A simple way to satisfy this requirement is the cipher block chaining (CBC) mode (Figure 6.4). In this scheme, the input to the encryption algorithm is the XOR of the current plain- text block and the preceding ciphertext block; the same key is used for each block. In effect, we have chained together the processing of the sequence of plaintext blocks.

**CIPHER BLOCK CHAINING MODE**

To overcome the security deficiencies of ECB, we would like a technique in which
the same plaintext block, if repeated, produces different ciphertext blocks. A simple
way to satisfy this requirement is the **cipher block
chaining **(**CBC**)
mode (Figure 6.4). In
this scheme, the input to the encryption algorithm is the XOR of the current
plain- text block and the preceding ciphertext block; the same key is used for each block. In effect, we have chained
together the processing of the sequence
of plaintext blocks.
The input to the encryption function
for each plaintext block bears no fixed relation- ship to the plaintext
block. Therefore, repeating patterns of *b *bits are not exposed.
As with the ECB mode, the CBC mode requires
that the last block be padded to a full *b *bits
if it is a partial
block.

For decryption, each cipher block is passed through the decryption algorithm. The result is XORed with the preceding ciphertext block to
produce the plaintext block. To see that this works,
we can write

*C**j *= E(*K*, [*C**j *- 1 Ⓧ *P**j*])

To produce the first block of
ciphertext, an initialization vector (IV) is XORed with the first block of
plaintext. On decryption, the IV is XORed with the output of the decryption
algorithm to recover the first block of plaintext. The IV is a data block that
is that same size as the cipher block. We can define CBC mode as

The IV must be known to both the sender and
receiver but be unpredictable by a third party. In particular, for any given plaintext, it must not be possible
to pre- dict the IV that will
be associated to the plaintext in advance of the generation of the IV. For
maximum security, the IV should be protected
against unauthorized changes.
This could be done by sending the IV using ECB encryption. One reason for protecting the IV is as
follows: If an opponent is able to fool the receiver into using a different value
for IV, then the opponent
is able to invert selected
bits in the first block of plaintext. To see this, consider

*C*1 = E(*K*, [IV Ⓧ *P*1])

*P*1 = IV Ⓧ D(*K*, *C*1)

Now use the notation that *X*[*i*] denotes the *i*th bit of the *b*-bit
quantity X. Then

*P*1[*i*] = IV[*i*] Ⓧ D(*K*, *C*1)[*i*]

Then, using the properties of XOR, we can state

*P*1[*i*]' = IV[*i*]' Ⓧ
D(*K*, *C*1)[*i*]

where the prime notation
denotes bit complementation. This means that if an oppo-
nent can predictably change bits in IV, the corresponding bits of the received value of
*P*1 can be changed.

For
other possible attacks based on prior knowledge of IV, see [VOYD83].

So long as it is unpredictable, the specific choice of IV is unimportant. Sp800-38a
recommends two possible
methods: The first method is
to apply the encryption function, under
the same key that is used for the encryption of the plain- text, to a **nonce**.2 The nonce must be a data block that is unique to each execution of the
encryption operation. For example,
the nonce may be a counter, a timestamp, or a message number. The second method is
to generate a random data block using a random number generator.

In
conclusion, because of the chaining mechanism of CBC, it is an appropriate mode
for encrypting messages of length greater than *b *bits.

In addition
to its use to achieve
confidentiality, the CBC mode can be used for
authentication. This use is described
in Chapter 12.

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Cryptography and Network Security Principles and Practice : One Symmetric Ciphers : Block Cipher Operation : Cipher Block Chaining(CBC) Mode |

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