# Tabula recta

Tabula recta

In cryptography, the tabula recta (from Latin tabula rēcta) is a square table of alphabets, each row of which is made by shifting the previous one to the left. The term was invented by the German author and monk Johannes Trithemius[1] in 1508, and used in his Trithemius cipher.

## Trithemius cipher

The Trithemius was published by Johannes Trithemius in his book Polygraphia, which is credited with being the first published work on cryptology.

Trithemius used the tabula recta to define a polyalphabetic cipher, which was equivalent to Leon Battista Alberti's cipher disk except that the alphabets are not mixed. The tabula recta is often referred to in discussing pre-computer ciphers, including the Vigenère cipher and Blaise de Vigenère's less well-known autokey cipher. All polyalphabetic ciphers based on Caesar ciphers can be described in terms of the tabula recta.

It uses a letter square with the 26 letters of the alphabet following 26 rows of additional letters, each shifted once to the left. This creates 26 different Caesar ciphers.[1]

This method removes the letter frequencies from the ciphertext, making it appear as a random string or block of data. However, if a person is aware that this method is being used, it becomes easy to break. The cipher is vulnerable to attack because it lacks a key, which is said to break Kerckhoffs' principle, a rule of cryptology.[1]

### Improvements

In 1553, an important extension to Trithemius's method was developed by Giovan Battista Bellaso called the Vigenère cipher.[2] Bellaso added a key to switch cipher alphabets every letter. This method was misattributed to Blaise de Vigenère, who published a similar autokey cipher in 1586.

## Usage

Each alphabet is shifted one letter to the left from the one above it. This forms 26 rows of shifted alphabets, ending with Z (as shown in image).

Data is encrypted by switching each letter of the message with the letter directly below, using the first shifted alphabet. The next letter is switched by using the second shifted alphabet, and this continues until you have encrypted the entire message.[3]

In order to encrypt a plaintext, one locates the row with the first letter to be encrypted, and the column with the first letter of the key. The letter where the line and column cross is the ciphertext letter.

## References

### Citations

1. ^ a b c Salmon, Data privacy, page 63
2. ^ Salomon, Coding for data, page 249
3. ^ Kahn, page 136