Cryptographic Hash Functions: Definition and Examples

What Are Cryptographic Hash Functions?

A cryptographic hash function is a mathematical function used in cryptography. Typical hash functions take inputs of variable lengths to return outputs of a fixed length.

A cryptographic hash function combines the message-passing capabilities of hash functions with security properties.

How Cryptographic Hash Functions Work

Hash functions are commonly used data structures in computing systems for tasks such as checking the integrity of messages and authenticating information. While they are considered cryptographically "weak" because they can be solved in polynomial time, they are not easily decipherable.

Cryptographic hash functions add security features to typical hash functions, making it more difficult to detect the contents of a message or information about recipients and senders. 

In particular, cryptographic hash functions exhibit these three properties:

• They are "collision-free." This means that no two input hashes should map to the same output hash. 
• They can be hidden. It should be difficult to guess the input value for a hash function from its output. 
• They should be puzzle-friendly. It should be difficult to select an input that provides a pre-defined output. Thus, the input should be selected from a distribution that's as wide as possible.

Examples of Cryptographic Hash Functions

Cryptographic hash functions are widely used in cryptocurrencies to pass transaction information anonymously. For example, Bitcoin, the original and largest cryptocurrency, uses the SHA-256 cryptographic hash function in its algorithm. Ethereum, the second most popular blockchain, uses Keccak-256 to hash information.

However, hashes have other applications in the real world. These are some of the most common cryptographic applications:

Password Verification

Storing passwords in a regular text file is dangerous, so nearly all sites store passwords as hashes. When a user inputs their password, it is hashed, and the result is compared to the list of hashed values stored on the company's servers. However, this is not a fool-proof practice—hackers have created databases of common passwords and their hashes, called rainbow tables, which make it easier for them to get into accounts whose information has been stolen.

Signature Generation and Verification

Verifying signatures is a mathematical process used to verify the authenticity of digital documents or messages. A valid digital signature, where the prerequisites are satisfied, gives its receiver strong proof that a known sender created the message and that it was not altered in transit.

A digital signature scheme typically consists of three algorithms: a key generation algorithm; a signing algorithm that, given a message and a private key, produces a signature; and a signature verifying algorithm.

Verifying File and Message Integrity

Hashes can ensure messages and files transmitted from sender to receiver are not tampered with during transit. The practice builds a "chain of trust." For example, a user might publish a hashed version of their data and the key so that recipients can compare the hash value they compute to the published value to make sure they align.

The Bottom Line

Cryptographic hash functions are programs that use a mathematical function, like an algorithm, to convert information to a hexadecimal form. These functions are also used in cryptocurrency to secure blockchain information.