Fundamental difference between Hashing and Encryption algorithms

Question

I see a lot of confusion between hashes and encryption algorithms and I would like to hear some more expert advice about:

1. When to use hashes vs encryptions<

Answer 1

Use hashes when you don't want to be able to get back the original input, use encryption when you do.

Hashes take some input and turn it into some bits (usually thought of as a number, like a 32 bit integer, 64 bit integer, etc). The same input will always produce the same hash, but you PRINCIPALLY lose information in the process so you can't reliably reproduce the original input (there are a few caveats to that however).

Encryption principally preserves all of the information you put into the encryption function, just makes it hard (ideally impossible) for anyone to reverse back to the original input without possessing a specific key.

Simple Example of Hashing

Here's a trivial example to help you understand why hashing can't (in the general case) get back the original input. Say I'm creating a 1-bit hash. My hash function takes a bit string as input and sets the hash to 1 if there are an even number of bits set in the input string, else 0 if there were an odd number.

Example:

Input    Hash
0010     0
0011     1
0110     1
1000     0

Note that there are many input values that result in a hash of 0, and many that result in a hash of 1. If you know the hash is 0, you can't know for sure what the original input was.

By the way, this 1-bit hash isn't exactly contrived... have a look at parity bit.

Simple Example of Encryption

You might encrypt text by using a simple letter substitution, say if the input is A, you write B. If the input is B, you write C. All the way to the end of the alphabet, where if the input is Z, you write A again.

Input   Encrypted
CAT     DBU
ZOO     APP

Just like the simple hash example, this type of encryption has been used historically.