Cryptography Reference
In-Depth Information
1.3 Basic Terminology
In the classical model of cryptography, two persons, conventionally named
Alice and Bob, communicate over a public channel, i.e., a channel accessible
to anybody. Alice acts as the sender and Bob plays the role of the receiver.
The information that Alice wants to send to Bob can be text or numerical
data in any natural or human-readable language and is called plaintext. Alice
uses a parameter, called a key, to transform this plaintext into encrypted
form which is called ciphertext and sends it over the public channel. If an
adversary, conventionally called Oscar, can see the entire ciphertext in the
channel by eavesdropping, but is not able to determine the corresponding
plaintext, then this transmission is called secure. However, Bob knows the key
and using it he can recover the plaintext from the corresponding ciphertext
easily. The transformation of the plaintext to ciphertext is called encryption
and the reverse process is called decryption. A system that transforms the
plaintext to ciphertext and vice versa is called a cryptosystem. On the other
hand, cryptanalysis aims at analyzing a cryptosystem to exploit its weaknesses
so as to gain some knowledge about the plaintext from the ciphertext without
knowing the key or retrieving the secret key from some known information.
The subject cryptology comprises of both cryptography and cryptanalysis.
We can formalize the above concepts as follows. Let M be a finite set of
possible plaintexts, called the message-space and C be a finite set of possible
ciphertexts, called the ciphertext-space and K be a finite set of possible keys,
called the key-space. Then, encryption is a function
E
k
e
(m) : M ×K → C
that takes as input a plaintext m ∈ M and produces a ciphertext c ∈ C,
according to the key k
e
∈K. On the other hand, decryption is a function
D
k
d
(m) : C ×K → M
that takes as input a ciphertext c ∈ C and produces a plaintext m ∈ M,
according to the key k
d
∈ K. k
e
and k
d
are called the encryption key and
the decryption key respectively. A cipher or a cryptosystem is a pair (E,D)
of two functions, such that for any plaintext m ∈ M and any encryption key
k
e
∈K, there exists a decryption key k
d
∈ K such that D
k
d
(E
k
e
(m)) = m.
