Let E be a symmetric key encryption algorithm, D the corresponding decryption algorithm and K a key. Let P₀, P₁,P₂,... be the plaintext blocks of data.

The most obvious way to encrypt the plaintext is

      C₀ = E_K(P₀),
      C₁ = E_K(P₁),
      C₂ = E_K(P₂), ....

Then decryption is

      P₀ = D_K(C₀),
      P₁ = D_K(C₁),
      P₂ = D_K(C₂), ....

This is known as electronic codebook (ECB) mode and is completely analogous to a (non-electronic) codebook.

There are some security problems with ECB mode. For example, identical blocks of plaintext will result in identical blocks of ciphertext. Also, a "cut-and-paste" attack might be possible, as illustrated here.

In order to avoid such problems, many other modes have been suggested. The most popular is cipher block chaining (CBC). In CBC mode we require and "initialization vector" or IV that is the size of a block. The IV is does not need to be secret. Then CBC mode is (where ⊕ is XOR)

      C₀ = E_K(IV ⊕ P₀),
      C₁ = E_K(C₀ ⊕ P₁),
      C₂ = E_K(C₁ ⊕ P₂), ....

and decryption is

      P₀ = IV ⊕ D_K(C₀),
      P₁ = C₀ ⊕ D_K(C₁),
      P₂ = C₁ ⊕ D_K(C₂), ....

CBC encryption and decryption can be viewed pictorially here and here, respectively.

With CBC, it is possible to modify the message and rearrange blocks (these attacks are described in your textbook). So CBC encryption does not assure message integrity.

Counter mode (CTR) is also popular. This mode allows for random access of files (as does CBC) and pre-computation of the key (actually a keystream). This mode also requires and IV and encryption is given by

      C₀ = P₀ ⊕ E_K(IV),
      C₁ = P₁ ⊕ E_K(IV + 1),
      C₂ = P₂ ⊕ E_K(IV + 2), ....

and decryption is

      P₀ = C₀ ⊕ E_K(IV),
      P₁ = C₁ ⊕ E_K(IV + 1),
      P₂ = C₂ ⊕ E_K(IV + 2), ....

Note that the block cipher is being used to generate a keystream and the encryption is like a stream cipher.