# Introduction

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Hash functions are mathematical functions that take an input (a message, text, file, password, etc.) and output a fixed-size value (the “hash” or “digest”). Cryptographic hash functions are designed with specific security properties to resist attacks.

### Types of hash functions

You can distinguish between a one-way hash function and a secure cryptograp*hic (or ideal)* hash function. A *one-way hash function* must be **preimage resistant** as well as **second preimage** **resistant,** while a ***secure cryptographic*****&#x20;or&#x20;*****ideal hash function*** must fulfil those requirements as well as being **collision resistant.** These topics will be covered in more detail in the following lessons, but simply explained this means:&#x20;

* **Preimage resistant:** Hard to retrieve the input from the hash&#x20;
* **Second preimage resistant:** Hard to retrieve a different input with the same hash
* **Collision resistant:** Hard to find any two inputs with the same hash

The hash functions we'll be looking at in this course are the ones used in BSV: **SHA-256** and **RIPEMD-160**. These are both secure cryptographi / ideal hash functions. Therefore, for the remainder of this course, when you see the term *hash function*, it means *secure cryptographic* or *ideal hash function*.

### Message Digest

The **output values of hash functions are often referred to as message digests, hash values, checksums, or hashes**. We will use these terms interchangeably throughout this course.

You can think of a message digest as analogous to a fingerprint for digital information. In the physical world, a fingerprint is an identifier unique to each individual person such that no two people ever share the same fingerprint. A hash function takes some input message (which can be almost anything as all digital information is essentially a binary string of ones and zeros), and produces a unique, compressed, fixed-length, digital fingerprint for that input message. Since message digests are digital fingerprints, they are very useful for making sure data hasn’t been tampered with.

As a result of their unique properties, hash functions are a very important tool in many areas of information technology, such as Hash Tables, Digital signatures, Keyed hashes, One-way transformations and Key derivation. These operations and techniques form the foundation of most digital storage and communication technologies.

However, the two fundamental uses of hash functions are **maintaining data integrity, and data storage & access efficiency**.&#x20;


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