Center for Cryptologic History The SIGABA / ECM II Cipher Machine : “A Beautiful Idea” This publication presents a historical perspective for informational and educational purposes, is the result of independent research, and does not necessarily reflect a position of NSA/CSS or any other U.S. government entity. This publication is distributed free by the National Security Agency. If you would like additional copies, please e-mail [email protected] or write to: Center for Cryptologic History National Security Agency 9800 Savage Road, Suite 6886 Fort George G. Meade, MD 20755 Timothy Mucklow was a senior historian on the staff of the Center for Cryptologic History fol- lowing a long career in information assurance at NSA and with the Air Force. After a decade in aca- demia, he served as a military historian at the wing, division, and major command levels and produced a series of monographs and articles on such topics as information assurance, telecommunications and computers, and national defense issues, and has offered IA seminars at military facilities around the world. He received his Ph.D. in 1982. He retired from the CCH in 2013. Acknowledgments. The Center for Cryptologic History is grateful to Dr. Craig Bauer, professor of mathematics at York College of Pennsylvania and editor-in-chief of the journal Cryptologia, for his assistance with this project, and to LeeAnn Tallman for earlier research. The SIGABA / ECM II Cipher Machine: “A Beautiful Idea” Timothy J. Mucklow National Security Agency Center for Cryptologic History 2015 Contents Introduction ....................................................................................... 1 And Hebern Saw the Wheel .................................................................... 2 Deus ex Machine ................................................................................. 5 Rowlett’s Epiphany .............................................................................. 7 Iacta Alea Est. [The Die Is Cast.] ........................................................... 10 Enter the Navy ..................................................................................12 A Disagreeable but Rewarding Surprise ....................................................14 SIGABA Is Built ...................................................................................16 An Impenetrable Machine .....................................................................22 The Big Machine That Did .....................................................................25 Appendix A: Technical Analysis of SIGABA’s Key Space ..................................29 Appendix B: The Mechanics of SIGABA ......................................................32 Notes ..............................................................................................38 Selected Bibliography ..........................................................................42 SIGABA / ECM II Cipher Machine Introduction During World War I, both the Americans and the the “design of the system should not require secrecy, Europeans had used manual code and cipher systems and compromise of the system should not inconve- to secure their critical information. With the advent nience the correspondents.”1 His argument was that of the machine age, however, it was only a matter of neither the elements of an encryption algorithm nor time before cryptography became mechanized. Two the workings of an encryption machine should con- decades later, as the world embroiled itself in another stitute the basis of a cipher’s security. Instead, an eas- major conflict, the use of cipher machines became ily changeable key should be the critical component. commonplace, and the old craft of cryptology at long In the 1930s, the U.S. Army cryptologist Wil- last became mathematically based. With the dawn of liam Friedman and his assistant Frank Rowlett drew this new cryptologic age, a worldwide scramble for on this simple precept to conceive a cipher machine even stronger encryption began. that was easy to use, simple to rekey, and ostensibly Well before the First World War, much work had impossible to break. Then, in a fit of collaboration been done to formalize the cryptographic discipline. with the Navy, as unprecedented as it was peculiar, One of those who made a major contribution to the two services went on to perfect and jointly field this process was the 19th-century polyglot Auguste their device. To the Army it was known as SIGABA, Kerckhoffs, who, besides teaching languages, dabbled to the Navy, ECM (Electric Cipher Machine) II. in cryptography. In 1883 he penned a two-essay series, (The technical aspects of SIGABA’s operation can La Cryptographie Militaire, for the Journal des Sciences be found in Appendixes A and B.) Not only was Militaire, which earned him a niche in cryptographic SIGABA the most secure cipher machine of World history. Kerckhoffs in his writings had articulated six War II, but it went on to provide yeoman service for basic principles of cryptography, but he is most com- decades thereafter. The story of its development is monly remembered for his second, which states that improbable. Its impact was incalculable. 1 1 And Hebern Saw the Wheel Mr. Edward Hebern of Madera, California, is posed, but using a set of cipher wheels whose generally credited with inventing the first American wiring was to be unknown to Friedman … electromechanical rotor cipher machine.2 Accord- Friedman was successful in his attack on the ing to lore, he came up with the idea around 1912 system.4 while serving a term in the state penitentiary for With little effort, Friedman was able to decipher horse thievery. If there were any connection between every Hebern-enciphered message sent his way. To breaking rocks and his cryptographic epiphany, do this, Friedman, who had already married crypt- Hebern never offered one. By the end of 1915 he analysis and mathematics, used a statistical approach had built a working model, filed a patent, and was along with a “divide-and-conquer” strategy to break knocking on the doors of potential buyers.3 It was the Hebern machine. As Friedman saw it, there were not long before the U.S. Navy began showing inter- only two unknowns, the cipher wheel (with twenty- est in Hebern’s device, and in the years that followed six characters) and the rest of the machine. Since the the Navy would buy and test a number of his suc- cipher wheel stepped regularly and predictably, the cessive machines. As something of a historical twist, rest of the machine could be considered a constant. one of Hebern’s early employees, Agnes (Meyer) It was then a simple matter of sequentially analyzing Driscoll, went on to become a luminary of American the individual components. cryptology in her own right. Friedman realized from experience that the regu- Half a century after Hebern set out to peddle lar advancement of the Hebern cipher rotors, like all his original device, the Army cryptologist Frank machines of that era, posed an intrinsic cryptologic Rowlett acknowledged in his memoirs that the vulnerability that was mathematically exploitable. He Hebern cipher machine was an important inven- conjectured that to make a cryptographically sound tion in pre-World War II American cryptography. machine, one would need a countermeasure to address Rowlett, nevertheless, went on to add, predictable rotor movements. But just how such pseu- Navy cryptographers asked [William] dorandom movement could be achieved consumed Friedman for his assessment of the security Friedman’s thoughts for years. Friedman’s solution, it afforded … [T]he Navy [supplied] a set when it finally came to him around 1926, was concep- of messages prepared exactly in accordance tually simple and the technology proven.5 It occurred to with the procedures which they had pro- him that paper tape similar to that used by telegraphers 2 And Hebern Saw the Wheel Edward Hebern and his electromechanical rotor cipher machine (courtesy of Ralph Simpson, CipherMachines.com) could also be used to dictate the move- ments of the cipher wheels. Friedman reasoned that it would be relatively easy to generate long sequences of random five- unit keys and that the tape itself was eas- ily replaceable and relatively inexpensive. Holes punched in a tape would permit feeler contacts to turn an electrical cur- rent on or off, causing a cipher machine’s rotors to step. Thus, with each key stroke, randomly placed holes in a five-group tape would produce an apparent random step- ping for one or more of the cipher rotors. The cipher text is printed on a small tape. The decryption process simply works in reverse. Key tape could be manufactured in secure facilities, distributed to the appropriate recipients, and inserted into the machine according to rigidly imposed, William Friedman with AT&T printing telegraph, 1920 (courtesy 6 pre-established schedules. of the George C. Marshall Foundation, Lexington, Virginia) 3 SIGABA / ECM II Cipher Machine The crypto rotor wheels William Friedman envisioned for his device were flattened cylinders with an alphabet around the circumference. One face of the cylinder had twenty-six spring-loaded copper pins protruding from it; the other face had twenty-six flush copper contacts. Inside each cylinder was a wire maze connecting the electrical contacts on one side to the pins on the other. Thus, an electrical impulse beginning with, say, the letter A on one side might connect to H on the other side and so on around the wheel in random fashion. Several cylinders serially juxtaposed