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Merge branch 'master' of git.juju.re:juju/juju.re

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Julien CLEMENT 2023-05-03 01:49:50 +02:00
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25
jujure/content/writeups/fcsc_2023/brachiosaure.md
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@ -10,7 +10,7 @@ toc: true
Brachiosaure is a math/puzzle challenge from `\J` for the 2023 edition of the
FCSC. It's difficulty is not in the reversing process, which is fairly trivial
here, but in solving of underlying problem.
here, but in solving the underlying problem.
{{< image src="/brachiosaure/meme.jpg" style="border-radius: 8px;" >}}
@ -170,9 +170,9 @@ Cutting drama right now, it is simply a matrix dot product:
Alright so to recap what actually happens:
- In check serial, we perform the dot product of the user digest, interpreted a
linearized 8 * 8 matrix, with itself, effectively squaring it, which gives us
our serial (also in a linearized 8 * 8 matrix).
- In check serial, we perform the dot product of the user digest, interpreted
as a linearized 8 * 8 matrix, with itself, effectively squaring it, which
gives us our serial (also in a linearized 8 * 8 matrix).
- In main, we perform the dot product of the user and serial IMAGES, and we can
see from the code that the return value indicates wether or not the resulting
@ -242,11 +242,11 @@ over this bigger matrix, infinetely recursing.
OK, so after this misadventure, the next step is to understand that a single
element of coordinates (i, j) from the dot product is impacted by all elements
of the ith line of the first matrix and all elements of the jth line. (You
actually already needed to understand this to implement my dumb idea but now we
will make it interesting).
of the ith line of the first matrix and all elements of the jth column of the
second. (You actually already needed to understand this to implement my dumb
idea but now we will make it interesting).
Let's say that I take my first QR code and I double it's size and width like
Let's say that I take my first QR code and I double it's height and width like
this where the purple ones are all 0 matrices and the green one is the identity:
{{< image src="/brachiosaure/resizing.png" style="border-radius: 8px;" >}}
@ -301,9 +301,10 @@ And there is a really interesting property indeed:
{{< image src="/brachiosaure/invertible.png" style="border-radius: 8px;" >}}
By adding empty matrices and an identity matrix in the bottom right corner, the
resulting matrix is always invertible, and the inverse can be trivially computed
since it is simply moving matrices arround and negating the original image modulo 256 `notice the "-(QRuser)" in the inverted matrix`.
By adding identity matrices and an empty matrix in the bottom right corner, the
resulting matrix is always invertible, and the inverse can be trivially
computed since it is simply moving matrices arround and negating the original
image modulo 256 `notice the "-(QRuser)" in the inverted matrix`.
## Putting everything together
@ -332,7 +333,7 @@ from the remote service and the upload of the images to recover the flag.
But before leaving this writeup there is still something I want to show you at the end.
{{< code file="/static/brachiosaure/solve_writeup.py" language="c" >}}
{{< code file="/static/brachiosaure/solve_writeup.py" language="python" >}}
```console

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jujure/static/brachiosaure/solve_writeup.py
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@ -88,7 +88,7 @@ matrix_img_serial = img_to_matrix(img_serial)
def invert(usr, serial):
# Add empty and identity matrices to maka it invetible
# Add empty and identity matrices to make it invetible
usr = make_invertible(usr)
serial = make_invertible(serial)