Cryptographic hash function

A cryptographic hash function takes an input message of any length, such as a file, message, or password, and uses a mathematical formula to produce a fixed-size output (hash). The primary function of cryptographic hash functions is to verify the authenticity and integrity of input data. 

For example, to safely email a confidential attachment such as a medical report or financial statement, you can use this function to create a hash to accompany the original file. The recipient can use the same function to generate a hash of the file and compare it to the original to ensure both are identical.

In cryptography, hash functions must be:

Non-invertible — This ensures that only a trial-and-error approach, or “brute force,” can lead to discovering the original message from its hash output, also called a “digest.” If you only have the digest, it should be nearly impossible to trace it back to the original data 

Quick to compute — Given the frequency of generating new hash functions, hash functions must calculate quickly to ensure efficient and uninterrupted operations

Tamper-resistant — Any modification made to the original message, no matter how minor, must result in a completely different hash output. This process allows for detection of even the smallest alterations

Collision-resistant — No two messages should produce the same digest, preventing confusion and enhancing security

A hash function in cryptography is like a fast (quick to compute) blender. Imagine throwing in fruits (data) and getting a smoothie (digest). It’s impossible to retrieve the original fruits from the smoothie (non-invertibility), any changes in fruits results in a different smoothie (tamper-resistant), and it’s unlikely that different combinations of fruit will produce the exact same smoothie (collision-resistant). 

Cryptographic hash functions are foundational in ensuring secure data handling and communication in digital systems. 

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