Symmetric Cryptosystem Model

• A source produces a message in plaintext: $X=[X_1,X_2,\dots ,X_i]$.
• An encryption key of the form $K=[K_1,K_2,\dots ,K_j]$ is generated.
• Encryption algorithm forms ciphertext $Y=E(K,X)=[Y_1,Y_2,\dots ,Y_n]$.
• Intended receiver, who is in possession of key $K$, is able to invert transformation $X=D(K,Y)$.

The attacker knows the encryption ($E$) and decryption ($D$) algorithms. Observing $Y$ but not having access to $K$ or $X$, may attempt to recover $X$ or $K$ or both by generating $\hat{X}$ or $\hat{K}$.