# Cryptosystem

Time：2021-6-3

Generally, a cryptosystem can have the following parts:

1. Message space m (also known as plaintext space): the set of all possible plaintext M;

2. Ciphertext space C: the set of all possible ciphertext C;

3. Key space K: the set of all possible key K, in which each key K is composed of encryption key K and decryption key K_ D, i.e. k = (k)_ e,k_ d);

4. Encryption algorithm e: a group of encryption transformation from m to C controlled by encryption key;

5. Decryption algorithm D: a group of decryption transformation from C to m controlled by decryption key.

The five yuan ancestors {m, C, K, e, D} are called a cryptosystem. In the cryptosystem, for each key K, the encryption algorithm will determine a specific encryption transformation, the decryption algorithm will determine a specific decryption transformation, and the decryption transformation is the inverse of the encryption transformation. For each plaintext m in plaintext space m, encryption algorithm e encrypts plaintext m into ciphertext C under the control of encryption key K; And in key K_ Under the control of D, the ciphertext C is decrypted into the same plaintext m, that is, for all m in M, (k)_ e,k_ d) In K, with D_{ k_ d}(E_{ k_ e}(m)) = m 。

In the above communication model, there is also a ciphertext C which can be intercepted by a cipher attacker or a cipher breaker from the ordinary channel. Its working goal is to recover the plaintext m or key K from the ciphertext C without knowing the key K. If the cryptanalysis can deduce plaintext or key from ciphertext only, or deduce key from plaintext and ciphertext, then the cryptosystem is said to be cracked. On the contrary, the cryptosystem is said to be indecipherable.