Cryptography Reference
In-Depth Information
key cryptography and corresponding techniques, whereas the latter employs public
key cryptography and corresponding techniques.
As already mentioned in Section 2.1.1, an asymmetric encryption system
requires a family of trapdoor functions. Each public key pair yields a public key
that represents a one-way function and a private key that represents the inverse of
this function. To send a secret message to a recipient, the sender must look up the
recipient's public key, apply the corresponding one-way function to the message,
and send the resulting ciphertext to the recipient. The recipient, in turn, is the only
person who is supposed to know the trapdoor (information) necessary to invert the
one-way function. Consequently, he or she is the only person who is able to properly
decrypt the ciphertext and to recover the original (plaintext) message accordingly.
In the literature, the encryption (decryption) algorithm is often denoted as
E
(
D
), and subscripts are used to refer to the entities that hold the appropriate keys. For
example,
E
A
refers to the encryption algorithm fed with the public key of A, whereas
D
A
refers to the decryption algorithm fed with the private key of A. Consequently,
it is implicitly assumed that the public key is used for encryption and the private
key is used for decryption. If the use of the keys is not clear, then the keys in use
may be subscript to
E
and
D
. In this case, for example,
E
k
A
refers to the encryption
algorithm fed with A's public key, whereas
D
k
−
1
A
refers to the decryption algorithm
fed with A's private key.
'
%
%
!
Figure 2.7
The working principle of an asymmetric encryption system.
The working principle of an asymmetric encryption system is illustrated in
Figure 2.7. On the left side, the sender applies the recipient B's one-way function
(implemented by the encryption algorithm
E
parametrized with B's public key
k
B
)
to the plaintext message
m
, and sends the resulting ciphertext
c
=
E
B
(
m
)=
E
k
B
(
m
)
