible configurations in the three billion years since life appeared on earth. A brute-force approach to the four-rotor Enigma would have to test about 200,000 states per second to be assured of a solution in the fifteen billion years since the known universe began. During a critical period of the war, Bletchley Park succeeded in deciphering a strategically significant fraction of intercepted Enigma traffic within a few days or sometimes hours before the intelligence grew stale. This success was a product of human ingenuity on the part of the British matched by human error on the other side. “We benefited greatly from a combination of Nazi bombast and German methodicalness,”
recalled Peter Hilton, an Oxford undergraduate recruited in January 1942. “Nazi conceit dictated that great military successes should be announced to every German military unit everywhere; and the passion of the German military mind for good order and discipline dictated that these announcements should be made in exactly the same words and sent out at exactly the same time over all channels.”
²⁴

Polish cryptographers provided a head start by decoding three-rotor Enigma messages before the outbreak of the war. Three young Polish mathematicians (Henryk Zygalski, Jerzy Ró
ż
ycki, and Marian Rejewski), assisted by French intelligence and an interest in the German Enigma dating back to an interception by Polish customs officers in 1928, applied ingenious logic to narrow the search for rotor configurations so that electromechanical devices (called “bombas” by the Poles and “bombes” by the British) could apply trial and error to certain subsets that remained. The bombe incremented itself through a space of possibilities, and when a designated clue turned up it came to a stop. (The characteristic ticking, followed by sudden silence, may have given the machine its name.)

With wartime improvements to the Enigma and increasingly frequent rotor changes, even a growing array of far more powerful British bombes, designed with Turing's assistance and mass-produced by the British Tabulating Machine Company, could barely keep up. By the end of 1943, ninety thousand Enigma messages a month were being decrypted, with round-the-clock shifts of cryptanalysts at Bletchley supported by satellite bombe installations at Wavendon, Gayhurst, Stanmore, and Eastcote. “The bombes were bronze-coloured cabinets about eight feet tall and seven feet wide . . . [and] made a considerable noise as the drums revolved, each row at a different speed, so there was not much talking during the eight-hour spell,” recalled Diana Payne, who set up (programmed) bombes according to the day's cryptanalytic menus for more than three years. “For technical reasons which I never understood, the bombe would suddenly stop and we took a reading from the drums . . . it was a thrill when the winning stop came from one's own machine.”
²⁵

Fish traffic—longer messages, transmitted automatically in binary code over high-speed cable and radiotelegraph links—presented a challenge beyond the reach of the bombes. Electronic data processing offered the only hope of catching up. A series of punched-tape machines known as Heath Robinson (code-named after an English cartoonist, in the style of Rube Goldberg, “well known for his drawings of ludicrous tasks performed by fantastic machines”)
²⁶
were built, on the principle that by simultaneous scanning of two different
(and relatively prime) lengths of coded tape as continuous loops, all possible combinations of the two sequences could be compared. Based on standard teleprinter tape and standard 5-bit (Baudot) teleprinter code, but running at high speed through photoelectric heads, the Heath Robinsons used electronic circuits to count, combine, and compare the two sequences by means of Boolean operations performed at a tremendous pace. But it was difficult to maintain synchronization between two tapes. It was then proposed by Thomas H. Flowers, an engineer working for the British Post Office's telecommunications research station at Dollis Hill, to eliminate one of the tapes by transferring its sequence to the internal memory (or state of mind, in Turing's language) of an electronically more complicated but mechanically simpler machine. The internal sequence could then be precisely synchronized to the sequence of pulses input by the tape, which could be run without sprockets at much higher speeds by friction drive.

“The tapes were read at 5,000 characters per second,” recalled Jack Good. “There were parallel circuits, so that 25,000 binary digits were handled every second. . . . Teleprinter tapes have 10 characters to the inch, so that the speed of 5,000 characters per second implies a tape speed of nearly 30 miles per hour. I regard the fact that paper teleprinter tape could be run at this speed as one of the great secrets of World War II!”
²⁷
With practice, it was possible to run loops of tape as much as two hundred feet in length, although there were problems with the edges of the tape sawing through stainless-steel guide pins on longer runs. The new machine, constructed under the supervision of Thomas Flowers at the Dollis Hill research station and operated and programmed under the direction of M. H. A. Newman (under whose supervision Turing had written his paper on computable numbers in 1936), was code-named Colossus and incorporated fifteen hundred vacuum tubes, or, as the British more accurately described them, valves. The machine was so successful (and subspecies of Fish so prolific) that by the end of the war ten Colossi were in use, the later versions using twenty-four hundred vacuum tubes. The heaters were never turned off, since reheating was the most likely occasion for tubes to fail. “Ah, the warmth at two
A.M.
on a damp, cold, English winter!”
²⁸
recalled Howard Campaigne, a U.S. Navy cryptanalyst assigned to Bletchley Park in 1942. By the end of the war the Germans had begun to change the wheel patterns of both Enigma and Fish once a day instead of once a month.

The Fish were of two families: the
Geheimschreiber
, manufactured by Siemens, and the
Schlüsselzusatz
, manufactured by Lorenz. The
latter was targeted by the Colossus and known as Tunny to the British, with various subspecies (Jellyfish, Bream, Gurnard, Sturgeon, etc.) representing different branches of German command. The Fish were substantial pieces of automatic teletypewriter equipment that produced a sequence of 0s and 1s (the key) that was then added to the binary representation of an unenciphered (plaintext) message and output for transmission as ordinary 5-bit teletypewriter tape. The machine's twelve code wheels, of unequal length, were circumscribed by a combined total of 501 pins that could be shifted between two positions, giving the system a formidable number (2
⁵⁰¹
or about 10
¹⁵⁰
) of possible states and a period of 1.6 × 10
¹⁹
digits before the key produced by any given configuration began to repeat. The key was added modulo 2 to the plaintext message (counting by two the way we count hours by twelve, so that 0 + 1 = 1 and 1 + 1 = 0), with 1 and 0 represented by the presence or absence of a hole in the tape. Adding the key to the enciphered text a second time would return the original text. Each Fish was a species of Turing machine, and the process by which the Colossi were used to break the various species of Fish was a textbook example of the process by which the function (or partial function) of one Turing machine could be encoded as a subsidiary function of another Turing machine to produce simulated results. The problem, of course, was that the British didn't know the constantly changing state of the Fish; they had to guess.

Colossus was programmed, in Boolean logic mode, by a plugboard and toggle switches at the back of the machine. “The flexible nature of the programming was probably proposed by Newman and perhaps also Turing, both of whom were familiar with Boolean logic, and this flexibility paid off handsomely,” recalled I. J. Good. “The mode of operation was for a cryptanalyst to sit at Colossus and issue instructions to a Wren for revised plugging, depending on what was printed on the automatic typewriter. At this stage there was a close synergy between man, woman, and machine, a synergy that was not typical during the next decade of large-scale computers.”
²⁹
Colossus did not directly reveal a plaintext message, but, when successful, a succession of clues as to the configuration and initial position of the wheels that had produced the key sequence in use at the time. The search for clues, often assisted by a “crib,” or probable string of text, relied on certain subtle statistical characteristics of the German language, a process that remained one of the more closely guarded secrets of the war. In a demonstration of the machine intelligence that would absorb Turing and several of his colleagues in the aftermath of World War II, Colossus was trained to sense the direction of extremely
faint thermoclines that distinguished enciphered German from flat-random alphabetic noise. Said Andrew Hodges, “the line between the ‘mechanical' and the ‘intelligent' was very, very slightly blurred.”
³⁰

Colossus was not a stored-program computer (executing and modifying internally stored instructions), but it came almost as close as the U.S. Army–sponsored ENIAC, and some two years in advance. It was distinguished from other electronic calculators in that it was designed for performing Boolean operations, not producing numerical results. This counted against it by the standards of its day, but as a step toward the modern computer, these logical abilities placed it far ahead.

Turing's role in the history of Colossus remains shrouded by the layers of secrecy that surrounded the project, further obscured by the legendary aura surrounding the universal machine. Good wrote that Turing “made important statistical contributions, but had little to do with the Colossus,”
³¹
a view supported by Newman, Flowers, and others, although Brian Randell, after extensive interviews with these participants, noted “virtually all the people I have interviewed recollect wartime discussions of his idea of a universal automaton.”
³²
Peter Hilton wrote that Turing “was, in fact,—and quite consciously and deliberately—inventing the computer as he designed first the ‘Bombe' and then the ‘Colossus.'”
³³
By the time of the actual construction and operation of the Colossi, Turing had moved on to the problem of real-time voice encryption, among other things. Bletchley Park had grown into an operation employing seven thousand people, ten Colossi, innumerable bombes, large arrays of Hollerith equipment, and extensive telecommunications support. The Colossi were among the first programmable, if specialized, electronic digital computers. As an integrated data-processing installation the whole operation was years, if not decades, ahead of its time.

With the end of the war, the computational torch passed to the Americans, even though it was the alumni of Bletchley Park who were first to demonstrate a working stored-program computer (the Manchester Baby Mark I, which ran its first program on 21 June 1948) and first to construct a fully electronic memory (the electrostatic Williams tube). The driving force behind computer development was no longer the logical puzzle of cryptanalysis, but the numerical horsepower required to design atomic bombs. When Bletchley Park disbanded, the Official Secrets Act handicapped those who could not refer openly to their wartime work. The existence of Colossus would not be officially acknowledged for thirty-two years.