Block Cipher Principles

Block Cipher Principles

1. What a Block Cipher Is

A block cipher encrypts fixed-size blocks ($n = 64$ DES, $128$ AES) with a keyed invertible map:

For fixed $K$, $E_K$ is a permutation of $2^n$ blocks. Ideal ("random permutation") needs $\log_2(2^n!) \approx n \cdot 2^n$ key bits (huge: $64 \times 2^{64}$) — real ciphers approximate it with small keys via iterated rounds (DES $2^{56}$, AES $2^{128}$).

2. Stream vs Block (Exam Contrast)

Point	Stream cipher	Block cipher
Unit	Bit/byte at a time ($C_i = P_i \oplus k_i$)	Whole $n$-bit block
Keystream	Key + IV expanded; reuse = break	Key schedule → round subkeys
Error spread	One-bit error → one-bit error	One-bit error → full block garbled (with chaining, more)
Padding/mode	None needed	Padding + mode (ECB/CBC/...) for long messages
Examples	RC4, ChaCha20 (Module 4 Topics 6–7)	DES, AES (Topics 3, Module 4 Topic 2)

3. Shannon: Confusion and Diffusion (The Design Theory)

Claude Shannon (1949) demands two properties; every exam answer on "principles" centers them:

• Confusion: ciphertext statistics must not reveal key — complex nonlinear key↔cipher relation. Achieved by substitution (S-boxes): S-DES S0/S1, DES $6 \to 4$ S-boxes, AES SubBytes inversion in $GF(2^8)$.
• Diffusion: one plaintext bit must spread over many ciphertext bits (and vice versa) — kills frequency/digram statistics. Achieved by permutation/transposition: DES E-expansion + P-box, AES ShiftRows + MixColumns.

Feistel/SPN round = confusion + diffusion layered; after enough rounds (DES 16, AES 10–14) the cipher shows avalanche: 1 input bit flips $\approx 50\%$ of output bits; strict avalanche + bit-independence are the measurable criteria.

4. Feistel Structure (Why DES Can Decrypt)

Split block $(L_0, R_0)$; per round $i$ with subkey $K_i$:

Final $(L_n, R_n)$ (often swapped). Decryption = same circuit, subkeys reversed — because XOR cancels: $L_{i-1} = R_i \oplus F(L_i, K_i)$. $F$ need not be invertible (DES $F$ expands $32 \to 48 \to 32$) — Feistel's genius vs SPN (AES), where every layer must invert.

Ideal block cipher checklist (Stallings): large $n$ (birthday bound $2^{n/2}$), large key ($2^k$ brute force), complex key schedule (related-key resistance), no statistical weakness (confusion/diffusion), nonlinear S-boxes with avalanche.

Exam Points

• $C = E(K,P)$ definition + stream-vs-block table — 2–5 mark opener.
• Confusion (S-box, key hiding) vs diffusion (permutation, spreading) with DES/AES examples each — 5-mark theory core.
• Feistel equations + "F need not invert" + decrypt-with-reversed-keys proof sketch.
• Avalanche 50% + ideal-cipher checklist.