Write down decryption in CBC mode, and give a detailed explanation why it works

Sure, here is a step-by-step explanation of decryption in Cipher Block Chaining (CBC) mode:

1. Initialization Vector (IV): CBC mode starts with an initialization vector (IV) which is XORed with the first block of plaintext before it is encrypted. The IV is usually a random number and is as long as the block size.

2. XOR Operation: The result of the XOR operation is then passed through the decryption algorithm.

3. Decryption: The decryption algorithm uses the same key that was used for encryption. The output of the decryption algorithm is the original plaintext.

4. Chaining: The ciphertext of the first block is then XORed with the second block of plaintext, and this process continues for all the blocks of plaintext. This is why it's called "chaining".

Why it works:

The reason why CBC mode works is because of the XOR operation and the chaining mechanism. The XOR operation ensures that even if the plaintext has many identical blocks, the corresponding ciphertext blocks will be different because they are XORed with different values (the previous ciphertext block). This prevents patterns in the plaintext from being visible in the ciphertext.

The chaining mechanism ensures that each ciphertext block depends on all the previous plaintext blocks. This means that even a small change in the plaintext will result in a completely different ciphertext, which provides a high level of security.

However, it's important to note that the IV must be kept secret, just like the key. If the IV is known to an attacker, they can determine the first block of plaintext by XORing the IV with the first block of ciphertext.