CTFtime.org / Chaos Communication Camp 2019 / babyquantum / Writeup

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<div id="readme" class="Box-body readme blob js-code-block-container px-5"> <article class="markdown-body entry-content" itemprop="text"><p>So to start of the challenge we take a look at the instructions page and see the definitions for this random secret gate of theirs.</p> <p><a target="_blank" rel="noopener noreferrer" href="/MjSandberg/CTF-writeups/blob/solved/2019/ALLESCTF/tex/166ec9a8fa1d0703dd6161f0c1fabafb.svg?invert_in_darkmode&sanitize=true"><img src="/MjSandberg/CTF-writeups/raw/solved/2019/ALLESCTF/tex/166ec9a8fa1d0703dd6161f0c1fabafb.svg?invert_in_darkmode&sanitize=true" align="middle" width="163.18329224999997pt" height="24.65753399999998pt/" style="max-width:100%;"></a></p> <p><a target="_blank" rel="noopener noreferrer" href="/MjSandberg/CTF-writeups/blob/solved/2019/ALLESCTF/tex/9e8514ae528c0c828aea8603bce5e0a1.svg?invert_in_darkmode&sanitize=true"><img src="/MjSandberg/CTF-writeups/raw/solved/2019/ALLESCTF/tex/9e8514ae528c0c828aea8603bce5e0a1.svg?invert_in_darkmode&sanitize=true" align="middle" width="133.61367855pt" height="24.65753399999998pt/" style="max-width:100%;"></a></p> <p>Since I have worked we these kinds of gates before I see that the definitions closely resemble that of the gate used for a Deutsch algorithm. This is a algorithm that is used to minimize function calls to tell whether a function is balanced or constant. The algorithm uses a auxiliary qubit which is our second qubit in the <a target="_blank" rel="noopener noreferrer" href="/MjSandberg/CTF-writeups/blob/solved/2019/ALLESCTF/tex/ec2376fb49efb4243a3f5d76fe720bbb.svg?invert_in_darkmode&sanitize=true"><img src="/MjSandberg/CTF-writeups/raw/solved/2019/ALLESCTF/tex/ec2376fb49efb4243a3f5d76fe720bbb.svg?invert_in_darkmode&sanitize=true" align="middle" width="19.178149649999988pt" height="24.65753399999998pt/" style="max-width:100%;"></a> state. Both qubits are then brought into superposition using two hadamards and the unitary gate <a target="_blank" rel="noopener noreferrer" href="/MjSandberg/CTF-writeups/blob/solved/2019/ALLESCTF/tex/f30c6bdebe1ddebdec6bb56fee7a3364.svg?invert_in_darkmode&sanitize=true"><img src="/MjSandberg/CTF-writeups/raw/solved/2019/ALLESCTF/tex/f30c6bdebe1ddebdec6bb56fee7a3364.svg?invert_in_darkmode&sanitize=true" align="middle" width="17.68118549999999pt" height="22.465723500000017pt/" style="max-width:100%;"></a> is applied across the two qubits. The first qubit is then brought back to a single state using another hadamard. In the case of Deutsch reading the first qubit then gives us the function calls <a target="_blank" rel="noopener noreferrer" href="/MjSandberg/CTF-writeups/blob/solved/2019/ALLESCTF/tex/31a6bef948c533616d360da71a62ac2a.svg?invert_in_darkmode&sanitize=true"><img src="/MjSandberg/CTF-writeups/raw/solved/2019/ALLESCTF/tex/31a6bef948c533616d360da71a62ac2a.svg?invert_in_darkmode&sanitize=true" align="middle" width="92.69424285pt" height="24.65753399999998pt/" style="max-width:100%;"></a> which is completely equal to <a target="_blank" rel="noopener noreferrer" href="/MjSandberg/CTF-writeups/blob/solved/2019/ALLESCTF/tex/c73b6615f0c7bd519371e439b4efff6d.svg?invert_in_darkmode&sanitize=true"><img src="/MjSandberg/CTF-writeups/raw/solved/2019/ALLESCTF/tex/c73b6615f0c7bd519371e439b4efff6d.svg?invert_in_darkmode&sanitize=true" align="middle" width="30.05337719999999pt" height="24.65753399999998pt/" style="max-width:100%;"></a>.</p> <p>Thus xor'ing these two possible function calls is given by</p> <p><a target="_blank" rel="noopener noreferrer" href="/MjSandberg/CTF-writeups/blob/solved/2019/ALLESCTF/tex/70c04e97552b8950725615a8c02fc4b8.svg?invert_in_darkmode&sanitize=true"><img src="/MjSandberg/CTF-writeups/raw/solved/2019/ALLESCTF/tex/70c04e97552b8950725615a8c02fc4b8.svg?invert_in_darkmode&sanitize=true" align="middle" width="206.59578059999996pt" height="24.65753399999998pt/" style="max-width:100%;"></a></p> <p><a target="_blank" rel="noopener noreferrer" href="/MjSandberg/CTF-writeups/blob/solved/2019/ALLESCTF/tex/0fd22aefb18e071e1162d7d79754c301.svg?invert_in_darkmode&sanitize=true"><img src="/MjSandberg/CTF-writeups/raw/solved/2019/ALLESCTF/tex/0fd22aefb18e071e1162d7d79754c301.svg?invert_in_darkmode&sanitize=true" align="middle" width="166.08222179999999pt" height="24.65753399999998pt/" style="max-width:100%;"></a></p> <p>Where the first term will always be zero thus</p> <p><a target="_blank" rel="noopener noreferrer" href="/MjSandberg/CTF-writeups/blob/solved/2019/ALLESCTF/tex/95397cbaab58b38a581647f951865244.svg?invert_in_darkmode&sanitize=true"><img src="/MjSandberg/CTF-writeups/raw/solved/2019/ALLESCTF/tex/95397cbaab58b38a581647f951865244.svg?invert_in_darkmode&sanitize=true" align="middle" width="80.75801414999998pt" height="24.65753399999998pt/" style="max-width:100%;"></a></p> <p>So depending on the outcome of the first qubit we can find <a target="_blank" rel="noopener noreferrer" href="/MjSandberg/CTF-writeups/blob/solved/2019/ALLESCTF/tex/4fa3ac8fe93c68be3fe7ab53bdeb2efa.svg?invert_in_darkmode&sanitize=true"><img src="/MjSandberg/CTF-writeups/raw/solved/2019/ALLESCTF/tex/4fa3ac8fe93c68be3fe7ab53bdeb2efa.svg?invert_in_darkmode&sanitize=true" align="middle" width="12.35637809999999pt" height="14.15524440000002pt/" style="max-width:100%;"></a>. If the outcome is 0 then <a target="_blank" rel="noopener noreferrer" href="/MjSandberg/CTF-writeups/blob/solved/2019/ALLESCTF/tex/4fa3ac8fe93c68be3fe7ab53bdeb2efa.svg?invert_in_darkmode&sanitize=true"><img src="/MjSandberg/CTF-writeups/raw/solved/2019/ALLESCTF/tex/4fa3ac8fe93c68be3fe7ab53bdeb2efa.svg?invert_in_darkmode&sanitize=true" align="middle" width="12.35637809999999pt" height="14.15524440000002pt/" style="max-width:100%;"></a> is also 0 and the same for the outcome of 1.</p> <p>Now the trouble was that we are only given a specific <a target="_blank" rel="noopener noreferrer" href="/MjSandberg/CTF-writeups/blob/solved/2019/ALLESCTF/tex/4fa3ac8fe93c68be3fe7ab53bdeb2efa.svg?invert_in_darkmode&sanitize=true"><img src="/MjSandberg/CTF-writeups/raw/solved/2019/ALLESCTF/tex/4fa3ac8fe93c68be3fe7ab53bdeb2efa.svg?invert_in_darkmode&sanitize=true" align="middle" width="12.35637809999999pt" height="14.15524440000002pt/" style="max-width:100%;"></a> and we would really like all of <a target="_blank" rel="noopener noreferrer" href="/MjSandberg/CTF-writeups/blob/solved/2019/ALLESCTF/tex/6f9bad7347b91ceebebd3ad7e6f6f2d1.svg?invert_in_darkmode&sanitize=true"><img src="/MjSandberg/CTF-writeups/raw/solved/2019/ALLESCTF/tex/6f9bad7347b91ceebebd3ad7e6f6f2d1.svg?invert_in_darkmode&sanitize=true" align="middle" width="7.7054801999999905pt" height="14.15524440000002pt/" style="max-width:100%;"></a>. This part is probably obvious to most but it took me a while to figure out. I discovered after using Chrome's dev tools and looking around for a bit, that we get one cookie named "randomness" which is set to a specific numeric value. I figured that this is probably used to set the value for <a target="_blank" rel="noopener noreferrer" href="/MjSandberg/CTF-writeups/blob/solved/2019/ALLESCTF/tex/4fa3ac8fe93c68be3fe7ab53bdeb2efa.svg?invert_in_darkmode&sanitize=true"><img src="/MjSandberg/CTF-writeups/raw/solved/2019/ALLESCTF/tex/4fa3ac8fe93c68be3fe7ab53bdeb2efa.svg?invert_in_darkmode&sanitize=true" align="middle" width="12.35637809999999pt" height="14.15524440000002pt/" style="max-width:100%;"></a>. So I wrote up a script in python (Babyquantum.py in rep) using selenium passed the circuit from Deutsch as</p> <p>- H U1 H D</p> <p>X H U2 H D</p> <p>and went through the values 0-200 for the cookie, reading the output of the first qubit. this gave me a binary.</p> <p>10000010 00110010 00110010 10100010 11001010 11011110 11001110 11000110 00010110 01001110 11110110 10100110 00100110 10010110 01110110 11100110 10100110 01001110 11001110 11111010 01000110 10000110 01000110 10011110 10111110</p> <p>Which again I looked at for quite a while not able to make sense of it. I finally figured that since nothing else was given the flag probably had ALLES in the start, which almost fit with what I had, Mathing up the letters I realized that the binary string was flipped. Thus after flipping and converting to ascii I got a flipped string which I again flipped giving the flag</p> <p>ALLES{schroedingers_baby}</p> </article> </div>

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Original writeup (https://github.com/MjSandberg/CTF-writeups/tree/solved/2019/ALLESCTF/Babyquantum).

babyquantum

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