Hashing

Hashing is a deterministic transformation of input data (key) into a fixed-size output (usually an integer or hex value). This is done through a hash function. The result, called a hash code or digest, ideally should:

• Be quick to compute
• Minimize collisions (different inputs mapping to same output)
• Be evenly distributed across the output space

Mathematically, if we have a hash function h(x), then: $$ h: X \to Y \quad \text{where } X \text{ is the set of inputs, and } Y \text{ is the range of hash values} $$

For a hash table of size m, we often do: $$ \text{index} = h(x) \mod m $$

This lets us map the hash value to one of m buckets efficiently.

🧠 Popular Non-Cryptographic Hash Functions

These are typically used for data structures, databases, and indexing—not for security.

🔐 Cryptographic Hash Functions

These are designed with security in mind. Unlike standard hashes, cryptographic hashes must satisfy:

1. Pre-image Resistance: Given H(x), it should be computationally hard to find x.
2. Second Pre-image Resistance: Given x1, hard to find x2 != x1 such that H(x1) = H(x2).
3. Collision Resistance: It’s hard to find any two distinct inputs that hash to the same output.

Popular Cryptographic Hashes:

These are used in password storage, digital signatures, blockchains, etc.

🔍 Standard Hashing vs Cryptographic Hashing

Do we need both? Heck yes.

• You don’t want to hash your database keys with SHA-256—it’s overkill and slow.
• You must hash passwords with cryptographic hash functions or attackers could reverse them.