Cryptography Reference
In-Depth Information
with one key and then later decrypt the resulting ciphertext with a totally unrelated
key. The precise relationship between these keys defines not only the type of
cryptosystem, but also all of its resulting properties.
In
symmetric cryptosystems
the encryption key and the decryption key are
essentially the same (in situations where they are not
exactly
the same, they are
extremely closely related). All cryptosystems prior to the 1970s were symmetric
cryptosystems. Indeed, symmetric cryptosystems are still widely used today
and there is no sign that their popularity is fading. The study of symmetric
cryptosystems is often referred to as
symmetric cryptography
. Symmetric
cryptosystems are also sometimes referred to as
secret key cryptosystems
.
In
public-key cryptosystems
the encryption key and the decryption key are
fundamentally different. For this reason, public-key cryptosystems are some-
times referred to as
asymmetric cryptosystems
. In such cryptosystems it is
'impossible' (we often use the phrase
computationally infeasible
to capture
this impossibility) to determine the decryption key from the encryption key.
The study of public-key cryptosystems is often referred to as
public-key
cryptography
.
Symmetric cryptosystems are a 'natural' concept. In contrast, public-key
cryptosystems are quite counterintuitive. How can the decryption key and the
encryption key be 'related', and yet it be impossible to determine the decryption
key from the encryption key?
The answer lies in the 'magic' of mathematics. It is possible to design a
cryptosystem whose keys have this property, but it is not obvious how to
do so. Within the context of cryptographic history, the concept of public-key
cryptography is relatively new and there are far fewer public-key algorithms
known than symmetric algorithms. They are, however, extremely important as
their distinctive properties have useful applications, as we will see.
1.4.8
Secrecy of the encryption key
We already know that in any cryptosystem an interceptor must not know
the decryption key. In a symmetric cryptosystem, the encryption key and the
decryption key are the same. It follows that in a symmetric cryptosystem there is
only one key, and that this key is used for both encryption and decryption, which
is why it is often referred to as a
symmetric key
. The sender and the receiver must
be the only people who know this key.
On the other hand, in a public-key cryptosystem the encryption key and the
decryption key are different. Further, the decryption key cannot be determined
from the encryption key. This means that as long as the receiver keeps the
decryption key secure (which they must in any cryptosystem) there is no need for
the corresponding encryption key to be kept secret. It follows that the encryption
key could, at least in principle, be made publicly available (hence the term
public
