# The Three Important Properties of Hash Functions
## 1. Preimage Resistance: One-way
Hash functions are **computationally infeasible to reverse** β like trying to **unscramble an egg** or **put toothpaste back into its tube**.
* They are **one-way trap-door functions**: easy to compute a digest from an input, but practically impossible to find the original input from just the digest.
* To be considered **preimage resistant**, it should take about **2α΅ hash attempts** (where *m* is the output length in bits) to recover the input.
* If an input can be discovered in fewer attempts, the hash function is **no longer secure**.
π **Key takeaway:** Preimage resistance makes it **impractical to reverse a hash back into its original data**.
## 2 .Second Preimage Resistance: Deterministic
Hash functions are **deterministic**: the **same input always produces the same output hash**.
* Even if you change just **one bit** in the input, the resulting hash is **completely different**.
* This ensures that an attacker cannot find a **different input** that produces the same hash as a given input.
π **Key takeaway:** Second preimage resistance ensures that a hash is a **unique fingerprint** of its input.
## 3. Collision Resistance
Itβs **computationally infeasible** to find **two different inputs** that hash to the **same output**.
* Because the output length is fixed, collisions are theoretically possible, but a **good hash function** makes them so unlikely they can be safely ignored.
* Ideally, with an output of length *m*, it should require about **2^(m/2) operations** to find a collision.
* The **birthday attack** illustrates this: in a set of 2α΅ possible values, about 2^(m/2) random attempts are needed to expect a collision.
* If collisions can be found faster than this, the hash function is **broken**.
π **Key takeaway:** Collision resistance is **critical to security**, especially in **BSVβs proof-of-work system**, where trust depends on preventing duplicate results.
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