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    <p>I don't think so.</p> <p>There is no easy way to show why it's not possible. If there was, then this would itself be the basis of an algorithm to find collisions.</p> <p>Longer analysis: </p> <p>The preprocessing makes sure that there is always at least one <code>1</code> bit in the input.</p> <p>The loop over <code>w[i]</code> will leave the original stream alone, so there is at least one 1 bit in the input (words 0 to 15). Even with clever design of the bit patterns, at least some of the values from 0 to 15 must be non-zero since the loop doesn't affect them.</p> <p>Note: <code>leftrotate</code> is circular, so no 1 bits will get lost.</p> <p>In the main loop, it's easy to see that the factor <code>k</code> is never zero, so <code>temp</code> can't be zero for the reason that all operands on the right hand side are zero (<code>k</code> never is).</p> <p>This leaves us with the question whether you can create a bit pattern for which <code>(a leftrotate 5) + f + e + k + w[i]</code> returns 0 by overflowing the sum. For this, we need to find values for <code>w[i]</code> such that <code>w[i] = 0 - ((a leftrotate 5) + f + e + k)</code></p> <p>This is possible for the first 16 values of <code>w[i]</code> since you have full control over them. But the words 16 to 79 are again created by <code>xor</code>ing the first 16 values.</p> <p>So the next step could be to unroll the loops and create a system of linear equations. I'll leave that as an exercise to the reader ;-) The system is interesting since we have a loop that creates additional equations until we end up with a stable result.</p> <p>Basically, the algorithm was chosen in such a way that you can create individual 0 words by selecting input patterns but these effects are countered by <code>xor</code>ing the input patterns to create the 64 other inputs.</p> <p>Just an example: To make <code>temp</code> 0, we have</p> <pre><code>a = h0 = 0x67452301 f = (b and c) or ((not b) and d) = (h1 and h2) or ((not h1) and h3) = (0xEFCDAB89 &amp; 0x98BADCFE) | (~0x98BADCFE &amp; 0x10325476) = 0x98badcfe e = 0xC3D2E1F0 k = 0x5A827999 </code></pre> <p>which gives us <code>w[0] = 0x9fb498b3</code>, etc. This value is then used in the words 16, 19, 22, 24-25, 27-28, 30-79.</p> <p>Word 1, similarly, is used in words 1, 17, 20, 23, 25-26, 28-29, 31-79.</p> <p>As you can see, there is a lot of overlap. If you calculate the input value that would give you a 0 result, that value influences at last 32 other input values.</p>
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