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CHAPTER 2. SUBSTITUTION CIPHERS
7. A description of cryptanalysis of Playfair ciphers can be found in U.S.
Army Field Manual 34-40-2 [28]. Find a copy of this manual, and
write a summary of how it describes Playfair cipher cryptanalysis.
8. Find some information about two-square and four-square ciphers, and
write a summary of your findings.
9. Find some additional information about the Beale ciphers, and write
a summary of your findings.
2.4
The Navajo Code
While simple substitution ciphers are not very secure, and even ciphers
such as Playfair that substitute for digraphs can be broken through a type
of frequency analysis on longer ciphertexts, not all ciphers based on substitution alone are easy to break. The Navajo code, a cipher famously created
by Native Americans, primarily from the Navajo Nation that occupies a
large region of Utah, Arizona, and New Mexico, and used effectively by
the Americans throughout the Pacific Campaign during World War II, was
essentially a substitution cipher. The Navajo language was at the time exclusively oral, very complex, and unknown to virtually everyone outside the
Navajo Nation. The idea of using Navajos basically speaking their native
language as a means for encrypting messages originated in 1942 with a man
named Philip Johnston. Having grown up the son of a missionary to the
Navajo, 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, where he may have seen Native
Americans, specifically from the Choctaw Nation, encrypting messages for
the U.S. Army basically by speaking their native language. More likely,
Johnston first read of the use of Choctaw by the U.S. Army during World
War I shortly after the Japanese attack on Pearl Harbor that thrust the
U.S. into World War II. Whatever the origin of his idea, Johnston recruited
four Navajos to demonstrate to a group of U.S. Marine officers how they
could quickly and flawlessly translate English messages into the Navajo
language, communicate these messages to each other via radio, and then
translate these messages back into English. Convinced of the potential
of the Navajo language, the Marines 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 training course is shown in Figure 2.1 on page 23.
Before this 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
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2.4. THE NAVAJO CODE
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Figure 2.1 Graduation picture of the original Navajo code talkers.
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 word SUBMARINE was
given the literal English translation IRON FISH, which was translatable in
the Navajo language as BESH-LO. A few examples of military words and
some other words, the literal English translations of these words used by
the Navajo code talkers, and the Navajo translations, or code words, of
these literal translations are shown in Table 2.2 on page 24.
An encoded phonetic alphabet was also created so less common English
words to be translated one letter at a time. Individual letters in such words
were also indicated by literal English translations of things for which translations existed in the Navajo language, and 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 2.3 on page 25. Multiple translations were used for most letters
to increase the difficulty of attacking the code using frequency analysis.
By the conclusion of World War II, the full Navajo code included approximately 800 code words. A list of the code words in the full code can
be found at https://www.history.navy.mil/research/library/online-readingroom/title-list-alphabetically/n/navajo-code-talker-dictionary.html [21].
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CHAPTER 2. SUBSTITUTION CIPHERS
English word
ABANDON
AMERICA
ASSAULT
BATTALION
BRITAIN
CAPTAIN
DIVE BOMBER
GERMANY
ORDER
SAILORS
SUBMARINE
THE
Literal translation
RUN AWAY FROM
OUR MOTHER
FIRST STRIKER
RED SOIL
BETWEEN WATERS
TWO SILVER BARS
CHICKEN HAWK
IRON HAT
ORDER
WHITE CAPS
IRON FISH
BLUE JAY
Navajo code word
YE-TSAN
NE-HE-MAH
ALTSEH-E-JAH-HE
TACHEENE
TOH-TA
BESH-LEGAI-NAH-KIH
GINI
BESH-BE-CHA-HE
BE-EH-HO-ZINI
CHA-LE-GAI
BESH-LO
CHA-GEE
Table 2.2 Navajo code words for selected English words.
Example 2.8 Consider the plaintext THE DIVE BOMBER SANK THE SUBMARINE. The English word SANK was translated in Navajo one letter at
a time. Thus, by Tables 2.2 and 2.3, one possible ciphertext of Navajo code
words for this message is CHA-GEE GINI DIBEH TSE-NILL A-CHIN KLIZZIEYAZZIE CHA-GEE BESH-LO. The literal English translation of this ciphertext
is BLUE JAY CHICKEN HAWK SHEEP AXE NOSE KID BLUE JAY IRON FISH.
!
Example 2.9 Consider the ciphertext of Navajo code words BESHLEGAI-NAH-KIH WOL-LA-CHEE LIN BE-LA-SANA TOISH-JEH KLIZZIE BELA-SANA A-KEH-DI-GLINI AH-NAH CHA-GEE BE-EH-HO-ZINI. The literal
English translation of this ciphertext is TWO SILVER BARS ANT HORSE APPLE
BARREL GOAT APPLE VICTOR EYE BLUE JAY ORDER. By Tables 2.2 and 2.3,
the plaintext for this message is CAPTAIN AHAB GAVE THE ORDER.
!
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, though, since their language had never had a written script.
William McCabe, one of the original 29 code talkers, noted: “In Navajo,
everything is in the memory—songs, prayers, everything. That’s the way
we were raised.”
The speed, accuracy, and security of the Navajo code proved it highly
successful. Messages that would have taken hours to encrypt or decrypt
using rotor machines like the Enigma were encrypted or decrypted in just
minutes using the Navajo code. Just as importantly, the Navajo code is not
known to have ever been broken, and it played a critical role in the American
success in the Pacific Campaign during World War II. U.S. Major Howard
Connor, 5th Marine Division signal officer at Iwo Jima, noted: “Were it
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2.4. THE NAVAJO CODE
Letter Literal
Code word
A
ANT
WOL-LA-CHEE
A
APPLE
BE-LA-SANA
A
AXE
TSE-NILL
B
BADGER
NA-HASH-CHID
B
BARREL
TOISH-JEH
B
BEAR
SHUSH
C
CAT
MOASI
C
COAL
TLA-GIN
C
COW
BA-GOSHI
D
DEER
BE
D
DEVIL
CHINDI
D
DOG
LHA-CHA-EH
E
EAR
AH-JAH
E
ELK
DZEH
E
EYE
AH-NAH
F
FIR
CHUO
F
FLY
TSA-E-DONIN-EE
F
FOX
MA-E
G
GIRL
AH-TAD
G
GOAT
KLIZZIE
G
GUM
JEHA
H
HAIR
TSE-GAH
H
HAT
CHA
H
HORSE
LIN
I
ICE
TKIN
I
INTESTINE
A-CHI
I
ITCH
YEH-HES
J
JACKASS
TKELE-CHO-GI
J
JAW
AH-YA-TSINNE
J
JERK
YIL-DOI
K
KETTLE
JAD-HO-LONI
K
KEY
BA-AH-NE-DI-TININ
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Letter
K
L
L
L
M
M
M
N
N
N
O
O
O
P
P
P
Q
R
R
R
S
S
T
T
T
U
U
V
W
X
Y
Z
Literal
KID
LAMB
LEG
LION
MATCH
MIRROR
MOUSE
NEEDLE
NOSE
NUT
OIL
ONION
OWL
PANT
PIG
PRETTY
QUIVER
RABBIT
RAM
RICE
SHEEP
SNAKE
TEA
TOOTH
TURKEY
UNCLE
UTE
VICTOR
WEASEL
CROSS
YUCCA
ZINC
Code word
KLIZZIE-YAZZIE
DIBEH-YAZZIE
AH-JAD
NASH-DOIE-TSO
TSIN-TLITI
BE-TAS-TNI
NA-AS-TSO-SI
TSAH
A-CHIN
NESH-CHEE
A-KHA
TLO-CHIN
NE-AHS-JAH
CLA-GI-AIH
BI-SO-DIH
NE-ZHONI
CA-YEILTH
GAH
DAH-NES-TSA
AH-LOSZ
DIBEH
KLESH
D-AH
A-WOH
THAN-ZIE
SHI-DA
NO-DA-IH
A-KEH-DI-GLINI
GLOE-IH
AL-NA-AS-DZOH
TSAH-AS-ZIH
BESH-DO-TLIZ
Table 2.3 Navajo code words for alphabet letters.
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,
from their tireless work in making the code a success to their humility in
keeping the code and their role in its success a secret. Not until years
after the code was declassified in 1968 did the code talkers begin to receive
the recognition they so richly deserved. In 1982, President Ronald Reagan
signed a resolution declaring August 14 National Navajo Code Talkers Day.
On July 26, 2001, President George W. Bush presented the original 29
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.
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2.4 Exercises
1. For the plaintext in Example 2.8, use the part of the Navajo code in
Tables 2.2 and 2.3 to find two ciphertexts different from the one in
this example, and give the literal English translation of each.
2. Repeat Exercise 1 using the plaintext in Example 2.9.
3. For the following plaintexts, use the part of the Navajo code in Tables 2.2 and 2.3 to encrypt the plaintext, and give the literal English
translation of the resulting ciphertext.
(a) ABANDON HOPE.
(b) AMERICA THE BEAUTIFUL
4. For the following ciphertexts, which were formed using the Navajo
code, use Tables 2.2 and 2.3 to give the literal English translation,
and decrypt the ciphertext.
(a) NA-AS-TSO-SI BE-LA-SANA BE DZEH YEH-HES TSAH TOH-TA
(b) TSIN-TLITI TSE-NILL CHINDI AH-NAH TKIN A-CHIN BESH-BECHA-HE
5. For the following plaintexts, use the full Navajo code given in [21] to
encrypt the plaintext, and give the literal English translation of the
resulting ciphertext.
(a) TANK AMMUNITION DEPLETED.
(b) POSITIVE ON AERIAL RECONNAISSANCE
6. For the following ciphertexts, which were formed using the Navajo
code, use the full Navajo code given in [21] to give the literal English
translation, and decrypt the ciphertext.
(a) AL-TAH-JE-JAY DIBEH SHI-DA GAH TKIN NA-HASH-CHID WOLLA-CHEE MOASI TSE-GAH YEH-HES AH-DI HA-YELI-KAHN
(b) KLESH NO-DA-IH AH-LOSZ A-CHI SHUSH BE-LA-SANA TLA-GIN
LIN TKIN BIN-KIE-JINH-JIH-DEZ-JAY UT-ZAH-HA-DEZ-BIN
7. Use the full Navajo code in [21] to encrypt a plaintext of your choice
with at least four words for which Navajo code words existed and at
least two words that were translated in Navajo one letter at a time.
8. Find some information about efforts by Carl Gorman to obtain recognition for the Navajo code talkers, and summarize your findings.
9. Find some information about the Cherokee, Choctaw, and Comanche
code talkers used by the U.S. military, and summarize your findings.
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