Cryptography Reference
In-Depth Information
Milan, Italy. In his younger years, he assisted his father who was a lawyer and
a mathematics lecturer primarily at the Platti foundation in Milan. Cardano
himself came to be known as one of the greatest mathematicians of his time.
He wrote more than 130 topics in his lifetime. The two that are best known for
his mathematical contributions are Liber de ludo aleae ,or Topic on Games of
Chance , considered to be the first topic on probability theory, and Ars Magna
(1545), considered to be one of the great topic in the history of algebra. The
ones of interest to us from a cryptographic perspective were his topics, De
Subtilitate (1550), and a follow-up called, De RerumVarietate (1556). In these
two topics, he introduced the idea of an autokey , meaning that the plaintext,
itself, is used as its own key. However, Cardano implemented the idea in a flawed
manner, which allowed for multiple possible decryptions as well as the fact that,
in his implementation, the receiver of the message was in no better position
than a cryptanalyst at trying to determine the first plaintext word, from which
there would be total decryption. Thus, the idea of an autokey has not been
attributed to Cardano. He is remembered for an invention of a steganographic
device, which we call the Cardano grille . Cardano's idea involved the use of a
metal (or other rigid substance) sheet consisting of holes about the height of a
written letter and of varying lengths. The sender of a message places the grill
on a piece of paper and writes the message through the holes. Then the grille is
removed and the message is filled in with some innocuous verbiage. Use of the
Cardano grille continued well into the seventeenth century, and has even popped
up in various places in modern times. Thus, it is the case that due to his flawed
idea for an autokey, he is remembered largely for his steganographic device. He
died on September 21, 1576, in Rome with his fame not attached to the greater
cryptographic record that he sought. That fame would go to another.
Blaise de Vigenere
Blaise de Vigenere (1523-1596) had his first contact with cryptography at
age 26 when he went to Rome on a two-year diplomatic mission. He familiar-
ized himself with the works of his predecessors, Alberti, Belaso, Cardano, and
Trithemius. His own work, published in 1585, containing his contributions to
cryptography, is called Traicte des Chiffres . Vigenere discussed steganographic
techniques, and a variety of cryptographic ideas. Among them was the idea for
an autokey polyalphabetic substitution cipher.
He employed the idea that Cardano had invented of using the plaintext as
its own key. However, he added something new, a priming key , which is a single
letter (known only to the sender and the legitimate receiver), that is used to
decipher the first plaintext letter, which would, in turn, be used to decipher the
second plaintext letter, and so on. To understand the details of how this works,
we use a Vigenere square, given on page 56, with the full 26-letter alphabet, as
opposed to Trithemius' use of 24. It rightfully deserves to be called a Trithemius
square, as the reader will note, but history has deemed it to have Vigenere's
name attached to it.
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