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Concept
Tabula recta
Summary
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 in 1508, and used in his Trithemius cipher.
The Trithemius cipher was published by Johannes Trithemius in his book Polygraphia, which is credited with being the first published printed 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 order of the letters in the target alphabet is 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 the Caesar cipher can be described in terms of the tabula recta.
The tabula recta uses a letter square with the 26 letters of the alphabet followed by 26 rows of additional letters, each shifted once to the left from the one above it. This, in essence, creates 26 different Caesar ciphers.
The resulting ciphertext appears as a random string or block of data. Due to the variable shifting, natural letter frequencies are hidden. However, if a codebreaker is aware that this method has been used, it becomes easy to break. The cipher is vulnerable to attack because it lacks a key, thus violating Kerckhoffs's principle of cryptology.
In 1553, an important extension to Trithemius's method was developed by Giovan Battista Bellaso, now called the Vigenère cipher. Bellaso added a key, which is used to dictate the switching of cipher alphabets with each letter. This method was misattributed to Blaise de Vigenère, who published a similar autokey cipher in 1586.
The classic Trithemius cipher (using a shift of one) is equivalent to a Vigenère cipher with ABCDEFGHIJKLMNOPQRSTUVWXYZ as the key. It is also equivalent to a Caesar cipher in which the shift is increased by 1 with each letter, starting at 0.
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