###### Books / Practical Cryptography for Developers (Unfinished) / Chapter 2

# Hash Functions

In computer programming **hash functions** map text (or other data) to integer numbers. Usually different inputs maps to different outputs, but sometimes a **collision** may happen (different input with the same output).

**Cryptographic hash** functions transform text or binary data to fixed-length **hash value** and are known to be **collision-resistant** and **irreversible**. Example of cryptographic hash function is **SHA3-256**:

```
SHA3-256("hello") = "3338be694f50c5f338814986cdf0686453a888b84f424d792af4b9202398f392"
```

The above SHA3-256 hash calculation can be coded in Python like this:

```
import hashlib, binascii
sha3_256hash = hashlib.sha3_256(b'hello').digest()
print("SHA3-256('hello') =", binascii.hexlify(sha3_256hash))
```

Run the above code example: https://repl.it/@nakov/SHA3-256-hello-in-Python.

The same SHA3-256 hash calculation can be coded in JavaScript like this (after `npm install js-sha3`

):

```
sha3 = require('js-sha3');
let sha3_256hash = sha3.sha3_256('hello').toString();
console.log("SHA3-256('hello') =", sha3_256hash);
```

Run the above code example: https://repl.it/@nakov/SHA3-256-hello-in-JS.

## Hashing (in Software Engineering)

The process of calculating the value of certain hash function is called “**hashing**”.

In the above example the text `John Smith`

is hashed to the hash value `02`

and `Lisa Smith`

is hashed to `01`

. The input texts `John Smith`

and `Sandra Dee`

both are hashed to `02`

and this is called “**collision**”.

Hash functions are **irreversible by design**, which means that there is no fast algorithm to restore the input message from its hash value.

In programming **hash functions** are used in the implementation of the data structure “**hash-table**” (associative array) which maps values of certain input type to values of another type, e.g. map product name (text) to product price (decimal number).

A **naive hash function** is just to sum the bytes of the input data / text. It causes a lot of collisions, e.g. `hello`

and `ehllo`

will have the same hash code. **Better hash functions** may use the Merkle–Damgård construction scheme, which takes the first byte as **state**, then **transforms the state** (e.g. multiplies it by a prime number like 31), then **adds the next byte** to the state, then again transforms the state and adds the next byte, etc. This significantly reduces the rate of collisions and produces better distribution.

## Cryptographic Hash Functions

In cryptography, **hash functions** transform **input data** of arbitrary size (e.g. a text message) to a **result** of fixed size (e.g. 256 bits), which is called **hash value** (or hash code, message digest, or simply hash). Hash functions (hashing algorithms) used in computer cryptography are known as “**cryptographic hash functions**”. Examples of such functions are **SHA-256** and **SHA3-256**, which transform arbitrary input to 256-bit output.

### Cryptographic Hash Functions - Examples

As an **example**, we can take the cryptographic hash function `SHA-256`

and calculate the hash value of certain text message `hello`

:

```
SHA-256("hello") = "2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824"
```

The above SHA-256 calculation can be coded in Python like this:

```
import hashlib, binascii
sha256hash = hashlib.sha256(b'hello').digest()
print("SHA-256('hello') = ", binascii.hexlify(sha256hash))
```

Run the above code example: https://repl.it/@nakov/SHA-256-hello-in-Python.

There is no efficient algorithm to find the input message (in the above example `hello`

) from its hash value (in the above example `2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824`

). It is well-known that cryptographic hash functions **cannot be reversed** back, so they are used widely to encode an input without revealing it (e.g. encode a private key to a blockchain address without revealing the key).

As another **example**, we can take the cryptographic hash function `SHA3-512`

and calculate the hash value of the same text message `hello`

:

```
SHA3-512("hello") = "75d527c368f2efe848ecf6b073a36767800805e9eef2b1857d5f984f036eb6df891d75f72d9b154518c1cd58835286d1da9a38deba3de98b5a53e5ed78a84976"
```

### Cryptographic Hash Functions - Live Demo

**Play** with most popular cryptographic hash functions **online**: https://www.fileformat.info/tool/hash.htm.

**Cryptographic hash functions** are widely used in cryptography, in computer programming and in blockchain systems.