The Code Work
When you were a kid, did you have a "Captain
Midnight" decoder ring? With it, you could send messages to a friends that
no one else could read. Or perhaps you remember using special symbols to write
notes to your "squeeze" in class. If the note was intercepted , your
teacher, could learn nothing about your romance.
In more serious uses, codes and ciphers are used by our
military and diplomatic forces to keep confidential information from
unauthorized eyes. Businesses also send data that has been encoded to try and
protect trade secrets and back-room deals. After all, you wouldn't want your competitor
to know that you were about to acquire their company with a leveraged buy-out.
For a cipher to be useful, several things must be known
at both the sending and receiving ends.
- The algorithm or method used
to encipher the original message (known as the plaintext).
- The key used
with the algorithm to allow the plaintext to be both enciphered and
deciphered.
- The period or time during
which the key is valid.
By way of analogy, to get into your home you would put a
key in a lock to open the door. This process (the use of a key and a lock) is
the method or algorithm. Now this method only works if you have the proper key
to stick in the lock, and your key will be valid only as long as you are the
resident of the particular abode. The next resident will have the locks changed
to a different key to make sure that you cannot enter even though you may know
the method.
The selection of the above three items - algorithm, key
and period - depend on your needs. If you are in the battlefield and are
receiving current tactical data, you want an algorithm that makes it easy to
decipher the message in the heat of battle. On the other hand, you must also
assume that your opponent has intercepted your enciphered message and is busy
trying to break it. Therefore you must choose an algorithm (method) that is
complicated enough so that by the time your opponent figures it out, the data
will be worthless. The easier the algorithm you choose, the more often you will
have to change the key that unlocks the code - if you want to keep your enemy
in the dark.
Ciphers are broken into two main categories; substitution
ciphers and transposition ciphers. Substitution ciphers replace letters in the
plaintext with other letters or symbols, keeping the order in which the symbols
fall the same. Transposition ciphers keep all of the original letters intact,
but mix up their order. The resulting text of either enciphering method is
called the ciphertext. Of course, you can use both methods, one after the
other, to further confuse an unintended receiver as well. To get a feel for
these methods, let's take a look at some ciphers.
Substitution ciphers and decoder rings
We use substitution ciphers all the time. (Actually,
substitution ciphers could properly be called codes in most cases.) Morse code,
shorthand, semaphore, and the ASCII code with which these characters are being
stored in inside my Macintosh are all examples. (ASCII stands for American
Standard Code for Information Interchange, just in case you're interested.) The
only difference between these and the spy codes is that the above examples are
standardized so that everybody knows them.
The Captain Midnight decoder ring (which is an
"encoder" ring as well) allows you to do a simple substitution
cipher. It usually has two concentric wheels of letters, A through Z. You
rotate the outside ring and substitute the letters in your message found on the
outside ring with the letters directly below on the inside ring (see diagram).
Here, the algorithm is to offset the alphabet and the key is the number of
characters to offset it. Julius Caesar used this simple scheme, offsetting by 3
characters (He would have put the "A" on the outer ring of letters
over the "D" on the inner ring if he had owned a Captain Midnight
decoder ring.)
The word "EXPLORATORIUM" thus becomes "HASORUDWRULXP". Such a scheme was easily broken and showed a certain level of naivete on Caesar's part concerning the enemy's intelligence.
The word "EXPLORATORIUM" thus becomes "HASORUDWRULXP". Such a scheme was easily broken and showed a certain level of naivete on Caesar's part concerning the enemy's intelligence.
Substitution cipher wheels
Click here to
download a copy of the cypher wheels (12k PDF). Copy and cut out the
two wheels. Place the smaller wheel on top of the larger wheel and rotate them
so your "key letter" on the small wheel is beneath the "A"
of the large wheel. Now you can encipher your plaintext and pass it to your
friend who knows the proper key letter.
You could make your ciphertext a little tougher to decode
if you threw 26 pieces of paper into a hat, each with a letter of the alphabet
written on it, drew them out one at a time, and put them side-by-side under a
normal alphabet. The result might look like this (I just used the order of the
keys on my keyboard, so you might call this a "Qwerty" code):
Plaintext letter
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Ciphertext letter
Q W E R T Y U I O P A S D F G H J K L Z X C V B N M
You can construct a secret message from the above table.
Every time you see an "I" you would substitute the "O"
beneath and so on for the other characters. The message "Meet me after
school behind the gym," would read
"DTTZ DT QYZTK LEIGGS WTIOFR ZIT UND."
Word lengths - especially the short words - give great
clues as to the nature of the code (see frequency charts). To help conceal your
message, ignore the spaces and break the message up into equal-sized chunks.
Five letters are customary in the spy biz, so your message comes out like this
(Note that an extra "dummy" character "M" is added at the
end to make it come out with a 5-letter group. Your recipient should have no
trouble with the extra character.):
DTTZD TQYZT KLEIG GSWTI OFRZI TUNDM
Another popular system called a diagrammatic cipher, used
by many children in school, substitutes symbols for letters instead of other
letters. This system is, in essence, the same as the letter substitution
system, but it's easier to remember than 26 randomly picked letters. It uses
the tic-tac-toe boards and two X's as shown below.
Even though it looks like undecipherable outer-space
alien text, this would take an arm-chair cryptologist only about 10 minutes or
less to figure out. Why? Given enough ciphertext, certain patterns become
obvious. Notice how often the empty four-sided box appears: six times out of a
total of 29 characters or about 20% of the time. This would immediately
indicate that the empty box was almost certainly the symbol for "E,"
the most frequently used letter in English. Other letters can also be
determined by their frequency and by their association with other nearby
characters (see "Frequencies"). Almost all substitution ciphers are open
to this kind of analysis.
Francis Bacon created one of the more interesting
substitution ciphers. He used two different type faces slightly differing in
weight (boldness). He broke up his ciphertext into 5 character groups, each of
which would represent one character in his plaintext. Depending on which
characters of the group were bold, one could determine the plaintext character
using the following table (* stands for a plain character and B for a bold
character)
A=***** G=**BB* M=*BB** S=B**B* Y=BB***
B=****B H=**BBB N=*BB*B T=B**BB Z=BB**B
C=***B* I=*B*** O=*BBB* U=B*B**
D=***BB J=*B**B P=*BBBB V=B*B*B
E=**B** K=*B*B* Q=B**** W=B*BB*
F=**B*B L=*B*BB R=B***B X=B*BBB
Our same secret message as above would appear thusly
(Bacon's bold and plain characters were less obvious than those below):
To be
or not to be that is the question.
Whether
'tis nobler in the mind to
suffer
the slings and arrows of
outrageous
fortune or to take arms
against
a sea of troubles and by
opposing end them?
To decipher, we just break the characters into groups of
5 and use the key above to find the plaintext message.
M E
E T M
E B E
Tobeo rnott obeth atist
heque stion Wheth ertis
H
I N D
T H E
G
noble rinth emind tosuf
ferth eslin gsand arrow
Y M
A F T
E R S
sofou trage ousfo rtune
ortot akear msaga insta
C H
O O L
seaof troub lesan dbyop posin
gendt hem?
Transposition ciphers
Going back to your school days, oo-day oo-yay emember-ray
ig-pay atin-lay? Pig-latin is a form of transposition cipher where the original
letters are kept intact (albeit with the addition of the suffix
"ay"), but rearranged in some way.
Going back way before your school days, to the 5th
century B.C., the Spartans used an interesting transposition cipher called a scytale.
The scytale utilized a cylinder with a ribbon wrapped helically around it from
one end to the other. The message was written across the ribbons, and then
unwrapped from the cylinder. Only someone with an identical diameter cylinder
could re-wrap and read the message.
The scytale depended on a piece of hardware, the
cylinder, which if captured by the enemy, compromised the whole system. Also,
the receiver could lose or break the cylinder and therefore lose the ability to
decipher any message. It would be better if the method were completely
"intellectual" and could be remembered and used without resorting to
a physical device.
Since both the sender and receiver of a transposed
ciphertext must agree on and remember this algorithm or method for enciphering
and deciphering, something easy would be nice. Since geometrical figures are
easy to remember, they serve as the basis for a whole class of transposition
ciphers. Let's put our message into the shape of a box. Since there are 29
characters, we'll add a dummy ("O") to make 30 and write the message
in a six by five box.
M E E T M E
A F T E R S
C H O O L B
E H I N D T
H E G Y M O
We can now transcribe the message by moving down the
columns instead of across the rows. Once again we'll break the characters into
groups of five to give no clues about word sizes. The result looks like this :
MACEH EFHHE ETOIG TEONY MRLDM ESBTO
The real variety begins when you realize that you don't
have to write your plaintext into the box row by row. Instead, you can follow a
pattern that zig-zags horizontally, vertically or diagonally, or one that
spirals in or spirals out (clockwise or counterclockwise), or many other
variations (see diagram below).
Once you've put the text in the chosen form using one
route, you can then encipher it by choosing a different route through the text.
You and your partner just have to agree on the reading route, the transcription
(enciphering) route, and the starting point to have yourselves a system. These
systems are called route transcriptions.
Here's our message again. The reading route spirals
counterclockwise inward, starting at the lower right corner (left diagram). The
transcription route (right diagram) is zig-zag diagonal starting at the lower
left corner. The ciphertext becomes:
EAMTN FTDIE EHOTE RHMEM BYESC GLOHO
To decipher, you fill the in box following the zig-zag
route and read the message using the spiral route.
Another type of transposition cipher uses a key word or
phrase to mix up the columns. This is called columnar transposition. It works
like this: First, think of a secret key word. Ours will be the word SECRET.
Next, write it above the columns of letters in the square, and number the
letters of the key word as they would fall if we placed them in alphabetical
order. (If there are duplicate letters, like the "E", they are
numbered from left to right.)
5 2 1 4 3 6
S E C R E T
M E E T M E
A F T E R S
C H O O L B
E H I N D T
H E G Y M O
Now write the columns down in the order indicated by the
numbers. The resulting ciphertext looking like this:
ETOIG EFHHE MRLDM TEONY MACEH ESBTO
As you can see, this is just a different arrangement of
the previous ciphertext, but at least it isn't in some regular pattern. We
could have easily made it a little more difficult by filling the square
following a more complicated path. We could also use a geometric shape other
than a rectangle and combine substitution and transposition. The only problem
that might occur is that the deciphering may become so complicated that it will
remain a secret at the receiving end forever! Come to think of it, she never
did meet me behind the gym...
Frequencies
Order of frequency of single letters:
E T O A N I R S H D L C W U M F YG P B V K X Q J Z
E T O A N I R S H D L C W U M F YG P B V K X Q J Z
Order of frequency of digraphs (two letter
combinations):
th er on an re he in ed nd ha at en es of or nt ea ti to it st io le is ou ar as de rt ve
th er on an re he in ed nd ha at en es of or nt ea ti to it st io le is ou ar as de rt ve
Order of frequency of trigraphs:
the and tha ent ion tio for nde has nce edt tis oft sth men
the and tha ent ion tio for nde has nce edt tis oft sth men
Order of frequency of most common doubles:
ss ee tt ff 11 mm oo
ss ee tt ff 11 mm oo
Order of frequency of initial letters:
T O A W B C D S F M R H I Y E G L N P U J K
T O A W B C D S F M R H I Y E G L N P U J K
Order of frequency of final letters:
E S T D N R Y F L O G H A R M P U W
E S T D N R Y F L O G H A R M P U W
One-letter words:
a, I, 0.
a, I, 0.
Most frequent two-letter words:
of, to, in, it, is, be, as, at, so, we, he, by, or, on, do, if, me, my, up, an, go, no, us, am...
of, to, in, it, is, be, as, at, so, we, he, by, or, on, do, if, me, my, up, an, go, no, us, am...
Most frequent three-letter words:
the, and, for, are, but, not, you, all, any, can, had, her, was, one, our, out, day, get, has, him, his, how, man, new, now, old, see, two, way, who, boy, did, its, let, put, say, she, too, use...
the, and, for, are, but, not, you, all, any, can, had, her, was, one, our, out, day, get, has, him, his, how, man, new, now, old, see, two, way, who, boy, did, its, let, put, say, she, too, use...
Most frequent four-letter words:
that, with, have, this, will, your, from, they, know, want, been, good, much, some, time, very, when, come, here, just, like, long, make, many, more, only, over, such, take, than, them, well, were...
that, with, have, this, will, your, from, they, know, want, been, good, much, some, time, very, when, come, here, just, like, long, make, many, more, only, over, such, take, than, them, well, were...
Comments
Post a Comment