How Code Breakers Work

Introduction to How Code Breakers Work

Information is an important commodity. Nations, corporations and individuals protect secret information with encryption, using a variety of methods ranging from substituting one letter for another to using a complex algorithm to encrypt a message. On the other side of the information equation are people who use a combination of logic and intuition to uncover secret information. These people are cryptanalysts, also known as code breakers.

Carston Müller, SXC Binary code is the basis for many modern ciphers.

A person who communicates through secret writing is called a cryptographer. Cryptographers might use codes, ciphers or a combination of both to keep messages safe from others. What cryptographers create, cryptanalysts attempt to unravel.

Throughout the history of cryptography, people who created codes or ciphers were often convinced their systems were unbreakable. Cryptanalysts have proven these people wrong by relying on everything from the scientific method to a lucky guess. Today, even the amazingly complex encryption schemes common in Internet transactions may have a limited useful lifetime -- quantum computing might make solving such difficult equations a snap.

You Say Cryptology, I Say CryptographyIn English, the words cryptology and cryptography are often interchangeable -- both refer to the science of secret writing. Some people prefer to differentiate the words, using cryptology to refer to the science and cryptography to refer to the practice of secret writing.

Polybius Squares and Caesar Shifts

Although historical findings show that several ancient civilizations used elements of ciphers and codes in their writing, code experts say that these examples were meant to give the message a sense of importance and formality. The person writing the message intended for his audience to be able to read it.

The Greeks were one of the first civilizations to use ciphers to communicate in secrecy. A Greek scholar named Polybius proposed a system for enciphering a message in which a cryptographer represented each letter with a pair of numbers ranging from one to five using a 5-by-5 square (the letters I and J shared a square). The Polybius Square (sometimes called the checkerboard) looks like this:

A cryptographer would write the letter "B" as "12". The letter O is "34". To encipher the phrase "How Stuff Works," the cryptographer would write "233452 4344452121 5234422543." Because he replaces each letter with two numbers, it's difficult for someone unfamiliar with the code to determine what this message means. The cryptographer could make it even more difficult by mixing up the order of the letters instead of writing them out alphabetically.

Julius Caesar invented another early cipher -- one that was very simple and yet confounded his enemies. He created enciphered messages by shifting the order of the alphabet by a certain number of letters. For example, if you were to shift the English alphabet down three places, the letter "D" would represent the letter "A," while the letter "E" would mean "B" and so forth. You can visualize this code by writing the two alphabets on top of one another with the corresponding plaintext and cipher matching up like this:

Plaintext

a

b

c

d

e

f

g

h

i

j

k

l

m

Cipher

D

E

F

G

H

I

J

K

L

M

N

O

P

Plaintext

n

o

p

q

r

s

t

u

v

w

x

y

z

Cipher

Q

R

S

T

U

V

W

X

Y

Z

A

B

C

Notice that the cipher alphabet wraps around to "A" after reaching "Z." Using this cipher system, you could encipher the phrase "How Stuff Works" as "KRZ VWXII ZRUNV."

Both of these systems, the Polybius Square and the Caesar Shift, formed the basis of many future cipher systems.

In the next section, we'll look at a few of these more advanced methods of encryption.

Deciphering the LanguageTo encipher a message means to replace the letters in the text with the replacement alphabet. The readable message is called the plaintext. The cryptographer converts the plaintext into a cipher and sends it on. The recipient of the message uses the proper technique, called the key, to decipher the message, changing it from a cipher back into a plaintext.

The Trimethius Tableau

After the fall of the Roman Empire, the Western world entered what we now call the Dark Ages. During this time, scholarship declined and cryptography suffered the same fate. It wasn't until the Renaissance that cryptography again became popular. The Renaissance was not only a period of intense creativity and learning, but also of intrigue, politics, warfare and deception.

Cryptographers began to search for new ways to encipher messages. The Caesar Shift was too easy to crack -- given enough time and patience, almost anyone could uncover the plaintext behind the ciphered text. Kings and priests hired scholars to come up with new ways to send secret messages.

One such scholar was Johannes Trimethius, who proposed laying out the alphabet in a matrix, or tableau. The matrix was 26 rows long and 26 columns wide. The first row contained the alphabet as it is normally written. The next row used a Caesar Shift to move the alphabet over one space. Each row shifted the alphabet another spot so that the final row began with "Z" and ended in "Y." You could read the alphabet normally by looking across the first row or down the first column. It looks like this:

As you can see, each row is a Caesar Shift. To encipher a letter, the cryptographer picks a row and uses the top row as the plaintext guide. A cryptographer using the 10th row, for example, would encipher the plaintext letter "A" as "J."

Trimethius didn't stop there -- he suggested that cryptographers encipher messages by using the first row for the first letter, the second row for the second letter, and so on down the tableau. After 26 consecutive letters, the cryptographer would start back at the first row and work down again until he had enciphered the entire message. Using this method, he could encipher the phrase "How Stuff Works" as "HPY VXZLM EXBVE."

Trimethius' tableau is a good example of a polyalphabetic cipher. Most early ciphers were monoalphabetic, meaning that one cipher alphabet replaced the plaintext alphabet. A polyalphabetic cipher uses multiple alphabets to replace the plaintext. Although the same letters are used in each row, the letters of that row have a different meaning. A cryptographer enciphers a plaintext "A" in row three as a "C," but an "A" in row 23 is a "W." Trimethius' system therefore uses 26 alphabets -- one for each letter in the normal alphabet.

In the next section, we'll learn how a scholar named Vigenère created a complex polyalphabetic cipher.

The Vigenère Cipher

In the late 1500s, Blaise de Vigenère proposed a polyalphabetic system that is particularly difficult to decipher. His method used a combination of the Trimethius tableau and a key. The key determined which of the alphabets in the table the decipherer should use, but wasn't necessarily part of the actual message. Let's look at the Trimethius tableau again:

Let's assume you are encrypting a message using the key word "CIPHER." You would encipher the first letter using the "C" row as a guide, using the letter found at the intersection of the "C" row and the corresponding plaintext letter's column. For the second letter, you'd use the "I" row, and so on. Once you use the "R" row to encipher a letter, you'd start back at "C". Using this key word and method, you could encipher "How Stuff Works" this way:

Key

C

I

P

H

E

R

C

I

P

H

E

R

C

Plain

H

O

W

S

T

U

F

F

W

O

R

K

S

Cipher

J

W

L

Z

X

L

H

N

L

V

V

B

U

Your enciphered message would read, "JWL ZXLHN LVVBU." If you wanted to write a longer message, you'd keep repeating the key over and over to encipher your plaintext. The recipient of your message would need to know the key beforehand in order to decipher the text.

Vigenère suggested an even more complex scheme that used a priming letter followed by the message itself as the key. The priming letter designated the row the cryptographer first used to begin the message. Both the cryptographer and the recipient knew which priming letter to use beforehand. This method made cracking ciphers extremely difficult, but it was also time-consuming, and one error early in the message could garble everything that followed. While the system was secure, most people found it too complex to use effectively. Here is an example of Vigenère's system -- in this case the priming letter is "D":

Key

D

H

O

W

S

T

U

F

F

W

O

R

K

Plain

H

O

W

S

T

U

F

F

W

O

R

K

S

Cipher

K

V

K

O

L

N

Z

K

B

K

F

B

C

To decipher, the recipient would first look at the first letter of the encrypted message, a "K" in this case, and use the Trimethius table to find where the "K" fell in the "D" row -- remember, both the cryptographer and recipient know beforehand that the first letter of the key will always be "D," no matter what the rest of the message says. The letter at the top of that column is "H." The "H" becomes the next letter in the cipher's key, so the recipient would look at the "H" row next and find the next letter in the cipher -- a "V" in this case. That would give the recipient an "O." Following this method, the recipient can decipher the entire message, though it takes some time.

The more complex Vigenère system didn't catch on until the 1800s, but it's still used in modern cipher machines [source: Kahn].

In the next section, we'll learn about the ADFGX code created by Germany during World War I.

ADFGX Cipher

After the invention of the telegraph, it was now possible for individuals to communicate across entire countries instantaneously using Morse code. Unfortunately, it was also possible for anyone with the right equipment to wiretap a line and listen in on exchanges. Moreover, most people had to rely on clerks to encode and decode messages, making it impossible to send plaintext clandestinely. Once again, ciphers became important.

Germany created a new cipher based on a combination of the Polybius checkerboard and ciphers using key words. It was known as the ADFGX cipher, because those were the only letters used in the cipher. The Germans chose these letters because their Morse code equivalents are difficult to confuse, reducing the chance of errors.

The first step was to create a matrix that looked a lot like the Polybius checkerboard:

Cryptographers would use pairs of cipher letters to represent plaintext letters. The letter's row becomes the first cipher in the pair, and the column becomes the second cipher. In this example, the enciphered letter "B" becomes "AD," while "O" becomes "FG." Not all ADFGX matrices had the alphabet plotted in alphabetical order.

Next, the cryptographer would encipher his message. Let's stick with "How Stuff Works." Using this matrix, we'd get "DFFGXD GFGGGXDADA XDFGGDDXGF."

The next step was to determine a key word, which could be any length but couldn't include any repeated letters. For this example, we'll use the word DEUTSCH. The cryptographer would create a grid with the key word spelled across the top. The cryptographer would then write the enciphered message into the grid, splitting the cipher pairs into individual letters and wrapping around from one row to the next.