Cipher Block Chaining Mode

cryptography

Definition

Cipher Block Chaining Mode

Cipher Block Chaining (CBC) is a mode of operation for a block cipher in which each plaintext block is XORed with the encryption of the previous block before being encrypted. The first block is XORed with a randomly generated initialisation vector (IV).

Encryption

For plaintext blocks $m_1,m_2,\dots ,m_n$ and a randomly chosen IV:

$$c_1=\mathsf{Enc}(k,m_1\oplus \text{IV})c_i=\mathsf{Enc}(k,m_i\oplus c_{i-1})\text{ for }i>1$$

Encryption is non-deterministic: the same pair (plaintext, key) might produce different ciphertexts due to the random IV.

¹

Decryption

$$m_1=\mathsf{Dec}(k,c_1)\oplus \text{IV}{m}_i=\mathsf{Dec}(k,c_i)\oplus c_{i-1}\text{ for }i>1$$

¹

Properties

Parallelisation

Parallelisation of decryption and random read access are possible. Encryption cannot be parallelised due to the dependency on the previous ciphertext block.

Error Propagation

A bit flip in a ciphertext block produces random errors in the corresponding plaintext block and a bit flip at the same position in the next plaintext block. A bit flip in the IV causes a flip of the corresponding bit in the first plaintext block.

Footnotes

1. 192.019 Introduction to Security ↩ ↩²