# Uniform distribution on 255 from text [closed]

I'm trying to create a way to link letters from a text to a position between 1 to 255.

For example, the text is : "stackexchange" I would like to link every letter to a number between 1 and 255. The same word should have the same output and the overall should be uniform (if I give lots of input, I would like to have an uniform distribution.) // And of course, I want that "stackexchange" always give the same output.

// e.g. s=>12 || t=>88 || a=>65 || c=>214 || ... || c=>142 ||...

Could you help me ? Thanks !

## closed as not a real question by russellpierce, gung - Reinstate Monica♦, Peter Flom - Reinstate Monica♦, Andy W, cardinalMar 7 '13 at 2:20

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• What does overall should be uniform mean? If $c$ is so much less common thn $a$ how can the distribution be uniform? i.e. $65$ will occur much more often than $214$. – curious_cat Mar 4 '13 at 14:25
• Well, because the letter c shouldn't always give 214. (c=>142 for the 2nd time) – fast_cen Mar 4 '13 at 14:48
• @MrBenderV You said "the same letter should have the same number". And in the comment "the letter c shouldn't always give 214". Can you clarify? – ziggystar Mar 4 '13 at 15:16
• @ziggystar Clarified, I meant the same word to have the same input (an array of length(word) of number between 1 and 255). – fast_cen Mar 4 '13 at 15:19
• Why not just use a random number generator then, and use the word as the seed for the generator, outputting N numbers for a word of length N? – Corone Mar 4 '13 at 15:32

Corone's comment is by far a simpler method as what I am proposing.

First, you don't want a function from letters to numbers, since then you would only produce about 50 values.

In general a function, which maps pairs of words and positions in those words to [1,255] seems what you want to have.

# Possible Solution

One possibility would be mapping the sequence of the k last letters in the word to numbers.

# Example for k=3

input: stackexchange
inputs:      s
(s)  t
(st) a
(ta) c
(ac) k
...


Then you have to find a mapping for all possible at most k-length sequences, which maximizes uniformity. This is probably done by training on some sample text body.

• +1; The sample body is going to be critical. For example, words like "a", "of", "the" etc may appear a bunch in a corpus and completely bork any attempt to make the distribution uniform. – russellpierce Mar 4 '13 at 18:21

Thanks to yours ideas, I think I have found something that can help.

I will sha-1 my word.

e.g. stackexchange will give "19f054f1f448ff152f1d586be39a56f179fe80c9"

Each letter had [10 (0 to 9) + (a-f) 6] => 16 output possible.
If I take two letter each time. I give me (16*16) 256 output different.

If the output is 256 (less than 0.5% chance), I don't take into account and move to the two next letter, and try again.

e.g. with stackexchange :

'19' = (1,9) => link to (16+10=26) 26

'f0' = (15,0) => link to (15*16+1=241) 241 ...

After I can easely solve the problem of output size, ect.

Again ;Thank you @ziggystar and @Corone for the help and the ideas !

• Well a SHA hash like the one you are describing takes on values between 0 and 255, so you don't have to worry about it turning out as 256, but you might have to worry about it coming out at 0 (although I can't imagine why). The other issue is that there are no guarantees that the distribution of values in a SHA hash are uniform (a quick adhoc look suggests that they might not be). – russellpierce Mar 5 '13 at 4:21
• SHA should pass uniformity for single use, otherwise this would lead to cryptographic weakness. However, the vector properties may not be uniform, e.g. if you take N words and SHA them together, that might not be uniform in N dimensional space. – Corone Mar 5 '13 at 9:43