Editing Hash Functions and Digital Signatures (section)

== <span style="color: #FFFFFF;">Understanding</span> ==
Hashing is understood through **Fingerprinting**, while signatures are about **Ownership**.

**1. The Three Rules of a Good Hash**:
* **Deterministic**: The same input must *always* produce the same hash.
* **Efficient**: It must be fast to calculate.
* **Pre-image Resistant**: You can't "Reverse" the hash. If you see `a1b2c3`, you have no way to know if it came from a 10GB movie or the word "Hello."

**2. The Digital Signature Process**:
To sign a 100-page contract:
1. Alice **Hashes** the contract to get a short "Digest."
2. Alice **Encrypts** the digest with her **Private Key**. This is the "Signature."
3. Bob receives the contract and the signature.
4. Bob **Decrypts** the signature with Alice's **Public Key** to get the digest.
5. Bob **Hashes** the contract himself.
6. If the two digests match, Bob knows: (A) The contract wasn't changed, and (B) Only Alice could have signed it.

**3. Why not sign the whole file?**:
Public-key math is very slow. Signing a 1GB video would take minutes. Hashing the 1GB video takes seconds, and signing the tiny 256-bit hash takes milliseconds. This is why we always "Hash then Sign."

**Rainbow Tables**: These are pre-computed lists of common passwords and their hashes. If a hacker steals a database of hashes, they can just look them up. This is why we use **Salt**—adding a random string like "x9!z" to every password so that every "123456" results in a completely different, unique hash.
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