Julien CLEMENT 5358dc632f fixing typos

Signed-off-by: Julien CLEMENT <julien.clement@epita.fr>

2022-09-04 21:40:59 +02:00

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Intro

Diplodocus is I think by far my favorite challenge of the 2022 edition of the FCSC. First it is a reverse challenge, my reference category, then it does not feature weird unknown CPU architecture, just plain x64 with the only layer of obfuscation being the heavy optimization of the compiler. Finally it is an algorithmic problem, and I love algorithms.

The complexity of this challenge relies on the underlying problem it implements. Diplodocus is the successor of Triceratops, a similar challenge from the 2021 edition of the FCSC where you were also asked to solve an NP-complete puzzle to get the flag.

The twist here is that a conceptual flaw of the program allows us to recover the flag without actually solving the intended puzzle, but more on that later.

{{< image src="/diplodocus/yee-dinosaur.gif" style="border-radius: 8px;" >}}

Challenge description

reverse | 477 pts 10 solves :star::star::star:

Trouvez une entrée qui valide, et soumettez-la au service en ligne pour obtenir
le flag.

`nc challenges.france-cybersecurity-challenge.fr 2201`

SHA256(`diplodocus`) =
`9af3062da630d2b94ad3bfa0b5fd67328d2c6c7bbb79607d7d2fa28a67c7ff9c`.

Author: \J

Given files

diplodocus

Writeup

Overview

As stated the program is simply an x64 stripped ELF.

$ file diplodocus
diplodocus: ELF 64-bit LSB shared object, x86-64, version 1 (SYSV),
dynamically linked, interpreter /lib64/ld-linux-x86-64.so.2,
BuildID[sha1]=c489721789271e74d301cda200feb877bd22d80a, for GNU/Linux 3.2.0,
stripped

If we try to execute the program, it reads a line from standard input and exits with status code 1.

$ ./diplodocus
input
$ echo $status
1

stracing and ltracing doesn't apport much more information, the program indeed only calls read(2).

Main

It's now time to open our favorite decompiler and investigate the main function.

After cleaning up the decompiler output and renaming the variables we get the following code:

The code is really simple here, it reads the standard input and pass the input to a function that seems to perform a check.

If the check is sucessful, the program prints the flag, otherwise it exits with 1.

Check

The Check function starts by setting up some local variables like a pointer to the start and to the end of the input and what seems to be a struct that I called context that may contain informations relevant to the ongoing puzzle. Most of this struct is set to 0:

Instruction fetching and dispatch

My first observation of this main function made me think it was a really small virtual machine. We can see it goes through every character in the input and matches it against opcodes between 0 and 4 included. Every other values seems to end the main loop with a return value of 1, indicating an error.

Since I see that the return value is set by oring a field of the context (which I assumed at that time was a processor structure) I assume that this field holds some sort of error flags that will invalidate our puzzle.

We then have the main dispatcher, processing the correct instruction. One thing that can be noted is the two break statement in case 0, this is obviously my decompiler trolling me but what he is trying to say is that this case will end the main loop as well. It thus probably is the only way to end the function with a return value of 0. It must then be the instruction performing the final check after executing all our instructions. We will take a look at it last since other instructions will give us a better idea of the internal structure of the context and are easier to reverse.

Case 1

This instruction is really simple, it makes one field of the context cycle between 0 and 3 included. Let's simply remember the offset of this field (0xa0) for now to see where it is used.

Case 2

Well we did not need to wait a long time to see where the field from case 1 is used. Right at the beginning of case 2, the program matches the value of the variable against all its possible values, it then creates a copy of two other variable of the context and update them depending on our matching.

The 2 variables are then bound checked against 0xb and used to index what seems to be an array of int32_t. We can therefore understand that the two variables are indexes of this array and that the variable from case 1 is an enum describing possible movements in this array. I therefore name them move, i and j.

Next we notice that we check that the jth bit of the ith row of the array, if is not set, it sets the said bit and update the coordinates in the context. If however it is already set, the program sets the error flag that we already identified earlier.

Clearly this is some sort of 12 * 12 bitboard implementation, the first thing that came to my mind is chess since I'm familiar with bitboard based chess engines programming so it was at this exact moment that I understood this problem was probably a puzzle or some sort of board game.

So to rephrase all this information, this instruction changes our coordinates on a 12 * 12 board based on a preselected move from case 1, it places a marker at our new coordinates and errors if we already visited this tile.

I now know one rule of the game: I cannot step twice on the same tile. By lack of inspiration, I name this bitboard visited since it keeps track of all my visited tiles.

Bellow is the cleaned up pseudo-C code from the decompiler with all variables renamed accordingly.

And here is the moves enum to understand better how case 1 manipulates our moves.

Case 3

Case 3 uses a variable from the context that we previously saw initialized to 0xffffff at the very start of the check function without understanding it.

We can now see that it is in fact a queue of 24 bits that is popped in case 3 to place the said bit on a different bitboard than case 2 but with the same coordinates. If the bit queue is empty then we output an error.

So I understand here that we must place 24 bits on another board while simultaneously moving on the first one that tracks the tiles we already visited.

Seems easy enough, however, the instruction does not end here, it calls a function passing the row of the bitboard as parameter, if the return value of this function is more than 2 we output an error.

{{< code file="/static/diplodocus/case3_stripped.c" language="c" >}}

Pop count

Here is the said function, so it seems to perform magic bitwise operation. Could be anything really, my intuition tells me it count the number of bits set on the line but it may as well be some weird bitboard magic, I mean you never know the stuff I found on chess programming while working on chess engines really blows my mind.

By googling the first constant 0x5555555555555555 I confirm really fast my intuition. It is indeed a population count function, the fifth result of the search being, guess what? Chess programming wiki on population count. I now really start thinking that this is actually a chess problem.

With this information we can now rename the variables and symbols from case 3 and we now understand that we place a bit from the bit queue on the board, we cannot allign more than 2 bits on the same line.

Case 4

Do not be misled, this instruction seems simple enough but is by far the hardest one of the challenge.

So first this instruction fetch 2 operand, these operands are later used to access a third bitboard, so I name them accordingly i and j.

Then we check if our bit queue is empty, if it is not then we output an error. This mean that we can call this instruction only when we placed all the 24 points at our disposition.

Now comes the fun part, we call a function passing the coordinates and the whole context as parameter, this function will output a bit that will be placed on a third bitboard at the coordinates indexed by the operands.

So my decompiler really despise this function, I told you it took the whole context as parameters but its not exactly true as it actually packs the whole context in 10 int128_t arguments using SIMD instructions. I cleaned up the function call for your eyes so you do not have de keep track of the 12 parameters of the function.

{{< code file="/static/diplodocus/case4_stripped.c" language="c" >}}

\J dabbing on me

You can see below a decompilation of the function, looks fun right? And this is actually cleaned up so you don't see the SIMD registers and weird struct packing. Now I really recommend you to not actually read this code but to get the main idea from the comments and my explanations. A much more readable python reimplementation is available right after for your sanity.

Most variables are not renamed correctly because I did not actually reverse and understood all this function. This is simply what it looked like in my decompiler at the moment I undestood enough to throw it by the window, modulo of course SIMD and stack fengshui 👀.

Let's not care too much about weird constants and implementation details for now as I did not understood them at the time either.

The main idea of this is code is that it will run through all possible increments combinations that will iterate on the second board (the one from case 3, where we manually place our bits from the bit queue).

Basically, we check every possible way we can run through the board.

For each of these increment combination we see a weird loop performing modulos of the increments. This is actually the euclidean algorithm that computes the GCD of 2 numbers. This GCD is compared to 1. If it is not one then we skip this increments combination and go to the next loop iteration. We are therefore only concerned about running through the board using coprime increments, confusing I know.

We then iterate on the board using these increments and count the number of bits set while doing so. If at any point we encounter more than 2 points during the same passing of the board we set a result flag. The function will output 1 if and only if no result flag was set for any iteration. Meaning for any traversal of the board, we did not encounter more than 2 bits.

Here I was really scared because I started to think that this was maybe \J trolling me with again a cryptography problem modelised using bitboards are something. And everyone who checks my results of the FCSC know how bad I am at cryptography.

{{< code file="/static/diplodocus/check_align.c" language="c" >}}

Alignement count

So now I am really unhappy, I was having fun finding out puzzle and placing bits on boards but now \J is throwing modular arithmetic at me.

I take a break crying in my bed after these findings before actually thinking.

Running through the array using coprime increments probably has a really interesting property that may be plotted visually.

So I reimplemented this function in python but instead of summing the bits I encountered, I mark the bits I would have summed to see the path that I take in the array.

Which gives us this much more readable code:

With this output (only a sample):

It is now obvious what this function is doing, it draws every straight line passing through the point given as parameter and checks if more than 2 points of the board are alligned.

If we remember the context were this function is used, it means that we will set a bit in the third bitboard if and only if no line passing through this point intersects more than 2 points.

Case 0 (Final check)

So case 0 is the instruction that performs the final check to see if our board match the desired state. Again there is a lot of SIMD magic going on so I tried to clean it a little bit, you lose the actual result of the decompilation but the code is semantically equivalent.

First we perform a pop count on all lines of the visited bitboard, comparing the total sum to 0x90 which is 12 * 12, the total number of tiles. We must therefore go through every single tile of the board exactly once.

Then, we pack the third bitboard (the one that stores if 3 points are alligned) into the zmm0 128 bit register because why not? And basically shifting and bitwise anding it to check that every bit of the board are set. So its basically the same check than before but for the third bitboard, meaning that no line drawn from any point on the board must intersect with more than 2 points.

The last check simply performs a xor on every line of the board and outputs an error if it is different from 0. This means that every column of the board must contain an even number of points.

Great we have everything ready to go! We simply need to go trough the board and place 24 points on it and make sure there are never 3 points alligned.

So it turns out this problem is NP-complete (I learned after solving the challenge that is called the Not-three-in-line problem), I might have a hard time solving it manually. I might start to implement a SAT solver or som...

But wait, did you spot something sus with this implementation ?

{{< image src="/diplodocus/the_rock.gif" style="border-radius: 8px;" >}}

Bypassing the puzzle

There are actually two distinct bugs in this implementation of the puzzle.

First, the program does not check that you place a point when there is already one. It does check that you do not go twice on the same tile but you can still place multiple points without moving.

The second, the one I exploited here, is that the weird function we reimplemented actually only count alligned points on all straight lines except for lines and columns.

The special case of the line is checked independently in case 3 when inserting the point if you remember well.

However the only columns check is in case 0 where it simply checks that there is an even number of point per column.

Nothing forbids us to put 12 points on the first and last column, which validates all our constraints.

|X| | | | | | | | | | |X|
|X| | | | | | | | | | |X|
|X| | | | | | | | | | |X|
|X| | | | | | | | | | |X|
|X| | | | | | | | | | |X|
|X| | | | | | | | | | |X|
|X| | | | | | | | | | |X|
|X| | | | | | | | | | |X|
|X| | | | | | | | | | |X|
|X| | | | | | | | | | |X|
|X| | | | | | | | | | |X|
|X| | | | | | | | | | |X|

{{< image src="/diplodocus/stop_the_count.png" style="border-radius: 8px;" >}}

Solve

We now simply need to write the input that will give instructions to the program to write this bugged board.

We first fill the first column, by going downward.

Then we go through the 10 next columns without placing any bit and we fill the last one.

Finally we need to fill the third bitboard by manually performing the alignment check for every point in the bitboard so we call case 4 for every coordinates.

We do not forget to put case 0 at the end to validate everything went fine.

$ ./solve.py | ./diplodocus
Well done! You can submit your input to the remote service to grab the flag!

$ ./solve.py | nc challenges.france-cybersecurity-challenge.fr 2201
Well done, the flag is FCSC{bf809d2614501166a890740116103410a69ede950b57a9186bf49eb734eaa1a1}

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