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    <p>A "hash" is the solution created to solve <strong>exactly</strong> the problem you are describing. See <a href="http://en.wikipedia.org/wiki/Hash_function" rel="nofollow noreferrer">wikipedia's article</a></p> <p>Any hash function you use will be nice; hash functions tend to be judged based on these criteria:</p> <ul> <li>The degree to which they prevent <em>collisions</em> (two separate inputs producing the same output) -- a by-product of this is the degree to which the function minimizes outputs that may never be reached from any input.</li> <li>The uniformity the distribution of its outputs given a uniformly distributed set of inputs</li> <li>The degree to which small changes in the input create large changes in the output.</li> </ul> <p>(see <a href="http://en.wikipedia.org/wiki/Perfect_hash_function" rel="nofollow noreferrer">perfect hash function</a>)</p> <p>Given how hard it is to create a hash function that maximizes all of these criteria, why not just use one of the most commonly used and relied-on existing hash functions there already are?</p> <p>From what it seems, turning integers into strings almost seems like another layer of encryption! (which is good for your purposes, I'd assume)</p> <p>However, your question asks for hash functions that deal <strong>specifically with numbers</strong>, so here we go.</p> <hr> <h1>Hash functions that work over the integers</h1> <p>If you want to borrow already-existing algorithms, you may want to dabble in <strong><a href="http://en.wikipedia.org/wiki/Pseudorandom_number_generator" rel="nofollow noreferrer">pseudo-random number generators</a></strong></p> <p>One simple one is the middle square method:</p> <ul> <li>Take a digit number</li> <li>Square it</li> <li>Chop off the digits and leave the middle digits with the same length as your original.</li> </ul> <p>ie,</p> <pre><code>1111 =&gt; 01234321 =&gt; 2342 </code></pre> <p>so, 1111 would be "hashed" to 2342, in the middle square method.</p> <p>This way isn't <strong>that</strong> effective, but for a few number of hashes, this has very low collision rates, a uniform distribution, and great chaos-potential (small changes => big changes). But if you have many values, time to look for something else...</p> <p>The grand-daddy of all feasibly efficient and simple random number generators is the (Mersenne Twister)[<a href="http://en.wikipedia.org/wiki/Mersenne_twister]" rel="nofollow noreferrer">http://en.wikipedia.org/wiki/Mersenne_twister]</a>. In fact, an implementation is probably out there for every programming language imaginable. Your hash "input" is something that will be called a "seed" in their terminology.</p> <p>In conclusion</p> <ol> <li>Nothing wrong with string-based hash functions</li> <li>If you want to stick with the integers and be fancy, try using your number as a seed for a pseudo-random number generator.</li> </ol>
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    1. POA function where small changes in input always result in large changes in output
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    1. USJUST MY correct OPINION
    1. USJustin L.
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    1. COThis is a great answer, *but*: one of my unsuccessful attempts was with the Mersenne Twister, so what I think I need is an actual example implementation, and pseudo code is OK. It's been at least a year (probably more) since I was experimenting with this, so I don't remember exactly what my problem was, though.
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      1. USPeter Jaric
    2. COOops, I didn't notice that you specifically mentioned trying pseudo-random numbers in your question. I feel sorta dumb now. Anyways, is there any reason you are attempting to write Mersenne from scratch, as opposed to using a pre-existing library? What language are you working in?
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      1. USJustin L.
    3. COsee Pete Kirkham's answer to Bob Jenkins' Mix function; it seems like something you could use.
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