Cryptography Reference
In-Depth Information
CHAPTER
1
A History of Cryptography
This chapter provides an overview of some of the classical methods of cryptography
and some idea of how they evolved. None of the methods described here is used today,
because they are considered either insecure or impractical. We begin with some definitions:
Definition
A cipher, or cryptosystem, is a pair of invertible functions:
•
f
k
(known as the enciphering function), which maps from a set
S
to a set
T
, based on
a quantity
k
called an enciphering key.
•
g
k
(known as the deciphering function), the inverse of
f
k
.
k
is known as the deci-
phering key.
The function
f
k
maps an element
x
in
S
to an element
f
k
(
x
) in
T
so that determining the
inverse mapping is extremely difficult without knowledge of
k
. An element of
S
is called
plaintext, whereas an element of
T
is called ciphertext.
Some ciphers are better at satisfying this definition than others. The terms encipher and
encrypt are synonymous, as are the terms decipher and decrypt.
Definition
If, for some cipher
k
=
k
, or if
k
is easily computable given
k,
such a
cipher is called a secret key cipher. However, if
k
is extremely difficult to obtain even
with knowledge of
k,
such a cipher is called a public key cipher. In this case
k
is called
a public key, whereas
k
is called a private key.
