Symmetric Encryption Scheme

cryptography

Definition

Symmetric Encryption Scheme

A symmetric encryption scheme with a key space $\mathcal{K}$, message space $\mathcal{M}$, and ciphertext space $\mathcal{C}$ is a triple of algorithms:

$$⟨\mathsf{Gen},\mathsf{Enc},\mathsf{Dec}⟩$$

where:

• The key generation algorithm $\mathsf{Gen}$ takes no input (arity 0) and returns a randomly selected key $k\in \mathcal{K}$.
• The encryption algorithm $\mathsf{Enc}$ takes a key $k\in \mathcal{K}$ and a message $m\in \mathcal{M}$, and produces a ciphertext $c\in \mathcal{C}$:

$$\mathsf{Enc}:\mathcal{K}\times \mathcal{M}\to \mathcal{C}$$

• The decryption algorithm $\mathsf{Dec}$ takes a key $k\in \mathcal{K}$ and a ciphertext $c\in \mathcal{C}$, and produces a plaintext $m\in \mathcal{M}$, or an error:

$$\mathsf{Dec}:\mathcal{K}\times \mathcal{C}\to \mathcal{M}$$