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<h1>The International Obfuscated C Code Contest</h1>
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<h2>2019/diels-grabsch2 - Most self-aware</h2>
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<h3>Self hashing</h3>
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<a class="Right" href="https://github.com/ioccc-src/winner/blob/master/2019/diels-grabsch2/prog.c">C code</a>
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<a class="Right" href="https://github.com/ioccc-src/winner/blob/master/2019/diels-grabsch2/prog.orig.c">Original C</a>
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<h2 id="author">Author:</h2>
|
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<ul>
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<li>Name: <a href="../../authors.html#Volker_Diels-Grabsch">Volker Diels-Grabsch</a><br>
|
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Location: <a href="../../location.html#DE">DE</a> - <em>Federal Republic of Germany</em> (<em>Germany</em>)</li>
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<h2 id="to-build">To build:</h2>
|
||
<pre><code> make</code></pre>
|
||
<h2 id="to-use">To use:</h2>
|
||
<pre><code> ./prog</code></pre>
|
||
<h2 id="try">Try:</h2>
|
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<pre><code> ./try.sh</code></pre>
|
||
<h2 id="judges-remarks">Judges’ remarks:</h2>
|
||
<p>Before running this one, stay calm. Chill out, have a cup of tea. Is this bad?</p>
|
||
<p>To understand what is going on here, please check if you are dreaming, or are you dreaming
|
||
that you are dreaming? Or is it, wake up from the simulation?</p>
|
||
<h2 id="authors-remarks">Author’s remarks:</h2>
|
||
<h3 id="almost-a-hash-collision">Almost a hash collision:</h3>
|
||
<p>This program prints its own SHA-512 hash. To verify, run:</p>
|
||
<pre><code> $ sha512sum prog.c; ./prog
|
||
43bd0c4381a5078d2850fca9ae5e0647596bcc03cd67d8d973ad02ff35c316c728e7b347ca70abe6c74e745e63646cc7643cb0cffcd3d9a969cbf31a7ce5bf68 prog.c
|
||
43bd0c4381a5078d2850fca9ae5e0647596bcc03cd67d8d973ad02ff35c316c728e7b347ca70abe6c74e745e63646cc7643cb0cffcd3d9a969cbf31a7ce5bf68</code></pre>
|
||
<p>It started as a complicated “hello world” program that prints some random hex
|
||
digits instead of “hello world”. Then, the digits were adjusted until the
|
||
resulting program matched its own SHA-512 hash, via brute force through all
|
||
2^512 possibilities. Just kidding.</p>
|
||
<p>This wasn’t brute force, but involved quite some math, using a variant of Jane
|
||
Doe’s algorithm for generating SHA-512 collisions efficiently. If you still
|
||
don’t believe me, you are right.</p>
|
||
<p>No crypto was broken in the making of this program!</p>
|
||
<p>The trick is that under the hood, this program is a quine! That is, it is aware
|
||
of its own source code in string representation. But instead of printing that
|
||
string (its own source), its SHA-512 hash is computed and printed. So two major
|
||
steps were needed to obfuscate this program:</p>
|
||
<ol type="1">
|
||
<li>Hide the quine.</li>
|
||
<li>Hide the SHA-512 computation.</li>
|
||
</ol>
|
||
<p>Note that both steps were achieved mostly algorithmically. The code
|
||
is otherwise as short and as clean as possible. The implementation is
|
||
portable C99 code for 32-bit and 64-bit systems that compiles without
|
||
any warnings on current GCC and Clang versions even with <code>-Wextra -Weverything</code>. The program is composed of mostly pure functions, and
|
||
the <code>#define</code>s are only used to shorten redundant parts of the code,
|
||
they are not meant to obfuscate much. Having that out of the way, how
|
||
are step 1 and step 2 achieved then?</p>
|
||
<p>Regarding step 1, note that the large string literal</p>
|
||
<pre><code> "`x{bh}ndbq..."</code></pre>
|
||
<p>in the last line doesn’t look like C code. Moreover, it is too short
|
||
to contain even a compressed representation of all preceding and
|
||
subsequent code. Instead, the preceding code including the <code>"</code>
|
||
character has already been run through the SHA-512 computation by an
|
||
external script. The internal state of the SHA-512 computation at
|
||
that point has been extracted and encoded into the string. This works
|
||
because the preceding code is exactly 1280 bytes, which is a multiple
|
||
of 1024 bits, the block size of SHA-512. The program itself then just
|
||
continues the SHA-512 computation from that point, adding the last
|
||
1024-bit block, finalizing the hash and printing it. The last block
|
||
is taken directly from the string literal at runtime, plus the
|
||
subsequent code which consists of just <code>"</code>, <code>;</code> and <code>\n</code>. Those 3
|
||
characters are short enough to be hidden in … well, let’s leave this
|
||
as an exercise for the reader.</p>
|
||
<p>To summarize, the main trick here is to move the string constant to
|
||
the end, so the preceding code can be pre-calculated and the subsequent
|
||
code is short enough to be hidden anywhere.</p>
|
||
<p>Regarding step 2, almost all macros, functions and variables have
|
||
meaningless single-letter names. Moreover, the SHA-512 computation is
|
||
reduced to the special case of adding just one block and immediately
|
||
finalizing it, where the total size is known in advance.</p>
|
||
<p>But this is not enough! For SHA-512 we need 8 initial hash values and 80 round
|
||
constants, which are very characteristic. If any of them appeared in the
|
||
source, a quick web search (e.g. for <code>0x428a2f98d728ae22</code>) would tell the reader
|
||
immediately what’s going on. Because of the pre-computation, the 8 initial hash
|
||
values are not needed, but the 80 round constants are.</p>
|
||
<p>It is almost impossible to hide those 640 bytes in the source.
|
||
Luckily, the round constants where not chosen by fair dice rolls.
|
||
They are the fractional parts of certain irrational numbers, namely,
|
||
the cube roots of the first 80 primes. So the round constants are
|
||
calculated at runtime, which makes the program shorter and adds
|
||
another layer of obfuscation.</p>
|
||
<p>While this sounds like just iterating primes and executing <code>pow(3)</code>, this
|
||
turned out to be harder than expected. If we were computing SHA-256,
|
||
it would have been as simple as that, because the round constants
|
||
would have been 32-bit values. However, SHA-512 needs the cube roots
|
||
at 64-bit precision, while <code>double</code> has only 53-bit mantissa precision.</p>
|
||
<p>Using higher-precision floating point is no option here, because the
|
||
program is meant to be portable C99. And implementing arbitrary-precision
|
||
arithmetic would have been overkill and would have increased the program size
|
||
dramatically.</p>
|
||
<p>Instead, the program just multiplies. That is, it computes cubes
|
||
instead of cube roots. It steps through cube root candidates via
|
||
bisection, and calculates their cubes until those match the given
|
||
prime. Thus, we don’t need floating point and can use 64-bit integers
|
||
instead. But that still doesn’t solve the problem as it poses the
|
||
following new challenges:</p>
|
||
<ul>
|
||
<li>Challenge 1: We can multiply at most two 32-bit numbers at once.</li>
|
||
<li>Challenge 2: We need to calculate with at least 67-bit precision.</li>
|
||
<li>Challenge 3: We need to truncate the cube root result.</li>
|
||
</ul>
|
||
<p>The reason for challenge 1 is that in portable C99, the result must
|
||
fit into the same data type. To multiply two 64-bit integers we would
|
||
need a 128-bit integer for the result. So we can at most multiply two
|
||
32-bit integers to get the 64-bit product at full precision. While
|
||
GCC and Clang both support 128-bit arithmetics, that isn’t standard
|
||
and wouldn’t have been portable C99.</p>
|
||
<p>The reason for challenge 2 is that cube root of the 80th prime is
|
||
around 7, so we need to compute with 3 bits for the integral part and
|
||
64 bits for the fractional part.</p>
|
||
<p>The reason for challenge 3 is that the cube of a 67-bit number is
|
||
<code>3*67=201</code> bits, but fortunately we only need to check if it is close
|
||
enough to the actual prime. It won’t be exactly <code>409.0000...</code>
|
||
anyway, but must be accurate enough to distinguish the correct cube
|
||
root from its neighbours, e.g. the same number with the 64th
|
||
fractional digit increased.</p>
|
||
<p>The solution here is to split the 67-bit input into 3 integers of
|
||
24-bit each. Those are cubed using the multiplication formulas
|
||
numbers with 3 “digits” of base <code>2^24</code> each. During that calculation,
|
||
at most two values are multiplied at once, and the accuracy of
|
||
intermediate values is reduced using right-shifts as far as allowable
|
||
for the computation. Finding working right-shift values was mostly
|
||
trial-and-error, producing correct results for the first 80 primes,
|
||
but not much more. Moreover, for some terms it was possible to leave
|
||
them out entirely, especially higher-order terms of the last digits.
|
||
Luckily, in the end, all intermediate results did fit into 64-bit
|
||
integer addition and multiplication, but that was not obvious at the
|
||
beginning.</p>
|
||
<p>That’s it.</p>
|
||
<p>Well, I could continue with details about the encoding of the internal
|
||
state values into the string, how to avoid escaping issues, how to
|
||
find short notations for various loops, how to get rid of <code>if()</code>, where
|
||
the final <code>"\";\n"</code> is stored, how to eliminate intermediate values and
|
||
arrays by reordering of operations, and so on. But those were all
|
||
minor issues compared to the challenges described above. What’s
|
||
documented here is all you need to know to write your own version of
|
||
that program.</p>
|
||
<p>I’d like to finish with an open problem:</p>
|
||
<p>Is it possible for the cubing and bisection to be implemented with
|
||
just two parts instead of three? That would simplify the formulas a
|
||
lot. For example, one could split the 67-value into two 34-bit parts,
|
||
but whenever one multiplies two of them, one needs to right-shift one
|
||
of them by at least 4 bits, or both by 2. Or, one splits the 67 bits
|
||
asymmetrically? I was unable to make it work with 2 parts, but that
|
||
doesn’t have to mean anything.</p>
|
||
<!--
|
||
|
||
Copyright © 1984-2024 by Landon Curt Noll. All Rights Reserved.
|
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|
||
You are free to share and adapt this file under the terms of this license:
|
||
|
||
Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
|
||
|
||
For more information, see:
|
||
|
||
https://creativecommons.org/licenses/by-sa/4.0/
|
||
|
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|
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<div id="inventory">
|
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<h1 id="inventory-for-2019diels-grabsch2">Inventory for 2019/diels-grabsch2</h1>
|
||
</div>
|
||
<h2 id="primary-files">Primary files</h2>
|
||
<ul>
|
||
<li><a href="https://github.com/ioccc-src/winner/blob/master/2019/diels-grabsch2/prog.c">prog.c</a> - entry source code</li>
|
||
<li><a href="https://github.com/ioccc-src/winner/blob/master/2019/diels-grabsch2/Makefile">Makefile</a> - entry Makefile</li>
|
||
<li><a href="https://github.com/ioccc-src/winner/blob/master/2019/diels-grabsch2/prog.orig.c">prog.orig.c</a> - original source code</li>
|
||
<li><a href="https://github.com/ioccc-src/winner/blob/master/2019/diels-grabsch2/try.sh">try.sh</a> - script to try entry</li>
|
||
</ul>
|
||
<h2 id="secondary-files">Secondary files</h2>
|
||
<ul>
|
||
<li><a href="2019_diels-grabsch2.tar.bz2">2019_diels-grabsch2.tar.bz2</a> - download entry tarball</li>
|
||
<li><a href="https://github.com/ioccc-src/winner/blob/master/2019/diels-grabsch2/README.md">README.md</a> - markdown source for this web page</li>
|
||
<li><a href="https://github.com/ioccc-src/winner/blob/master/2019/diels-grabsch2/.entry.json">.entry.json</a> - entry summary and manifest in JSON</li>
|
||
<li><a href="https://github.com/ioccc-src/winner/blob/master/2019/diels-grabsch2/.gitignore">.gitignore</a> - list of files that should not be committed under git</li>
|
||
<li><a href="https://github.com/ioccc-src/winner/blob/master/2019/diels-grabsch2/.path">.path</a> - directory path from top level directory</li>
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||
<li><a href="index.html">index.html</a> - this web page</li>
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</ul>
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<hr style="width:10%;text-align:left;margin-left:0">
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<h4>
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Jump to: <a href="#">top</a>
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Copyright © 1984-2025 by Landon Curt Noll. All Rights Reserved.
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You are free to share and adapt this file under the terms of this license:
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Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
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For more information, see:
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https://creativecommons.org/licenses/by-sa/4.0/
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<div class="footer">
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<div id="copyright"><h3>Copyright © 1984-2025 by Landon Curt Noll:
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<a href="https://creativecommons.org/faq/#what-does-some-rights-reserved-mean"
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target="_blank"
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rel="license noopener noreferrer">Some Rights Reserved</a></h3>
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<p>
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This work is <b>licensed by Landon Curt Noll</b> under
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<b><a href="https://creativecommons.org/licenses/by-sa/4.0/?ref=chooser-v1"
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target="_blank"
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rel="license noopener noreferrer"
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style="display:inline-block;">CC BY-SA 4.0</a></b>.
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<img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;"
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src="../../png/cc.png"
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alt="cc inside circle symbol">
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<img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;"
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src="../../png/by.png"
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alt="person inside circle symbol">
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<img style="height:22px!important;margin-left:3px;vertical-align:text-bottom;"
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alt="arrow looping back on itself inside circle symbol"><br>
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You should <b>carefully review</b> the
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target="_blank"
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rel="license noopener noreferrer">CC BY-SA 4.0 LEGAL CODE</a></b>
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before using the licensed material.<br>
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You may wish to review the
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<b><a href="../../license.html"
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target="_blank"
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rel="license noopener noreferrer">highlights of some of the key features and terms</a></b>
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of <b>CC BY-SA 4.0</b>.<br>
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</p>
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</div>
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<div id="coda"><h3>Coda</h3>
|
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<p>
|
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<a href="https://validator.w3.org/nu/?doc=https%3A%2F%2Fwww.ioccc.org%2F2019%2Fdiels-grabsch2%2Findex.html" rel="nofollow">Nu HTML check this web page</a><br>
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<a href="#top">Jump to top</a> <a href="#content">Jump to Content</a> <a href="#inventory">Jump to Inventory</a><br>
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