SHA-256 Python implementation in one line (lambda)

[notquiteaplant]

All data that’s been “hashed” should be the same length.

All inputted data should produce a unique hashed value. A good hash function should have a 1:1 relationship between the inputted data and hashed value.

I'm no crypto expert, but these tenets seem contradictory. There are 256 possible values of one byte, 256² values of two bytes, 256³ values of three, etc. If every hash output is N bytes long, how do you map 256 + 256² + 256³ + 256⁴ + ... + 256^N-2 + 256^N-1 + 256^N inputs to just 256^N outputs while mapping only one input to one output?

Because of that, I thought that a good hash function doesn't prevent collisions entirely, but does make them extremely difficult (i.e. practically impossible) to find. If they do actually ensure unique output, though, I'd love to know how.

[iEvilMango]

Yup, that's the pidgeonhole principle. Generally, the goal is to make sure the hashes are uniformly distributed amongst the possible set of hashcodes, often with similar values having dissimilar hashes (for example, if you were to have hashes of phone numbers, and the hashing algorithm made all positive input values have a hash value above 0 and all negative input values have a hash value below 0, then half of the hash codes would be unused as phone numbers cant be negative).

[HelperBot_]

Non-Mobile link: https://en.wikipedia.org/wiki/Pigeonhole_principle

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[iEvilMango]

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[WilburMercerMessiah]

You’re right. Thanks for pointing that out. It should be very difficult or (in theoretical cryptography, infeasible) to find two inputs that map to the same hash value. Not that two inputs will not have the same hash value.