Simplified DES

Simplified DES

1. Why S-DES Exists (Teaching Model of DES)

Simplified DES (Schaefer, 1996 — Appendix B of Stallings) is a toy 8-bit-block, 10-bit-key Feistel cipher with the exact structure of DES: initial permutation, 2 Feistel rounds with expansion/XOR/S-box, key schedule with shifts. Learn it once and real DES (Topic 3) is just bigger tables + 16 rounds. BEU asks full S-DES encrypt/decrypt traces — master the pipeline order.

2. Algorithm Pipeline (Memorize Order)

Key 10 bits → P10 → LS-1 → P8 → K1 ; LS-2 more → P8 → K2
Plain 8 bits → IP → (L0 | R0)
Round 1: L1 = R0 ; R1 = L0 ⊕ F(R0, K1)     [F = E/P → XOR K → S0/S1 → P4]
Swap (L1 | R1) → (R1 | L1)
Round 2: same with K2
→ IP⁻¹ → Cipher 8 bits
Decrypt: same steps, subkeys reversed (K2 then K1)

Tables: $IP = [2,6,3,1,4,8,5,7]$; $IP^{-1} = [4,1,3,5,7,2,8,6]$; $E/P = [4,1,2,3,2,3,4,1]$; $P4 = [2,4,3,1]$; $P10 = [3,5,2,7,4,10,1,9,8,6]$; $P8 = [6,3,7,4,8,5,10,9]$. S-boxes: $S0 = [[1,0,3,2],[3,2,1,0],[0,2,1,3],[3,1,3,2]]$, $S1 = [[0,1,2,3],[2,0,1,3],[3,0,1,0],[2,1,0,3]]$ — row = outer bits $(b_1 b_4)$, col = inner $(b_2 b_3)$, output 2 bits.

3. Key Schedule (Worked)

Key $K = 1010000010$. P10: positions $[3,5,2,7,4,10,1,9,8,6]$ → $1000001100$. Split $(10000 | 00110)$. LS-1 each → $(00001 | 01100)$. P8 $[6,3,7,4,8,5,10,9]$ on $0000101100$ → $K_1 = 10100100$. LS-2 more from post-LS-1 halves $(00001 \to 00100$, $01100 \to 10001)$ → $0010010001$ → P8 → $K_2 = 01000011$.

4. Full Encryption Trace (Classic Numerical)

$P = 10111101$, keys above. IP $[2,6,3,1,4,8,5,7]$ → $01111010 = (L_0 = 0111 | R_0 = 1010)$. $F(R_0, K_1)$: E/P $[4,1,2,3,2,3,4,1]$ on $1010$ → $11010101$; XOR $K_1$ $10100100$ → $01110001$; split $(0111 | 0001)$: S0 row $01 = 1$, col $11 = 3$ → $S0[1][3] = 0 = 00$; S1 row $00 = 0$, col $01 = 1$ → $S1[0][1] = 1 = 01$; combine $0001$ → P4 $[2,4,3,1]$ → $0100$. $R_1 = L_0 \oplus F = 0111 \oplus 0100 = 0011$; after round 1 $(1010 | 0011)$, swap → $(0011 | 1010)$. Round 2 with $K_2 = 01000011$: E/P on $1010$ → $11010101$ XOR $K_2$ → $10010110$; S0 $(1001)$: row $11 = 3$, col $00 = 0$ → $3 = 11$; S1 $(0110)$: row $00$, col $11 = 3$ → $3 = 11$; → $1111$ → P4 → $1111$. $R_2 = 0011 \oplus 1111 = 1100$. Pre-output $(0011 | 1100) = 00111100$ → $IP^{-1}$ $[4,1,3,5,7,2,8,6]$ → $C = 01110110$. Decrypt by rerunning with $(K_2, K_1)$.

5. What S-DES Teaches (Bridge to DES)

• Feistel invertibility: any $F$ works — decrypt = same circuit, reversed subkeys.
• Confusion from S-boxes (nonlinear), diffusion from E/P + P4 + swaps.
• S-DES is insecure (10-bit key, 2 rounds, $4 \times 4$ S-boxes) — its value is purely pedagogical; DES scales every table up.

Exam Points

• Pipeline order + all six tables (IP, IP⁻¹, E/P, P4, P10, P8) — 2-mark recalls.
• Key-schedule numerical ($1010000010 \to K_1 = 10100100$, $K_2 = 01000011$) — 5-marker.
• Full $10111101 \to 01110110$ trace with S-box row/col indexing — favourite 5–7 marker.
• Decrypt = encrypt with reversed subkeys justification.