Cryptology - Unofficial St. Mary's College of California Web Site

Chapter 3
The Introduction
of Numbers
“We shall see that cryptography is more than a
subject permitting mathematical formulation, for
indeed it would not be an exaggeration to state
that abstract cryptography is identical with abstract
mathematics.”
A. Adrian Albert, 1941
Professor of Mathematics
University of Chicago
The Caesar Ciphers we studied in Chapter 1 were very easy to use, and
seemed to offer some secrecy. But we quickly found several ways to decrypt
any message enciphered in this manner. What should we try to regain some
secrecy The Caesar method of “shift by three” or “add three” having failed,
to regain some secrecy we are going to try “multiply by three.”
Before we can study this new method, we need to first carefully analyze
our Caesar ciphers. Suppose our message is Stop, Turn Back. To encipher it
with a key of 3=D, we simply replace each letter in our message with the one
three letters further down the alphabet. To be very explicit, we think of which
position of the alphabet each letter is in (as in Figure 3.1), add three to that
number, and use the letter in this latter number’s position. Of course, since we
are comfortable with this process, we generally simply say “shift three” or “add
three”.
a b c d e f g h i j k l m n o p q r s t u v w x y z
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Figure 3.1: The Standard Translation of Letters into Numbers
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