# Tabula recta

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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 cipher was published by Johannes Trithemius in his book Polygraphia, which is credited with being the first published work on cryptology[citation needed].

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.[2]

The resulting ciphertext appears as a random string or block of data. However, the letter frequencies are just shifted: If e is the most frequent letter in the cleartext and the shift is 3, then h will be the most frequent letter in the ciphertext. Especially 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's principle, a rule of cryptology.[2]

### Improvements

In 1553, an important extension to Trithemius's method was developed by Giovan Battista Bellaso called the Vigenère cipher.[3] 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).

In order to decrypt the classic Trithemius cipher (which is equivalent to a Vigenere cipher with ABCDEFGHIJKLMNOPQRSTUVWXYZ as key), one should locate the first letter to decrypt in the first row (second letter in the second row etc.) in Tabula recta and the letter in the matching column is the decrypted one. Assuming it is shifted by 1, and no key is used, the encrypted text: HFNOS would be decrypted to: HELLO (H->H, F->E, N->L, O->L, S->O ).

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 the entire message is encrypted.[4]

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.

Programmatically, the cipher is computable, assigning ${\displaystyle A=0,B=1...}$, then the encryption process is ${\displaystyle ciphertext=(plaintext+key)\!\!\!\!{\pmod {26}}}$. Decryption follows the same process, exchanging ciphertext and plaintext. key may be defined as the value of a letter from a companion ciphertext in a running key cipher, a constant for a Caesar cipher, or a zero-based counter with some period in Trithemius's usage.[4]

## References

### Citations

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

### Sources

• Salomon, David (2005). Coding for Data and Computer Communications. Springer. ISBN 0-387-21245-0.
• Salomon, David (2003). Data privacy and security. Springer. ISBN 0-387-00311-8.
• King, Francis X. (1989). Modern Ritual Magic: The Rise of Western Occultism (2nd ed.). Prism Press. ISBN 1-85327-032-6.
• Kahn, David (1996). The Codebreakers. Simon and Schuster. ISBN 0-684-83130-9.