Cryptography Cheat Sheet

Intro to Computer Security — quick reference for exam traces

Algorithm Map

Symmetric: DES (block 64), RC4 (stream)
Asymmetric: RSA (encrypt), DH (key agree)
Hash: SHA-1 → 160 bits, no key

DES

64-bit block, 56-bit effective key
16 Feistel rounds: Lₙ=Rₙ₋₁, Rₙ=Lₙ₋₁⊕f(Rₙ₋₁,Kₙ)
f: E-expand → ⊕K → 8×S-box → P-permute
S-box: row=b₁b₆, col=b₂b₃b₄b₅
Key: PC-1 → shift C,D → PC-2 → Kₙ

RC4

KSA: j=(j+S[i]+T[i]) mod n, swap
PRGA: i=(i+1) mod n, j=(j+S[i]) mod n, swap
t=(S[i]+S[j]) mod n, k=S[t]
C = P ⊕ k
Real: n=256; toy: n=8 or 16

Diffie-Hellman

Public: prime q, generator α
Private: X → Public: Y = α^X mod q
Shared: K = Y_other^X mod q
Weakness: MITM without auth

RSA

n=pq, φ=(p−1)(q−1)
gcd(e,φ)=1, d=e⁻¹ mod φ
Encrypt: C=M^e mod n
Decrypt: M=C^d mod n
Use successive squaring

SHA-1

Output: 160-bit digest
Pad: msg + 1 + k zeros + 64-bit length
(L+1+k) ≡ 448 (mod 512)
512-bit blocks → 80 compression rounds
One-way, avalanche effect

Exam numbers to memorize

Algorithm	Canonical example
DES	M=`0123456789ABCDEF` → C=`85E813540F0AB405`
RC4 (3-bit)	P=[6,1,4] → C=[4,2,3]
RC4 (4-bit)	K=[3,5,2,7], P=[9,4,12,7,1] → C=[13,3,1,3,6]
DES K₁	Key `133457799BBCDFF1` → see DES Key Schedule
DH	q=353, α=3, X_A=97, X_B=233 → K=160
RSA	p=11,q=17,e=19,d=59, M=21→C=98
SHA-1 pad	96-bit msg → 351 zeros after "1"
SHA-1 W expand	`Wₜ = ROTL¹(Wₜ₋₃⊕Wₜ₋₈⊕Wₜ₋₁₄⊕Wₜ₋₁₆)` for t≥16

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