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Symmetric-key Cryptography

The use of a single key for both encryption and decryption, providing confidentiality when the key is kept secret. Examples include AES and DES.

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The statement of the theorem

Let

M

be the plaintext message and

K

be the secret key, where

M, K \in \{0, 1\}^n

. Define the encryption function

E_K: \{0, 1\}^n \to \{0, 1\}^m

and the decryption function

D_K: \{0, 1\}^m \to \{0, 1\}^n

. The system must satisfy the following properties for all valid inputs

M

and

K

:\n

\text{Decryption Property: } D_K(E_K(M)) = M

\text{Key Dependency: } E_K(M) \neq E_{K'}(M) \text{ for } K \neq K'

Source: Wikipedia