## What is a Hash Function?

A hash function takes an input of arbitrary length and generates a fixed-size output called a hash value or hash. The input data can be any size, such as a string, file, image, video, etc. The output is a hash value of fixed length, for example, 256 bits. Hash functions have the following basic properties:

- It takes variable length input and converts it to a fixed length output. This is called compression.
- The output is deterministic – the same input always generates the same hash value.
- It is infeasible to regenerate the input from the hash value, i.e., the process cannot be reversed.
- Even small changes in input lead to major changes in the hash value.

Hash functions are used when data of arbitrary size needs to be mapped to fixed-size values. The fixed-sized hash codes can be used for easy comparisons and lookups. Since hashes hide the original input, they can provide integrity-checking and fingerprinting capabilities.

## Key Takeaways

- Hash functions are mathematical algorithms that map data of arbitrary size to data of fixed size called a hash value or hash.
- Hash functions are used in applications such as cryptography, data structures, and databases to locate data quickly and check its integrity.
- Desired properties of cryptographic hash functions include preimage resistance, second preimage resistance, collision resistance, and avalanche effect.
- Popular cryptographic hash functions include MD5, SHA-1, SHA-2, SHA-3, RIPEMD, Whirlpool, Blake2 and Streebog.
- Hash tables, bloom filters, and data structures use non-cryptographic hash functions like sum hashes, lookup3 hash, and universal hashing.
- Hash functions optimize lookups by mapping keys to array indices but have risks like collisions, which can be mitigated via chaining.

## What are the Properties of Cryptographic Hash Functions

Cryptographic hash functions are a vital component in applications like digital signatures, message authentication codes, password storage, and blockchain technology. They are designed to be one-way functions that conceal the original input. Cryptographic hash functions aim to satisfy the following properties:

### Cryptographic Hash Functions

Cryptographic hash functions are designed to be one-way functions that conceal the original input. They are built using cryptographic primitives and aim to provide tamper resistance for security applications. Some examples include:

**MD5**: Produces 128-bit hash value. It was found to have extensive vulnerabilities.**SHA-1**: Outputs 160-bit digest. Has cryptographic weaknesses.**SHA-2**: SHA-256 SHA-512 produce 256-bit and 512-bit hashes respectively.**SHA-3**: Latest secure hash algorithm standard. Not derived from SHA-2.**RIPEMD**: Set of hash functions based on MD4. Variants like RIPEMD-128, RIPEMD-160 exist.**Whirlpool**: 512-bit hash function. Used in ISO/IEC 10118-3 standard.**Blake2**: Cryptographic hash function based on ChaCha stream cipher.**Streebog**: Russian national standard and GOST hash function. Produces 256-bit and 512-bit hashes.

### Non-Cryptographic Hash Functions

These hash functions are not designed to be cryptographically secure. They optimize for performance and are used in applications like:

**Hash tables:**Mapping keys to array indices**Data structures:**Hash maps, sets, linked lists**Databases:**Keyed lookups and indexing**Caching systems:**Key lookups and duplicates detection**Bloom filters:**Probabilistic set membership testing

Some examples of non-cryptographic hash functions include:

**Sum hash**: Simple addition of input characters**Lookup3 hash**: Fast hash optimized for performance**Universal hashing**: Family of hash functions with low collisions**Pearson hashing**: Simple hash using multiplicative hashing**Zobrist hashing**: Hashing used in chess game engines

## What are the Applications and Use Cases of Hash Functions

Some of the most common applications of hash functions include:

**Password storage**: Passwords are hashed using salt and slowly computed hash to protect even against brute force attacks.**Message digests**: Hash of data like file messages for integrity checking and detecting changes.**Digital signatures**: These are used in digital signature algorithms to provide authentication and non-repudiation.**Hash tables:**Keys mapped to array indices, which allow O(1) lookup time complexity, are used in languages and databases.**Data structures**: Hash maps, hash sets, and hash tries rely on hash functions for fast lookups.**Bloom filters**: Provides space-efficient probabilistic set membership testing using hash functions.**Caching**: The hash of the key can quickly find duplicates and cache hits instead of slow lookups.**Data fingerprinting**: Perceptual hashes are used for duplicate detection in files, images, videos, and other data.

## Hash Table Example Illustrating Hash Function Usage

Hash tables are one of the most common applications of hash functions. Here is a simple illustration:

- A hash function like SHA-256 is chosen, which can hash arbitrary strings to 256-bit values.
- A fixed-size array is taken, with each cell capable of storing records or pointers to records. The size depends on the expected inputs.
- When a key-value pair needs to be inserted, the key is passed through the hash function.
- The resulting 256-bit hash is modded with the hash table size to get an array index.
- The value is stored in this array cell. Multiple key-value pairs can hash to the same index, which is known as collisions.
- To look up a value, the key is hashed using the same hash function to derive the array index, which must be stored if present.

## Mitigating Hash Collisions

One of the risks of using hash functions is collisions: when two different inputs produce the same hash value. This can lead to errors in lookups and integrity checks. Some ways to mitigate hash collisions:

### Chaining

In hash tables, all records hashing to the same index can be stored as a linked list. This is called chaining. During lookup, the key is hashed, and the entire chain is traversed to find the record. This prevents collisions from causing records to be overwritten.

### Open Addressing

Records are stored in the hash table array itself instead of chains. On collision, the record is put in the next vacant slot based on a probing sequence like linear or quadratic probing. Lookup also follows the same probing sequence.

### Increasing Hash Output Size

Larger hash values have a lower probability of random collisions. This is why cryptographic hash functions aim for 256-bit+ digest sizes.

### Salts

Unique random salts are appended to keys before hashing to prevent precomputed lookup tables based on common keys. This mitigates brute force attacks.

### Multiple Hash Functions

Looking up records using multiple independent hash functions decreases the chance of all of them reporting a collision.

## Hash Function Security Considerations

While using hash functions, some aspects to consider from a security perspective:

**Rainbow table attacks**: The use of precomputed tables to reverse hashes should be prevented by using salts slowing functions.**Collision attacks**: Finding inputs hashing to the same value should be infeasible.**Length extension attacks**: Appending data to a hashed value should change the hash entirely.**Weaknesses**: Hash functions should withstand cryptanalysis and provide adequate security margins. Vulnerable algorithms like MD5 and SHA-1 should be avoided.**Salting:**Different users should have unique salts added to inputs before hashing to prevent brute-force attacks using precomputed tables.**Slowing functions:**Key strengthening techniques like key stretching, PBKDF2, bcrypt, and scrypt make brute forcing expensive by deliberately slowing down hashing.**Sensitive data**: Take precautions when handling passwords, crypto keys, and other sensitive data used as inputs for hashing.

## Final Words

Hash functions are essential techniques used in many areas of computer science and cybersecurity. Understanding the different types of hash functions, their properties, use cases, and security considerations allows proper selection and implementation.

Cryptographic hashes provide tamper resistance, while fast non-cryptographic hashes enable high-performance data structures and lookups. Hashes power vital technologies like blockchains, password storage, data fingerprinting, and integrity verification.

## Frequently Asked Questions (FAQs)

### What is a hash function?

A hash function is a mathematical algorithm that converts data of arbitrary size into a fixed-size value called a hash. It is a one-way function that is infeasible to invert.

### What are the applications of hash functions?

Cryptography, passwords, data structures, lookups, fingerprints, caching, integrity checks, and blockchains are major applications.

### What are the types of hash functions?

The main types are cryptographic hashes like SHA-2 and SHA-3 designed for security and non-cryptographic hashes like the lookup3 hash optimized for performance.

### What is a hash table?

A hash table is a data structure that uses a hash function to map keys to array indices, enabling fast key-value lookups. Hash collisions are handled via chaining or open addressing.

### What are the properties of a good hash function?

Desired properties are deterministic, uniform distribution, randomness, avalanche effect, infeasibility of inversion, collision resistance, and fast computation.

### How are hash collisions handled?

Chaining, open addressing, and using multiple independent hash functions are common ways to handle collisions. Increasing the hash output size also reduces collisions.

### What is the difference between MD5, SHA-1 and SHA-256?

MD5 is fast but completely broken. SHA-1 has weaknesses. SHA-256 provides much stronger cryptographic security.

Priya Mervana

#### Verified Web Security Experts

Priya Mervana is working at SSLInsights.com as a web security expert with over 10 years of experience writing about encryption, SSL certificates, and online privacy. She aims to make complex security topics easily understandable for everyday internet users.