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The Navajo Code Talkers of World War II

Rick Klima and Neil Sigmon

The ability to transfer information in a secure and confidential fashion using cryptography, the science and art of secret message writing, has long been and continues to be important in our society. Cryptography is appealing to a variety of fields due to the fact that it is truly multi-disciplinary. Students majoring in disciplines such as history, English, a foreign language, mathematics, and computer science can appreciate cryptography’s intrinsic value. The subject has often appeared in documentaries, movies, and television shows. Students also appreciate that cryptography has become a more important component used in everyday life, given the fact that information exchange is heavily reliant on computers.

Some of the most fascinating instances and stories of human achievement have resulted from the creating and breaking of cryptographic codes, often from unlikely sources. One extraordinary example of a cryptographic code that was never broken when in use was created by a group of Navajo Marines during World War II. In this article, we give a brief description of how this code was created, its usefulness during World War II, and its historical significance.

Development of the Code.

During World War II, much of the encrypted communications were done using rotor-driven cipher machines. For the Axis, examples included the Japanese Purple and German Enigma machines, and for the Allies, the American SIGABA and British Typex machines.

By avoiding mistakes that Japanese and German cipher operators made with their machines, the Allies were able to avoid having their encrypted messages broken throughout the war. However, a practical limitation the Allies saw in the use of their rotor-driven machines was the time and manpower they required. Messages had to be typed into the machines letter by letter by the cipher machine operator. The encrypted output then had to be recorded letter by letter and transmitted by a radio operator. The radio operator on the receiving end had to communicate the message to the cipher machine operator who, after setting the machine up with the correct key, had to decipher it by typing the ciphertext letter by letter into the machine. The process was extremely slow and it was easy for operators to make mistakes. Even a small mistake, such as a single letter being missed in decryption or dropped during transmission, could ruin the remainder of the message. Thus, rotor-driven cipher machines could be difficult to use, especially in the heat of battle.

To gain a better understanding of how tedious a rotor machine was, consider a simulation example of how the German Wehrmacht (Army) Enigma cipher encrypted messages. When a letter was encrypted or decrypted by a Wehrmacht Enigma, the letter was typed and an electric current designating the letter first went to the plugboard, where it was swapped or remained the same according to whether it had a cable connection to another letter. The electrical current passed from right to left through three rotors, each of which could change the current to designate a different letter. After passing through a reflector, which changed the current that signified a different letter, the current passed back through the rotors from left to right. Again, it went to the plugboard, and then finally arrived at the lampboard where it lit the bulb of the decrypted or encrypted letter.

The Germans normally used ten plugboard cables to connect 20 letters. To prevent letter frequency analysis attacks, when a key was pressed to encrypt a letter, the rotors turned in an odometer-like fashion, assuring a different path through the machine and that a single letter would not encrypt to the same ciphertext letter. The rotors could be oriented in the machine in 26 different ways with the orientation indicated by the letter showing through a window located on top of the machine. To further confuse the enemy, the outer ring on each rotor could be rotated into any of the 26 letter positions (known as the ring settings). Finally, the reflector to the left of the rotors was designed to swap letters and ensured that the path for the encryption of a letter was the same as the path for decryption.

In the field, each day the German Enigma operators used a codebook to configure their Enigma machines to the same initial settings. A video demonstrating an Enigma simulator and the steps for its configuration and use to encrypt the message CAPTAIN THE DIVE BOMBER SANK THE SUBMARINE AND BATTLESHIP can be found at the website https://breeze.radford.edu/p93vvzh29bu/.

  The Americans in the Pacific Campaign during World War II avoided the issues associated with the rotor machines by using Native Americans, primarily from the Navajo Nation located in a large region in Utah, Arizona, and New Mexico. Navajos serving in the U.S. Marines were able to create a cryptographic technique that involved encrypting messages by basically speaking their native language. The idea of using Navajos and their native language for encryption originated at the beginning of 1942 by a man named Philip Johnston. Having grown up the son of a missionary to the Navajo people, Johnston was very familiar with the Navajo culture, and was one of only a handful of non-Navajos who spoke the Navajo language fluently.

Johnston was a veteran of World War I, and was familiar with how the Choctaw had provided secure communication for the U.S. Army during World War I. Johnston recruited four Navajos to demonstrate to a group of Marine officers how they could quickly and flawlessly translate English messages into the Navajo language, communicate these messages in Navajo to each other via radio, and then translate these messages back into English.

Convinced of the potential of the Navajo language serving as an encryption device, the Marine Corps ordered a pilot project in which an eight-week communications training course was completed by a group of 29 Navajos, who became the original Navajo code talkers. A graduation picture from this communications training course is shown in Figure 1.


Figure 1. Original Navajo code talkers

Before the initial eight-week communications training course could commence, the Marines had to figure out a way to overcome a problem that had plagued attempts at using Native American languages as a means for encrypting messages during World War I—many military words, for example, SUBMARINE and DIVE BOMBER, had no translatable equivalent in Native American languages. To overcome this problem, the Navajo trainees decided that they would indicate such military words using literal English translations of things in the natural world for which they had Navajo translations. For example, the military word SUBMARINE was given the literal English translation IRON FISH, which is BESH-LO in the Navajo language. Other such translations are shown in Table 1.

Table 1. Navajo code words for select English words.

An encoded phonetic alphabet was also created to allow for less common English words to be translated one letter at a time. Individual letters in such words were indicated by literal English translations of things for which translations existed in the Navajo language. Then the words were encoded one letter at a time using the Navajo translations. The individual letters, the literal English translations of these letters used by the Navajo code talkers, and the Navajo translations of these literal translations are shown in Table 2.

Table 2. Navajo code words for alphabet letters.

Multiple translations were used for most letters to increase the difficulty of deciphering the code using frequency analysis. By the end of World War II, the full Navajo code included approximately 800 code words. A full list of the code words in Navajo can be found at the web site https://www.history.navy.mil/research/library/online-reading-room/title-list-alphabetically/n/navajo-code-talker-dictionary.html.

The Navajo code was completely oral and never written down. As a result, each code talker, of which there were more than 400 by the end of World War II, had to know every code word by memory. This was not difficult for the Navajos since their language lacked a written script. William McCabe, a code talker, said, “In Navajo, everything is in the memory—songs, prayers, everything. That’s the way we were raised.”

For example, consider the plaintext CAPTAIN THE DIVE BOMBER SANK THE SUBMARINE AND BATTLESHIP. Using Table 1, we see that CAPTAIN and DIVE BOMBER were translated literally as BESH-LEGAI-NAH-KIH and GINI, respectively. The word SANK had no literal translation, and thus was translated one letter at a time. Using Table 2, we see that one such translation, which depended on the single letter translations used, would be DIBEH TSE-NILL A-CHIN BA-AH-NE-DI-TININ. The entire ciphertext of Navajo code words for this message would thus be BESH-LEGAI-NAH-KIH CHA-GEE GINI DIBEH TSE-NILL A-CHIN BA-AH-NE-DI-TININ CHA-GEE BESH-LO DO LO-TSO.

In addition, note that the literal English translation of the message would be given by TWO SILVER BARS BLUE JAY CHICKEN HAWK SHEEP AXE NOSE KEY BLUE JAY IRON FISH AND WHALE. This literal translation illustrates an important point about the code — only trained code talkers had the ability to translate the code. Even if a person could speak Navajo fluently, he or she, without knowledge of the code, would be unable to translate a ciphertext into an English plaintext that made sense.

In the field, one Navajo code talker would translate an English plaintext into a Navajo ciphertext and communicate the ciphertext using a radio to another Navajo code talker on the receiving end, who would then translate the result back into English. This process would typically take a matter of seconds. A sample verbal translation of the previous example can be heard at the web site http://maplenet.radford.edu:8080/maplenet/cryptbook/SoundFiles/ncodevmt.wav.

This Navajo verbal translation readily demonstrates the time saved for encrypting and decrypting messages compared to encrypting and decrypting the same message using the rotor driven Enigma cipher.

Mathematically Describing the Code.

The fundamental objective of any cryptosystem is to enable two people to communicate over an insecure channel so that any opponent cannot understand what is being said. The two correspondents communicate confidentially using a pre-determined key that the sender uses to disguise the message and the recipient uses its inverse to reveal the message.

Intuitively, the Navajo code and substitution ciphers do not appear to have a mathematical representation. However, all cryptosystems, including the Navajo code, can be represented mathematically. In mathematical notation, a cryptosystem can be described as a five tuple (P, C, K, E, Dthe following four conditions:

1.      P is a finite set of undisguised symbols or phrases called plaintexts.

2.     C is a finite set of disguised symbols or phrases called ciphertexts.

3.     K is a finite set of possible keys, called the keyspace.

4.     For each kK, there is an encryption function ek: PC in E and a corresponding decryption function dk: CP  in D such that dk(ek(p)) = p  for every   dddd          plaintext element pP.

The Navajo code provides an excellent example of how functions are described and applied in non-traditional mathematical notation. The set P is the set of all English phrases to be disguised. The range C is the set of possible Navajo language phrases assigned to each English phrase. To encrypt an English phrase, a Navajo code talker chooses an encryption function ek: PC designed to encrypt that phrase. The encryption function maps the English phase pP to an element cC by computing ek(p) = c. The Navajo talker applies the key k by assigning the phrase p a literal translation and mapping the literal translation to the Navajo phrase representing the ciphertext element c. After receiving the ciphertext message c, another Navajo code talker finds the decryption function dk: CD needed to decipher and computes dk(c) = p, determining p by applying the key k to the literal English translation of the Navajo phrase represented by c.

For example, suppose using Table 1 that a Navajo code talker wants to encrypt the plaintext phrase AMERICA P. Then, choosing the proper encryption function ek, the code talker applies the key k and translates the message literally to OUR MOTHER, which translates to the Navajo codeword NE-HEH-MAH C. The process computes ek(AMERICA) = NE-HEH-MAH, which is transmitted. The Navajo code talker receiving NE-HEH-MAH chooses the proper decryption function dk, and after translating NE-HEH-MAH to OUR MOTHER, applies the key k to translate the original result back to AMERICA P. The process computes dk(NE-HEH-MAH) = AMERICA.

The entire process of encrypting and decrypting an entire message consisted of the Navajo code talker sending the message choosing a sequence of encryption functions to encrypt the message and the Navajo code talker receiving the message determining the sequence of decryption functions necessary to properly decrypt the message. The Navajo code talkers where the only persons who had knowledge of the keys necessary to translate the literal English messages to the intended desired plaintext and ciphertext messages.

Uses in the Field and Later Recognition.

The speed, accuracy, and security of the Navajo code proved highly successful. Messages that would have taken hours to encrypt or decrypt using rotor machines, such as the Enigma, were encrypted or decrypted in seconds using the Navajo code. Given that the code was exclusively oral, virtually unknown, and a very complex language that was described as a “weird succession of guttural, nasal, and tongue twisting sounds,” the Japanese were unsuccessful in cracking the code.

Given the speed of the Navajo code and the fact it was not broken led to it playing a critical role in the American success in the Pacific Campaign during World War II. First introduced at the Battle of Guadalcanal in August 1942, the code was successfully used in many island battles, including Saipan, Bougainville, and Iwo Jima. In fact, given that the Navajos passed over 800 error-free messages in a 48-hour period at Iwo Jima, U.S. Major Howard Connor, 5th Marine Division signal officer at Iwo Jima, noted, “Were it not for the Navajos, the Marines would never have taken Iwo Jima.”

The Navajo code continued to be used successfully by the Americans in the Korean War and in the early stages of the Vietnam War. The dedication and loyalty of the Navajo code talkers was remarkable. Their tireless work in making the code successful, to their humility in keeping the code and their role in its success a secret, is especially remarkable considering the treatment of the Navajo Nation by the U.S. government prior to World War II. Not until years after the code was declassified in 1968 did the Navajo code talkers begin to receive the recognition they so richly deserved. In 1982, President Ronald Reagan signed a resolution declaring August 14th National Navajo Code Talkers Day. On July 26, 2001, President George W. Bush presented the original 29 Navajo code talkers the Congressional Gold Medal, the highest civilian award in the United States. Four of the five surviving original code talkers were in attendance. More recently, in November 2017, the Navajo code talkers were honored by current President Donald Trump. As of this writing, only 13 of the code talkers are still living.

Final Thoughts.

The Navajo code provides an excellent example of the importance of cryptography and its significance. More details concerning the code and other historical ciphers can be found in an excellent book by Singh (1999).

Most courses in cryptography begin through the use of substitution ciphers. Substitution ciphers are examples of the earliest forms of ciphers and are often found in puzzles. The Navajo code is a significant historical example of this type of cipher and can be used as a way to introduce functions to students. Ways of representing substitution and other classic ciphers using mathematical functions can be found in Stinson (2006).

In addition, cryptography provides an excellent demonstration of applications of topics in mathematics involving linear algebra, abstract algebra, number theory, probability, and statistics, and can be implemented both before and after students study these subjects. Additional mathematical topics used in cryptography include prime numbers, solving systems of equations, and basic algebra concepts such as exponentiation. Details of these applications can be found in the textbook by Klima and Sigmon (2012).

Through the use of Maple, the authors have produced software that allows users to see and hear verbal simulations of the Navajo code. More information can be found by contacting the authors and by consulting the web site http://www.radford.edu/npsigmon/cryptobook.html.

 

References

Klima, R. E. and Sigmon, N. P. (2012). Cryptology Classical and Modern with Maplets. Boca Raton, FL: CRC Press.

Singh, S. (1999). The Code Book. New York: Anchor Books.

Stinson, D. R. (2006). Cryptology Theory and Practices. Boca Raton, FL: CRC Press.

 


Rick Klima

Professor

Appalachian State University

klimare@appstate.edu

 



Neil Sigmon

Professor

Radford University

npsigmon@radford.edu

 



 


Virginia Council of Teachers of Mathematics
PO Box 73593
Richmond, VA 23235
info@vctm.org 


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