From the Riddles of Ancient Egypt to Cryptography in the Renaissance — 3500 Years in the Making - Codes: The Guide to Secrecy from Ancient to Modern Times - page 49

In Figure 1.22 the plaintext letter z is enciphered as V , so in this setting (one
of the 26 possible cipher alphabets), the plaintext zebra , for instance, would be
enciphered as VZLYD . However, there is nothing new at this juncture that is
any different from, say, the Caesar cipher with the cipher alphabet having the
letter c below the Z . Alberti had an idea, however (which is why he wanted
the inner circle to be able to rotate). This idea would revolutionize the forward
movement of cryptological development. After a random number of plaintext
words had been enciphered, usually three or four, Alberti would move the inner
disk to a new setting. Hence, he would now be using a new cipher alphabet.
Suppose that he moved the inner circle so that z sits over K . Then zebra would
be enciphered as KADTR , a new ciphertext for the same plaintext as above since
we have a new cipher alphabet. This is polyalphabeticity in action, literally!
In fact, with his cipher disk, Alberti invented the first polyalphabetic cipher in
history. Yet, he did not stop there.
Alberti had 20letters, as depicted in Figure 1.22 1.5 and including the num-
bers 1 through 4 in the outer ring of his original disk. In a book, he used
these numbers in two-, three-, and four-digit sets from 11 to 4444 yielding 336
(= 4 2 +4 3 +4 4 ) codegroups. Beside each digit he would write a phrase such as
“Launch the attack” for the number 21, say. Then, with the setting in Figure
1.22, the code group 21 is enciphered as &P , enciphered code . Alberti was the
first to discover it, and it is a testimony to his being centuries ahead of his time
that enciphered code, when it was rediscovered at the end of the nineteenth
century, was simpler than that of Alberti!
Johannes Trithemius
Polyalphabeticity had another ally, and we have already met him in Section
1.3. In early 1508, Trithemius turned himself to the task of writing a book
dedicated solely to a serious cryptographic analysis, called Polygraphia , with
the o G cial title, Polygraphiae libri sex, Ioaonnis Trihemii abbatis Peopolitani,
quondam Spanheimensis, ad Maximilianum Caesarem ,or Six Topics of Polyg-
raphy, by Johannes Trithemius, Abbot at Wurzburg, formerly at Spanheim, for
the Emperor Maximilian . However, Trithemius died on December 15, 1516, in
Wurzburg before the topic was published. In July of 1518 it finally went to press,
and was reprinted (and plagiarized) many times after that. Polygraphia can be
said to be the first printed book on cryptography. In his book, he invented a
cipher where each letter was represented as a word taken from a sequence of
columns. The resulting sequence of words turned out to be a legitimate prayer.
Perhaps more importantly, from the viewpoint of the advancement of cryptog-
raphy, he also described a polyalphabetic cipher . Another way to think of such
a cipher is that there is more than one enciphering key, namely, that a given
symbol may be encrypted in different ways depending upon where it sits in the
plaintext. An accepted modern form for displaying this type of cipher is a rect-
angular substitution table, abo ut which we will learn a great deal more as we
1.5 This excludes the letters h , k , and y , deemed to be unnecessary, and since j , u , and w
were not part of his alphabet, this left 20 letters. The inner circle consists of the 24 letters of
the Latin alphabet, put in the cells at random, including & .