Feistel Network

Feistel Network

A Feistel network (Horst Feistel, IBM, 1973) is a symmetric structure used in many block ciphers including DES. Its key insight: you can build an invertible cipher from a non-invertible round function.

One Round

Split the block into two halves $L$ and $R$. Apply the round function $F$ with round key $K$:

$L' = R$ $R' = L \oplus F(R, K)$

The structure is automatically invertible — to reverse a round: $R = L'$ $L = R' \oplus F(L', K)$

Multi-round Encryption

Repeat the round with different subkeys $K_1, K_2, \ldots, K_n$. More rounds → more diffusion and confusion.

Our Simulation

We use 4-bit halves (from an 8-bit block: $L = \text{byte} >> 4$, $R = \text{byte} \& 0xF$) with round function:

$F(R, K) = (R + K) \bmod 256$

Combined in the round: $L' = R, \quad R' = L \oplus (R + K) \bmod 256$

DES

DES uses a 64-bit block with 16 Feistel rounds and 56-bit keys. It was the US federal standard from 1977 to 2001, superseded by AES.

Your Task

Implement:

• feistel_round(L, R, K) → (new_L, new_R) where new_L = R, new_R = L XOR (R+K)%256
• feistel_encrypt(plaintext, keys) — apply rounds with each key in sequence
• feistel_decrypt(ciphertext, keys) — apply rounds in reverse order using inverse round