Understanding Block Cipher Modes and Stream Ciphers

Block ciphers like AES or DES encrypt data in fixed-size blocks. To encrypt messages longer than a single block, different modes of operation are used. These modes define how the block cipher is applied repeatedly to encrypt a sequence of data blocks. Some modes can make a block cipher behave like a stream cipher, which encrypts data bit by bit or byte by byte.

What is a Stream Cipher?

A stream cipher generates a pseudorandom stream of bits, called a keystream, which is then combined (usually XORed) with the plaintext stream to produce the ciphertext stream. Decryption involves generating the same keystream and XORing it with the ciphertext stream.

The Concept of Self-Synchronizing Stream Ciphers

A key property for some stream ciphers is self-synchronization. A self-synchronizing stream cipher can recover from errors (like lost or inserted bits/bytes) in the ciphertext stream and resynchronize the decryption process automatically after processing a certain number of subsequent correct ciphertext bits. This is typically achieved by making the generation of the keystream dependent on a limited number of previous ciphertext bits.

Analyzing Block Cipher Modes

Let's examine the given block cipher modes to see which one functions as a self-synchronizing stream cipher.

• Electronic Codebook (ECB) Mode: In ECB mode, each plaintext block is encrypted independently using the same key. It does not involve any feedback or chaining between blocks. It is a block mode, not a stream mode, and offers no self-synchronization.
• Cipher Block Chaining (CBC) Mode: In CBC mode, each plaintext block is XORed with the previous ciphertext block before being encrypted. The first block is XORed with an Initialization Vector (IV). While it uses chaining, an error in one ciphertext block propagates to affect the decryption of the current and all subsequent blocks. It is not a self-synchronizing stream cipher; it's a block cipher mode with error propagation properties.
• Output Feedback (OFB) Mode: In OFB mode, the block cipher is used to generate a keystream, which is then XORed with the plaintext, similar to a stream cipher. The input to the block cipher for the next keystream block is the output of the current block cipher operation. The keystream generation is independent of the plaintext and ciphertext. An error in the ciphertext stream does not affect the keystream generation at the receiver, but if part of the ciphertext stream is lost, the receiver's keystream will be out of sync with the sender's, requiring external resynchronization. Thus, it is a synchronous stream cipher mode, not self-synchronizing.
• Cipher Feedback (CFB) Mode: In CFB mode, data is encrypted in smaller units (e.g., bits, bytes, or a portion of the block size). The previous ciphertext unit is fed into the block cipher, and the output (or a portion of it) is XORed with the current plaintext unit to produce the current ciphertext unit. The process for generating the "keystream" is dependent on the previous ciphertext. If some ciphertext units are lost or corrupted, the receiver can recover and resynchronize after processing a sufficient number of subsequent correct ciphertext units because the state of the keystream generator (the block cipher input) will eventually be filled with correct ciphertext units again. This dependency on previous ciphertext makes CFB mode behave like a self-synchronizing stream cipher.

Let's summarize the modes regarding their behavior as stream ciphers and self-synchronization:

Cipher Feedback (CFB) Mode as a Self-Synchronizing Stream Cipher

CFB mode uses feedback from the ciphertext. The input to the block cipher is derived from previous ciphertext. Specifically, to encrypt the \(i\)-th unit of plaintext (\(P_i\)), the block cipher is applied to a shift register containing recent ciphertext, and the output is XORed with \(P_i\) to produce \(C_i\). To decrypt \(C_i\), the block cipher is applied to the same shift register state, and the output is XORed with \(C_i\) to recover \(P_i\).

If an error occurs in the ciphertext stream, the shift register at the receiver will momentarily contain incorrect values. However, as correct subsequent ciphertext units are received and shifted into the register, the incorrect values are eventually pushed out. Once the shift register contains only correct ciphertext units, the keystream generated by the block cipher will again match the sender's keystream, and decryption will resynchronize automatically. The number of correct ciphertext units needed to resynchronize depends on the size of the shift register used in the CFB implementation.

Therefore, Cipher Feedback (CFB) Mode is the block cipher implementation that acts as a self-synchronizing stream cipher.

Revision Table: Block Cipher Modes

Additional Information: Applications and Considerations

The choice of block cipher mode depends heavily on the application requirements, such as the need for random access, tolerance for error propagation, and the need for self-synchronization. CFB mode is useful when data arrives in streams and the ability to recover from transmission errors without explicit resynchronization signals is important. However, like other feedback modes (CBC), CFB requires an Initialization Vector (IV) which should ideally be unique for each encryption session with the same key to prevent certain types of attacks.

While CFB provides self-synchronization, it also propagates errors for a short duration (equal to the shift register size). OFB mode, being a synchronous stream cipher, does not propagate errors but requires strict synchronization of the keystream at sender and receiver.