Cryptography Reference
In-Depth Information
Employing standard alphabets in his use of a keyphrase, Belaso created
a polyalphabetic cipher with much greater flexibility than that of Alberti or
Trithemius. With this use of a keyphrase, Belaso ensured that, instead of re-
peating the enciphering of each letter with 24 standard cipher alphabets, as
Trithemius proposed, the key could be changed at will. For example, if the key
were compromised in some fashion, it could be discarded and a new one issued
to, say, diplomats of the day for their correspondence. Even with keys of length
13, as in the above keyphrase from Belaso, there are 24
13
possible encipherments
of a given plaintext letter, more than a hundred quadrillion choices. Quite an
advancement! Nevertheless, however prodigious this contribution seems to be,
it would be for another individual to put together all the pieces in order to
create the first forerunner of a modern polyalphabetic cipher.
Porta and Cardano
Giovanni Battista Porta (1535-1615) was born in Naples, Italy, in 1535.
At the age of 22, he published his first topic,
Magia Naturalis
,or
Natu-
ral Magic
, a text on “experimental magic”. However, in 1563, he pub-
lished
De Furtivis LiterarumNotis
, which contained the cryptographic ad-
vances in which we are interested. In this topic is the first appearance of a
digraphic cipher
, meaning a cipher in which two signs represent a single symbol.
(Later, we will see how this notion was rein-
vented in the twentieth century by Lester Hill
using only elementary matrices (page 111), and
how the first
literal
digraphic cipher was in-
vented much later. Here Porta is using signs
rather than letters.) Moreover, he introduced
some of the modern fundamentals of cryptog-
raphy, namely a separation of
transposition ci-
phers
and
substitution ciphers
, as well as
sym-
bol substitution
(substituting an unusual symbol
for a letter). Porta also looked at methods, al-
beit elementary by modern standards, of crypt-
analyzing polyalphabetic ciphers. In fact, in a
second edition of his topic, published in 1602,
Porta added a chapter with these cryptanalytic
observations. Although Porta also ultimately
did glue together the ideas of Alberti, Belaso,
and Trithemius, by adding mixed alphabets and
shifts, to produce what we consider to be a ba-
sic polyalphabetic substitution cipher, there was
work to be done to make polyalphabetic ciphers
more secure, the essence of which was in how
the key was used.
The first to see how this could be accomplished was Girolamo Cardano
(1501-1576). Cardano was born on September 24, 1501, in Pavia, Duchy of
Figure 1.25: Natural Magic.
Image courtesy of Scott Davis:
http://homepages.tscnet.com
/omard1/jportat5.html
.
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