Cryptology: The Science
of Secret Codes and Ciphers
cipher wheel, part of the National Security Agency collection,
is similar to one described by Thomas Jefferson. It was
used to encode and decode messages.
The word Cryptology comes from the Greek word
kryptos, which means hidden and logos, which means
word. It is the branch of science that deals with secret communications.
To keep communications secret, it is necessary to use a code,
a cipher, or both.
A code is a system of symbols representing letters,
numbers or words. For example, you could create a code that
might represent the following words as:
The=01, in=02, Spain=03, mainly=04, rain=05,
falls=06, Germany=07, drops=08, on=09, plain=10
The encoded message might read:
01 05 02 03 06 04 09 01 10.
When you decoded the message by replacing the
number with the matching word you get:
The rain in Spain falls mainly on the plain.
Without the table showing what words go with which
numbers, it would be very hard to guess the meaning of the encoded
message. For this reason codes have been used for thousands
of years by people to protect private messages.
Codes are not used only to protect secret information.
Certain codes, like Morse Code, were developed before
the radio and the telephone to make it easy to send messages
great distances. The telegraph allowed a single tone, or beep,
to be sent through a wire to a remote location. Morse code translates
the letters of the alphabet into a series of short or long beeps.
For example, an A is sent as a short beep followed by
a long beep. Messages were sent letter by letter across the
telegraph wire as many long and short beeps. Morse code could
also be used to allow two ships to communicate through the use
of blinking signal lights. Even today Morse code is still used
in radio because the beeps sometimes can get through heavy static
that voice communications cannot.
The table that contains the translation of the
words to the code is often in the form of a book and is referred
to as a codebook.
A codebook does not need to be a special book
filled only with a code. Messages can be passed using any two
identical books as long as they contain the words in the message.
For example, a spy in country A can send a message to
a spy in country B as long as they have the same copy
and revision of the book. Take the code:
38-1-1, 213-27-4, 46-22-1
It is meaningless unless you know that the first
three numbers represent the page, line and number of words from
the left edge in the book Control of Nature by John
McPhee. The first three numbers give you the first word
of the coded message, the second three numbers the second word,
and so on. With this information it is possible to tell that
this encoded message is the first three words of:
The rain in Spain falls mainly on the plain.
The fourth word in this message points out a flaw
in this system. The book Control of Nature does not contain
the word Spain. Any spy would have to find an alternate
wording for his message. Even the words that can be found in
the book can be difficult to locate, making encoding and decoding
time consuming. One way of solving this problem is to use a
cipher instead of a code.
A cipher is a system for encoding individual letters
or pairs of letters in a message. One of the simplest ciphers
was said to have been used by Julius Caesar and for that reason
this type of cipher still bears his name. The Caesar cipher
shifts letters around. For example, every letter on the left
of the equal sign below corresponds to a letter on the right:
A=C, B=D, C=E, D=F, E=G, F=H, G=I, H=J, I=K,
J=L, K=M, L=N, M=O, N=P, O=Q, P=R, Q=S, R=T, S=U, T=V, U=W,
V=X, W=Y, X=Z, Y=A, Z=B
We refer to the message before it gets encrypted
as the plaintext. You could encrypt the plaintext:
Meet you at the corner
By substituting an O for the M, then a G for an
E, another G for the E, and so on until the whole message was
OGGV AQW CV VJG EQTPGT
This is called a substitution cipher. The
encoded message is nolonger readable. To make it even harder
to understand, the coder can break the letters up into arbitrary
groups of five or so (called code groups) with no spaces. Extra
meaningless letters are filled in at the end to make the last
code group the same length as the others. This hides the length
of each of the words in the message. After breaking the above
message up into code groups we get:
OGGVA QWCVV JGEQT PGTXY
Enigma encoding/decoding machine from WWII.
Is the message impossible to read without knowing
the secret of the Caesar cipher? No, it isn't. There is another
branch of this science known as cryptanalysis. The science
of cryptanalysis deals with "breaking" and reading secret codes
and ciphers. How would you go about using cryptanalysis to read
the above code? The primary tool for this is a frequency
list. Each language shows definite patterns in how often
certain letters appear in sentences. For example, in English
the letters "Q", "X" and "Z" are rarely used while the letter
"E" is used the most often. The order of letter frequency in
with E the most frequent and Z the
least used. We could attempt to decode the above message by
replacing the most frequently appearing letter in the code with
the letter E:
The next most frequently used letter is "T":
At this point replacing the third most popular
letter in the code with the third most frequent letter, "A",
would be a problem. In the encoded message the letters Q and
T appear twice each. Which is the "A"? While frequency lists
provide a guide for decoding a substitution cipher, there are
plenty of sentences in English in which "E" is not the most
frequent letter. To decode a message it might be necessary to
replace any of the frequently used code letters with any of
the five most popular English letters in different combinations
to see if the resulting sentence has meaning.
We could also try to see if there are any words
we can figure out based on the information we have so far. It
isn't hard to conclude that the first word of the message is
MEET. After all there are only a few words in English
where the end part is EET (Other ones include FEET,
Now things start to get a little more tricky.
A cryptoanalyst would substitute the remaining most frequent
letters in the code with the most frequent English letters in
different combinations working the letters like a puzzle. Eventually
the analyst would figure out that the Q and T must be O and
R. This would yield:
If we got this far, a little thought would take
us to the final message:
MEETY OUATT HECOR NER--
Or correctly spaced:
MEET YOU AT THE CORNER.
The Caesar code is extremely easy to break, because
after you discover that G is E and V is T, it is not difficult
to conclude that the code works by shifting the letter in the
alphabet by three places. More complicated is a substitution
cipher where each letter in the alphabet is randomly mapped
to the code letters. For example:
has no simple pattern. The message "Meet you at
the corner." With this code becomes:
UYYI OTQ NI ICY ZTHFYH
Another simple cipher uses columnar transposition.
With this cipher the message is written out as rows of five
letters with no spaces and arranged in columns. So Meet you
at the corner becomes:
The cipher is generated by reading the letters
off of each column top to bottom then left to right:
MOHNE UEEEA CRTTO XYTRX
Someone understanding the code could reverse the
process. To make it even more difficult to break the cipher
the way the columns are read off can be controlled by a key.
A key is a word or group of letters that is needed to read an
encrypted message. For example, the word "THUNDER" could be
used to further secure the above message within the columnar
transposition cipher. Each letter in the key would be given
a number equal to the order in which it appears in the alphabet.
Then the numbers are lined up over the message
placed in the same number of columns as the number of letters
in the key. Extra letters are added at the end to make the length
come out properly:
Then the columns are read off in the order of
the numbers to make the code:
YEYOC ZETET HXUOX MANETR
Even if you know that the message was encoded
using columnar transposition, it will not be easy to decode
without the keyword THUNDER which tells how many columns
were used and the order in which they were read off into the
Still, even this method of coding can be broken
by knowing the frequency certain letters appear in a language.
To counter this codemakers came up with ciphers that encode
letters as pairs. The following method is called digraphic
substitution. Let's use this method to encode just the first
word of our message: MEET.
the right are two matrixes of letters. The top left and bottom
right quadrants of each matrix have the alphabet written in
proper order with I and J sharing the same space to make things
come out evenly. The other two quadrants have the alphabets
in two different scrambled orders. By taking the first two letters
of MEET, ME we can create a box on the matrix
with the upper-left at M and lower-right at E (Look at the top
matrix). The other corners of the box represent the encoded
pair NX. For ET we get the encoded pair OB
(Shown on the bottom matrix). Notice that the pair of E's
in MEET now are represented by two totally different
letters in the code NXOB. This makes the E's hard
to find and the code difficult to break.
Encryption and Encoding Devices
All the ciphers we have discussed so far can be
encoded and decoded with a pencil and paper. As time went on,
mechanical devices were invented to make encryption and decryption
easier. One early device used by the Greeks was a rod on which
a belt was wrapped on an angle so it covered the rod from end-to-end.
A message was written on the belt along the length of the rod.
Then the belt was unwound from the stick and worn by the messenger.
When the messenger arrived at his destination, he would take
off the belt. When it was wound around another rod of the same
size the message would reappear.
Thomas Jefferson described a drum-like device
that was used to encode and decode messages. Jumbled alphabets
ran along rows the length of the device. The coder would pick
one row to be the plaintext and read the cipher off another
row matching the letters column by column. To decrypt the message
the decoder was required to know which number rows had been
A clever, but simple device was invented by Sir
Charles Wheatstone in 1867. This machine looked like a clock
face including the short and long hands. Instead of numbers
around the dial there were two alphabets, one running along
the outer edge and the other running a little further inside.
The outer alphabet was in proper order, while the inside one
was jumbled. The hands were connected by gears so that as the
person encrypting the message moved the big hand to a plaintext
letter, the inner hand moved to the corresponding cipher character.
The cipher character was written down, then the long hand moved
to the next plaintext letter. The hands were geared so the they
did not move at the same rate. This meant that while the first
E in a message might correspond to a cipher V,
the second E in the message would be a letter
different from V. This made figuring out the message
by using a frequency list difficult.
By the early part of the twentieth century, electro-mechanical
encryption machines were common. One famous device, called THE
ENIGMA, was used by the Germans during WWII. Despite it
being a fairly complicated machine with many gears, keys and
lights, it still used just a series of substitution ciphers
one after another to encode messages. By shifting the ciphers
by one letter each time a new letter was encoded, the builders
of the machine were able to minimize the chance that the frequency
of certain letters appearing in the code could be used to break
it. Even so, the messages generated by the ENIGMA machines
were broken continually by the Allies during the War and many
credit this feat of cryptoanalysis with shortening the conflict
and saving many lives.
The introduction of computers has revolutionized
crytography. Computers can be used to make ciphers far more
unbreakable than could ever be done with pencil and paper or
even a machine like the ENIGMA. Computers can also be
used to break codes that in the past might have seemed unbreakable.
So far, it is far easier for a computer to encrypt a message
than to break it.
Encryption is no longer the business of just government
and spies. The ability to safely encrypt communications is very
important to anyone who uses the internet. When somebody purchases
from an on-line store, they use a credit card number. The number
must be encrypted so that only the store can see it and it cannot
be intercepted by third parties that might use the number without
the cardholder's permission. Using the type of ciphers we've
discussed so far, this would be very difficult to do. The cipher
they use would need a key. How could both the computer on the
buyer's side and computer on the store's side know the key without
sending it across the internet where it could be intercepted?
The solution lies with a type of cipher that can
do what is known as public key encryption. These ciphers
don't just use one key, but two. One key is used to encrypt
a message, the other to decrypt it. The most important feature
of this type of cipher is that knowing the encryption key does
not help someone to know how to decrypt the message.
The transaction between the buyer and the bookstore
would go like this: The store's computer generates a pair of
keys (encryption and decryption, more commonly known as public
and private keys) and sends the public key to the buyer's
computer. The buyer's computer then uses that key to encrypt
the message. That message is sent across the internet to the
store's computer. The store's computer can then decrypt the
message using the private key. Anyone listening in on this transaction
would only see the public key and the encrypted message, not
enough information to find out what is in the text of the message.
Codes, ciphers and encrypts will continue to play
a greater role in our everyday lives as we continue into the
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