Block Cipher Modes

Block Cipher Modes of Operation

A block cipher encrypts fixed-size blocks of plaintext. The same key encrypts each block, but modes of operation define how blocks are chained together. The choice of mode dramatically affects security.

ECB — Electronic Codebook

The simplest mode: each block is encrypted independently.

$C_i = E_k(P_i)$

Fatal flaw: identical plaintext blocks produce identical ciphertext blocks. The famous "ECB penguin" — encrypting a bitmap in ECB mode reveals the image structure.

CBC — Cipher Block Chaining

Each block is XORed with the previous ciphertext block before encryption:

$C_i = E_k(P_i \oplus C_{i-1})$

The first block uses an Initialization Vector (IV):

$C_0 = E_k(P_0 \oplus IV)$

Decryption:

$P_i = D_k(C_i) \oplus C_{i-1}$

CBC eliminates the ECB pattern flaw. Each ciphertext block depends on all previous plaintext blocks.

Our Simulation

We simulate the block cipher $E_k$ with simple XOR: $E_k(x) = x \oplus k$.

• ECB: $C_i = P_i \oplus k$
• CBC encrypt: $C_i = (P_i \oplus C_{i-1}) \oplus k$, starting with $C_{-1} = IV$
• CBC decrypt: $P_i = (C_i \oplus k) \oplus C_{i-1}$

Your Task

Implement:

• ecb_encrypt(blocks, key) — XOR each block with key
• cbc_encrypt(blocks, key, iv) — CBC encryption
• cbc_decrypt(blocks, key, iv) — CBC decryption