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:

Trimethius Tableau
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.