Symmetric Cryptography

Context: Information Security and Cryptography · one shared secret scrambles + unscrambles the message · the systems view of Cryptosystem (FIT1058 number theory)

Quick Revision

• 🎯 Objective: a single key is shared between principals; use it to scramble a message so it is unreadable without the secret ➔ confidentiality, very fast.
• ⚡ Key Constraint: the key-distribution problem — both sides must first obtain the same secret over a secure channel; and keys scale as $\frac{n(n-1)}{2}$, i.e. $O(n^2)$.

📝 Core

• Shared key ➔ same secret at both ends; used for >3000 years (Skytale, Caesar, Vigenère substitution ciphers).
• Main idea ➔ use the shared secret to scramble a block so it cannot be understood without the key.
• Building blocks ➔ S-boxes (substitution boxes) = a look-up table replacing part of a message block; permutations = reorder the message parts. Modern ciphers repeat substitution + permutation over many rounds.
• AES (Advanced Encryption Standard) ➔ open NIST contest (15 designs, winner 2000); winner Rijndael (Daemen & Rijmen); block cipher, 14 rounds in the 256-bit version (each round: Byte Sub → Shift Row → Mix Column → Add Round Key).

🔗 Integrity: block chaining & CBC-MAC

• Confidentiality only ➔ AES on raw blocks gives secrecy but not integrity (blocks can be reordered, bits flipped).
• Block chaining ➔ start with an initialisation vector (IV) and combine each encrypted block with the next → wrong order won’t decrypt; a changed block disables decryption of the next.
• CBC-MAC ➔ Cipher Block Chaining produces a Message Authentication Code — one final block that checks integrity of the whole message $m_1{m}_2\dots m_x$. Used by WPA2/CCMP (AES + CBC-MAC).

⚠️ Common Mistakes

• 💡 Key distribution ➔ you still need a separate secure channel to share the secret → motivates Key Establishment and Diffie-Hellman and Public Key Cryptography.
• 💡 Scalability ➔ every pair needs a unique key → $\frac{n(n-1)}{2}$: 12 people = 66 keys, 1000 = 499,500, a million ≈ $5\times 10^{11}$ keys.
• 💡 No non-repudiation ➔ both parties hold the same key, so a key can’t prove which side produced a message.

🧠 Active Recall

Symmetric encryption is fast and secure — so why do we still need public-key cryptography?

Answer

• Short answer: symmetric crypto has three structural weaknesses — key distribution (needs a pre-shared secret), scalability ($O(n^2)$ keys), and no non-repudiation — none of which are about the cipher’s strength.
• Why: Shared-secret limits ➔ Public Key Cryptography and Key Establishment and Diffie-Hellman remove the pre-shared-secret requirement and enable signatures, while symmetric ciphers (AES) still do the bulk encryption afterwards.