Symmetric Encryption

In symmetric encryption, the same secret key both encrypts and decrypts. If Alice and Bob share a key, Alice scrambles a message into ciphertext and Bob unscrambles it back to plaintext. Anyone without the key sees only noise.

Step through the demo to watch each byte of plaintext combine with the key via XOR to form ciphertext, then decrypt back. Then tick the box to see why reusing one key is dangerous.

XOR and the one-time pad

The exclusive-or operation $\oplus$ is the simplest cipher. Encryption is $C = P \oplus K$ and decryption is $P = C \oplus K$, because XOR is its own inverse: $C \oplus K = (P \oplus K) \oplus K = P$.

If the key $K$ is truly random, as long as the message, and used only once, this is the one-time pad — provably unbreakable. Every plaintext is equally likely given the ciphertext, so the ciphertext leaks nothing.

Why key reuse breaks everything

The one-time pad’s guarantee evaporates the instant you reuse a key. With two messages under the same key, an eavesdropper computes:

$C_1 \oplus C_2 = (P_1 \oplus K) \oplus (P_2 \oplus K) = P_1 \oplus P_2.$

The key cancels out, leaking the relationship between the two plaintexts — often enough to recover both. The pad must be one-time, which is why true one-time pads are impractical: you would need to securely share as much key material as data.

Block ciphers: AES

Real systems use a block cipher such as AES, which encrypts fixed-size blocks (128 bits) under a short reusable key (128 or 256 bits) by scrambling them through many rounds of substitution and permutation. AES is fast (often hardware-accelerated) and has no known practical break.

To encrypt data longer than one block, you choose a mode of operation:

• ECB (electronic codebook) encrypts each block independently — avoid it. Identical plaintext blocks produce identical ciphertext blocks, leaking patterns (the infamous “ECB penguin”).
• CBC chains each block into the next using a random initialization vector (IV), so repeats vanish.
• CTR / GCM turn the cipher into a keystream. GCM also adds an authentication tag, giving authenticated encryption that detects tampering.

The lesson of key reuse generalizes: never reuse an IV or nonce with the same key, or the keystream repeats and the same XOR leak returns.

Takeaways

• Symmetric encryption uses one shared key; XOR with a random one-time key is the unbreakable one-time pad.
• Reusing a key (or IV/nonce) cancels it out and leaks $P_1 \oplus P_2$ — never reuse keystream material.
• Practical systems use AES with a safe mode; prefer authenticated modes like GCM and avoid ECB.

References

• “Crypto 101” by Laurens Van Houtven — free book; chapters on stream ciphers, block ciphers, and modes of operation.
• Dan Boneh’s Cryptography I course (Coursera) — the one-time pad, semantic security, and AES.
• NIST SP 800-38A: Block Cipher Modes of Operation — the official definitions of ECB, CBC, CTR, and friends.