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    <p><strong>Definition:</strong><br> <a href="http://en.wikipedia.org/wiki/Hash_function" rel="noreferrer">Hashing</a> is the application of a function <code>f()</code> to a variable sized input to produce a constant sized output.</p> <pre><code>A =&gt; f() =&gt; X B =&gt; f() =&gt; Y C =&gt; f() =&gt; Z </code></pre> <p>A hash is also a one-way function which means that there isn't a function to reverse or undo a hash. As well re-applying the hash <code>f(f(x))</code> isn't going to product <code>x</code> again.</p> <p><strong>The Details:</strong></p> <p>A hash function can be as simple as "add 13 to the input" or complex like a <a href="http://en.wikipedia.org/wiki/Cryptographic_hash_function" rel="noreferrer">Cryptographic Hash</a> such as <a href="http://en.wikipedia.org/wiki/MD5" rel="noreferrer">MD5</a> or <a href="http://en.wikipedia.org/wiki/SHA1" rel="noreferrer">SHA1</a>. There are many things that constitute a good hash function like:</p> <ul> <li><a href="http://en.wikipedia.org/wiki/Hash_function#Low_cost" rel="noreferrer">Low Cost</a>: Easy to compute</li> <li><a href="http://en.wikipedia.org/wiki/Hash_function#Determinism" rel="noreferrer">Deterministic</a>: if I hash the input <code>a</code> multiple times, I am going to get the same output each time</li> <li><a href="http://en.wikipedia.org/wiki/Hash_function#Uniformity" rel="noreferrer">Uniformity</a>: The input will be evenly distributed among the possible outputs. This falls in line with something called the <a href="http://en.wikipedia.org/wiki/Pigeonhole_principle" rel="noreferrer">Pigeonhole Principle</a>. Since there are a limited number of outputs we want <code>f()</code> to place those outputs evenly instead of in the same bucket. When two inputs compute to the same output this is known as a collision. It's a good thing for a hash function to produce fewer collisions.</li> </ul> <p><strong>Hashing applied to Passwords:</strong></p> <p>The hashing of passwords is the same process as described above, however it comes with some special considerations. Many of the properties that make up a good hash function are not beneficial when it comes to passwords.</p> <p>Take for example <em>determinism</em>, because hashes produce a deterministic result when two people use the same password the hash is going to look the same in the password store. This is a bad thing! However this is mitigated by something called a <a href="http://en.wikipedia.org/wiki/Salt_(cryptography)" rel="noreferrer">salt</a>.</p> <p><em>Uniformity</em> on the other hand is beneficial because the desire is for the algorithm to limit collisions. </p> <p>Because a hash is <em>One-Way</em> means the input cannot be determined from the output, which is why hashing is great for passwords!</p>
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