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 11

domestic affairs as noted above by Seutonius, but also in his military affairs as
he documented in his own writing of the Gallic Wars .

Table 1.2
Plain a b c d e f g h i j k l m
Cipher D E F G H I J K L M N O P
Plain n o p q r s t u v w x y z
Cipher Q R S T U V W X Y Z A B C

This substitution cipher is even easier to use than that invented by Polybius,
which we discussed above. In this case there is merely a shift to the right of
three places of each plaintext letter to achieve the ciphertext letters. This is
best illustrated by Table 1.2.
Table 1.2 is an example of a cipher table , which is defined to be a table
of (ordered) pairs of symbols ( p, c ), where p is a plaintext symbol and c is its
ciphertext equivalent. For instance, in the Caesar cipher table, ( b, E ) is the pair
consisting of the plaintext letter b together with its ciphertext equivalent E .
An example of a cryptogram made with the Caesar cipher is: brutus becomes
EUXWXV . Also, this simple type of substitution cipher is called a shift cipher .
Moreover, the mechanism for enciphering in the Caesar cipher is a shift to the
right of three letters. So the value 3 is an example of a key , which we may regard,
in general, as a shared secret between the sender and the recipient, which unlocks
the cipher. So 3, in this case, is the enciphering key . Since shifting 3 units left
unlocks the cipher, then 3 is also the deciphering key . This is an example of
a symmetric-key cryptosystem , namely, where one can “easily determine” the
deciphering key from the enciphering key and vice versa. (We will formalize this
notion in Chapter 3, when we study symmetric-key cryptosystems in detail,
but for now, this will suGce.) Thus, the key must be kept secret from all
unauthorized parties. (This is distinct from a cryptosystem, about which we
will learn in Chapter 4, where the enciphering key can be made publicly known!
Yet, nobody can determine the deciphering key from it.) There is a method of
employing the Caesar cipher with numbers that simplifies the process. Consider
Table 1.3 that gives numerical values to the English alphabet.
Now, if we take zebra as the plaintext, the numerical equivalent is
25 , 4 , 1 , 17 , 0, and using the Caesar cipher we add 3 to each number to get
the ciphertext. However, notice that when we get to x, y, z , adding 3 will take
us beyond the highest value of 25. The Caesar cipher, Table 1.2, actually loops
these three letters back to A, B, C .

a b c d e f g h i j k l m
0 1 2 3 4 5 6 7 8 9 10 11 12
n o p q r s t u v w x y z
13

Table 1.3

14 15 16 17 18 19 20 21 22 23 24 25

Hence, what we have to do here is to throw away any multiples of 26 and
treat them as zeroes in our addition, and only accept nonnegative numbers (the