Trithemius, Bellaso, Vigenère Origins of the Polyalphabetic Ciphers

The purpose of this paper is to show how polyalphabetic ciphers developed, using primary sources, from Trithemius and Bellaso to Vigenère, including the recent discovery of the Bellaso 1552 zero cipher.


Primary Sources
Doing research using only primary sources is of course impossible, except for a few limited cases. A great number of mistakes, small or big, arise from using secondary sources; errors of transcription, translation, interpretation accumulate, migrate from book to book, even of the most authoritative authors, and are very hard to die. I will try to use this method about the origin of poly-alphabetic ciphers. Nowadays Google Books, great libraries and others publish more and more digitized original books, making possible the use of primary sources without the burden of visiting remote libraries.
The rst polyalphabetic cipher published in print (1518) is the one of abbot Trithemius, the Recta Tabula present in the Libri Polygraphiae VI. 1 The second well known polyalphabetic cipher is the one of G.B. Bellaso published in Venice in 1553, which for the rst time introduces what today is called a password or pass-phrase as the key. Bellaso writes in the preface this cipher was a remake of a 1552 cipher printed on leaets; and it was one of these 1 As a matter of fact Leon Battista Alberti had written a treatise on ciphers before 1470, proposing an encrypting disk and a few ways to use it, but the book was kept secret for about a century and published in Venice only in 1568. This is a common problem with many ciphers, kept secret for years or even centuries. leaets the one I found in November 2018 in the State Archives of Venice. 2 See gure 1.
The best known polyalphabetic cipher remains the one of Blaise de Vigenère, published in 1586. Vigenère in his work mentions both Trithemius and Bellaso, and merges their ideas into his square table.
These ciphers are all basically square tables, as shown in the gure at the end of this paper (7). One should use the rst alphabet to encrypt the rst letter, the second alphabet to encrypt the second letter and so on. So the same plaintext letter may be encrypted using dierent ciphertext letters, thus confusing frequency analysis.   So Vigenère converts Bellaso's cipher into a Trithemius like square, using a key word; it is simpler to use than Bellaso's and safer than Trithemius's. You look for the letter of the plaintext (p) among the column labels and the letter of the key (k) among the row labels or viceversa, the operation is commutative. The cipher (c) is anyway at the crossing of column and row. want to express: and the perpendiculars to the left side descending downward, for the keys. I have put here two rows: one in black, the other in red, to show that the alphabets of the text, as well as those of the keys, can be shifted and changed in as many sorts as one wants [...] 9 (Vigenere, 1587) p. 49v. The table has red headings and black headings. One can shift the alphabets of s steps; starting with the letter E the shift is of 4 steps.
Indeed it is a simplication, without the shifting, of the table in gure 6, the one that became popular as Vigenère's table: Mathematically, assigning to every letter his ordinal number in the alphabet, stating from 0, the encoding procedure is a simple arithmetic addition modulo 20 (for a 20 letters alphabet).
The introduction of the shifting improved the security only a bit, mathematically it just removes the constant s from the addition: c = p + k mod 20 Security depends mainly on the length of the key. The longer the key, the safer the cipher. 6 Conclusion Figure 7 is the best summary of this paper, showing at a glance the evolution of these ciphers, here written in square table form for better comparison. The classic Vigenère table is a Trithemius like cipher, using a Bellaso's like keyword.