Cryptography Reference
In-Depth Information
a Greek historian and statesman. He invented a means of enciphering letters
into pairs of numbers as follows.
The Polybius Square
1 2 3 4 5
1
a b c d e
2
f g h ij k
3
l m n o p
4
q r s t u
5
v w x y z
Table 1.1
Label a 5 by 5 square with the numbers 1 through 5 for the rows and columns,
and string the English alphabet through the rows, considering “ij” as a single
letter, as given in Table 1.1.
Then, look at the intersection of any row and column (with row number
listed first and column number listed second) as the representation of the letter
in question. For instance,
k
is 25 and
q
is 41. Hence, the letters are plaintext
and the numbers are ciphertext. This device is called the
Polybius checkerboard
or
Polybius square
. Polybius' intended use of his square was to send messages
great distances by means of torches and hilltops. The sender would hold a torch
in each hand, then raise the torch in the right hand the number of times to signal
the row, and the torch in the left hand the number of times to signal the column.
There is no evidence that these were actually used in this fashion or any other in
ancient Greece. However, there are many variations of his cipher that have been
constructed. The reader may even concoct one by pairing different letters than
“ij”, and stringing the alphabet in a different way from the straightforward one
given in Table 1.1. One such interpretation of Polybius' cipher involved turning
the digits into sounds. A known application in the twentieth century was the
one developed by Russian prisoners who used
knocks
to convey speech. For
instance, using Table 1.1, a prisoner might knock on a wall twice, followed by
three knocks for the letter “h”, then proceed in this fashion to send a complete
message. Hence, this came to be known as the
knock cipher
.
Polybius' substitution cipher has found great acceptance among cryptogra-
phers up to modern times, who have used it as the basis for numerous ciphers.
We will mention some as we encounter them later in our cryptographic voyage.
Julius Caesar
Although the ancient Greeks made no claim to actually using any of the
substitution ciphers that they invented, the first use in both military and do-
mestic affairs of such a cipher is well documented by the Romans. In
The Lives
of the Twelve Caesars
[276, page 45], Suetonius writes of Julius Caesar: “.... if
there was occasion for secrecy, he wrote in cyphers; that is, he used the alpha-
bet in such a manner, that not a single word could be made out. The way to
decipher those epistles was to substitute the fourth for the first letter, as
d
for
a
, and so for the other letters respectively.” What is being described here is a
simple substitution cipher used by Julius Caesar. He not only used them in his
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