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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

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2  
That's not a hash function, that's a permutation. –  delnan Apr 26 at 18:25
    
@delnan that is a very interesting way to think about it. But a permutation won't map data, it will just permute a random string. –  μακακας Apr 26 at 18:31
3  
It's a permutation of the space of possible strings. In other words, a permutation of a, b, c, ..., z, aa, bb, ..., zzz might be hro, z, , fas, ..., mfx, so that in function form f(a) = hro, f(b) = z, f(zzz) = mfz. It's a bijective mapping of strings. Block ciphers are commonly considered a family of permutations/bijective maps (one for each key), though with constraints that differ slightly from yours. –  delnan Apr 26 at 18:35
    
For what purpose do you need such a function? –  eBusiness Apr 26 at 20:43
1  
A function with no collisions and the output length depending on the input length seems more like a true encryption algorithm than a hash algorithm to me. Something like AES would meet your requirement. –  Snowman Apr 26 at 23:45

2 Answers 2

up vote 3 down vote accepted

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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Interesting idea. But how random/adjustable can this algorithm be? Also is it guaranteed to be one-to-one? –  μακακας Apr 26 at 19:09
    
I'm not sure what "how random" means, but both algorithms "look" random. Skip32 is harder to reverse (neither is secure against reversal). Skip32 can be adjusted to produce different numbers by changing the key. Multiplicative Inverses can be adjusted to produce different numbers by selecting different multiplicative inverses (and by selecting different ranges). The range of Multiplicative inverses can be selected very precisely, whereas the range of Skip32 encoding is always 32bit. –  Brian Apr 26 at 19:19

I'd use a perfect hash function to map your set of n inputs to a unique integer < n, then use that as an index into either an array of outputs (eg a list of n colours) or map it to a unique string in your character set (e.g. convert the number to base 26 and render each base-26 digit as that letter of the alphabet).

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