Algorithms – Randomized Hash Function with No Collisions

algorithmshashingmath

Related to the question Which hashing algorithm is best for uniqueness and speed?

Is there a way to create a hash function, or find one, whose hash length depends completely on the input length, has an adjustable hash character set (Since it must be 1-to-1 function the input must comply to this character set constraint as well).

Moreover the most important part is that the hash function generates as random as possible strings. So for example it would be possible to get the following two different results. 

Hash(aaaa)->blue // for character set a-z

and 

Hash(aaaz)->pink  // for character set a-z

More examples:

Hash(aa@12a)->dakj@4   // for character set a-z, @, 0-9

and 

Hash(a2#46Ww)->@3#0Pdw // for character set a-z A-Z, !-), 0-9

Notice
the character length between input and output and the character sets.

What I thought so far was a probability distribution function, there are random distribution functions but I am not sure how to get there.

http://en.wikipedia.org/wiki/Probability_distribution

http://en.wikipedia.org/wiki/Normal_distribution

Best Answer

This is not a hash function. It's either an encoding function or an encryption function.

Usually when I've encountered a problem of this form, it is because I have some sort of IDs that I want to "look" random. Assuming I don't care about security, I'll normally create an algorithm which works as follows:

  1. Map my data to numbers (usually, by treating a string in a character set containing X characters as a baseX number).
  2. Map my numbers to new numbers. Eric Lippert suggests using Multiplicative Inverses for this purpose. Skip32 encoding (AKA Skip32 encryption, but it's not secure) also works for this purpose.
  3. Reverse the mapping in step 1.

To decode, perform the same steps in reverse.

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