6 Character Short Hash Algorithm

Question

My goal is to generate a short Hash string of 6 characters (possibly containing characters [A-Z][a-z][0-9]) for a string which is 42 case-insensitive alphanumeric characters in length. Uniqueness is the key requirement. Security or performance is not so important.

Is there a specific algorithm which will give this result or should I stick to truncating a MD5 Hash or a SHA-1 Hash (Like in this question)? If so, what is the probability of a collision?

Answer 1

Your best bet would be the truncating well-known hash function (MD5 or SHA-family) because these algorithms have statistically good uniform distributions of the hash values (and also using full hash and not just 6 chars there).

Now some calculations for probability of collision

- Number of letters in English alphabet: 26
- Add capitals: 26
- Add numerics: 10
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In total you get 26 + 26 + 10 = 62 characters. 

Now you have 6 places, which gives you 62^6 possible combinations.
That is 56.800.235.584 ~ 57 billion combinations. 
This is a space of possible hash values - N.
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To compute collisions let's use the formula 

Pcollision = K^2 / 2N

Which is a very rough approximation of collision probability

Now let's see the result table for a number of items in a table - K

# items     | Probability of collision
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10          |  1.7 * 10^-9
100         |  1.7 * 10^-7
1K          |  1.7 * 10^-5
10K         |  1.7 * 10^-3
100K        |  0.17

This formula can only be used for small K, but it shows that given 100K entries in the hash table you would roughly have 17% chance of collision.

Links

Collision probability