What Is a Hash Function? How It Works, Types, Examples, and Applications

A hash function is a mathematical function that takes input data and produces a fixed-size output, commonly called a hash value, hash code, or hash digest. Hash Functions have widespread applications in computer science and cybersecurity, including password encryption, data integrity, digital signatures, database operations, blockchain technology, and caching.

Input for a hash function could be any form of data, such as passwords, text, documents, images, software files, or even database keys.

For example:

Input: "Hello World"
        ↓
     SHA-256
        ↓
Fixed-Length Hash

Another characteristic of cryptographic hashes is that any small change to the input results in a very different output value. Cryptographic hashes also have the property of being unidirectional, which means it is easy to calculate a hash but nearly impossible to determine what the input was from the hash itself.

Let’s understand how hash functions work, their important properties, types, and real-world applications.

What is a Hash Function?

A hash function takes data of arbitrary size and maps it to an output of a predefined size.

The basic process looks like:

Input Data
    ↓
Hash Function
    ↓
Hash Value

For a deterministic hash function, identical input produces identical output.

For example:

hash("Moon") → Hash A
hash("Moon") → Hash A
hash("moon") → Hash B

Although “Moon” and “moon” differ by only one character, their cryptographic hashes should look significantly different.

This predictable mapping makes hashing useful when applications need to verify data, locate information efficiently, or compare values without handling the original information in the same way.

How Does a Hash Function Work?

A hash function processes input through a series of mathematical and logical operations and produces a fixed-length result.

A simplified workflow is:

Original Data
↓
Convert to Bytes
↓
Hashing Algorithm
↓
Mathematical Transformations
↓
Fixed-Length Digest

It differs for each type of algorithm. Functions like SHA-256 go through many rounds of transformation using bitwise and mathematical operations on the input data.

These algorithms are usually better left to be implemented in already existing programming libraries.

For example, Python provides SHA-256 through hashlib:

import hashlib
message = "Hello World"
result = hashlib.sha256(
message.encode()
).hexdigest()
print(result)

Regardless of whether the input contains a few characters or a large amount of data, SHA-256 produces a 256-bit digest.

Key Properties of Cryptographic Hash Functions

Not every hash function is intended for security. Cryptographic hash functions require several important properties that make them suitable for security-sensitive applications.

hash("data") → ABC123
hash("data") → ABC123

SHA-256 → 256 bits
SHA-512 → 512 bits

Input → Hash Function → Hash

Hash → ??? → Original Input

hash(Input A) = XYZ
hash(Input B) = XYZ

Input A ≠ Input B

Input 1: Hello World
Input 2: hello World

Types of Hash Functions

Hashing algorithms are created to serve various purposes. A hashing algorithm meant for database indexing will have other requirements than one meant for digital signatures or passwords.

Cryptographic Hash Functions

Cryptographic hash functions prioritize security properties such as preimage and collision resistance.

SHA-256
SHA-512
SHA-3

How Are Hash Functions Used for Passwords?

Applications should never store passwords directly in plaintext.

Instead of storing:

Username: john@example.com

Password: Password123

the application stores an appropriately generated password hash.

During login:

Entered Password
↓
Password Hashing Function
↓
Verification Against Stored Hash
↓
Match?
↙     ↘
Yes      No
↓        ↓
Login    Reject

The application does not need to recover the original password. It only needs to verify whether the submitted password matches the stored representation.

What Is a Salt?

A salt is unique random data incorporated into password hashing.

Suppose two users select the same password:

User A → Password123
User B → Password123

Using different salts means their stored password hashes can still be different:

Password123 + Salt A → Hash A
Password123 + Salt B → Hash B

Salting makes precomputed password attacks more difficult and prevents identical passwords from automatically producing identical stored values.

Modern password-hashing libraries generally manage salts as part of their intended implementation.

What Is a Hash Table?

Hash functions are also used extensively outside cybersecurity.

A hash table is a data structure that uses hashing to determine where information should be stored.

For example:

Key: "user_123"
↓
Hash Function
↓
Index 7
↓
Stored Value

When the application needs that value again, it hashes the same key and determines the expected storage location.

Hash-based data structures appear as:

1. Dictionaries
2. Maps
3. Associative arrays
4. Sets
5. Caches

The hash functions used for these applications usually prioritize speed and efficient distribution rather than cryptographic security.

Hash Functions for Data Integrity

One of the most practical uses of cryptographic hashing is verifying whether data has changed.

Suppose a software provider publishes:

application.zip
SHA-256:
ABC123...XYZ

After downloading the application, the user calculates the file’s SHA-256 hash.

If:

Downloaded File Hash = Published Hash

the downloaded file matches the content represented by the published digest.

If the file changes because of corruption or modification, its cryptographic hash should also change.

However, the expected hash must come from a trustworthy source. If an attacker can replace both the software and its published hash, checksum comparison alone cannot establish authenticity.

Hash Functions in Digital Signatures

Cryptographic hashing is also an important building block in digital signature systems.

A simplified workflow is:

Document
↓
Hash Function
↓
Digest
↓
Digital Signature Process
↓
Signature

During verification, the relevant cryptographic process can determine whether the signed data has changed and whether the signature corresponds to the expected public key.

This helps provide integrity and authenticity for documents, software, messages, and other digital information.

Hash Functions in Blockchain

Blockchain technologies make extensive use of cryptographic hashes.

Depending on the blockchain architecture, hashes can help identify transactions, link data structures, create Merkle trees, and participate in consensus mechanisms.

A simplified blockchain relationship can look like:

Block 1
Hash: ABC
↓
Block 2
Previous Hash: ABC
Hash: DEF
↓
Block 3
Previous Hash: DEF
Hash: XYZ

If information in an earlier block changes, its hash changes. The reference stored in the following block would then no longer correspond to the modified data.

This relationship helps make unauthorized historical modifications detectable.

Common Mistakes When Using Hash Functions

One error developers make is assuming all hash algorithms offer the same level of security. Some algorithms focus on speed, while others are designed for cryptographic purposes.

You should also avoid using SHA-256 to store passwords in its raw form. In most cases, passwords require special algorithms such as Argon2, scrypt, bcrypt, or PBKDF2.

Another error is using deprecated algorithms such as MD5 or SHA-1 in applications that require collision resistance.

Also, it is better to avoid designing custom cryptographic hash functions, as cryptography is hard to get right and may have flaws in the design.

Lastly, hashing is not appropriate when you need to recover the original data.

How Moon Technolabs Helps With Secure Software Development?

Moon Technolabs offers support to organizations that require secure web, mobile, cloud, and enterprise applications that need secure authentication, credential storage, data integrity, secure APIs, and data management.

We have development teams that can deliver secure authentication systems, secure password storage systems based on existing libraries, encryption methods, role-based access control systems, API security, database security, and cloud security based on application needs.

We can also support updating legacy applications that use insecure hashing methods, password storage, authentication, or other insecure components.

Conclusion

The hash function turns input data into a fixed-length hash value using a certain mathematical formula. Hashing has a variety of uses in cybersecurity, including verifying passwords, digital signature validation, blockchain technology, databases, caching, data structures, and checking file integrity.

Cryptographic hash functions have properties such as determinism, preimage resistance, collision resistance, and the avalanche effect. Still, different purposes require different hashing methods.

Hashing, cryptographic hashing, password hashing, and non-cryptographic hashing are not the same. Developers should also distinguish between hashing, encryption, and encoding.

By using modern algorithms, trusted libraries, dedicated password-hashing methods, and secure software development, you can use hash functions as an essential building block for secure, reliable software.