FUNction Plotter

Misc, 50 points

Description

One of Santa's elves found this weird service on the internet. He doesn't like maths, so he asked you to check if there's anything hidden behind it.

Remote Server: nc challs.xmas.htsp.ro 13005 Author: yakuhito

Solution

Let's connect to the server and see what's going on.

╭─face0xff@aniesu-chan /den/ctf/xmas  
╰─$ nc challs.xmas.htsp.ro 13005
Welcome to my guessing service!
Can you guess all 961 values?


f(27, 5)=0
Pretty close, but wrong!

f(26, 6)=1
Pretty close, but wrong!

f(4, 20)=0
Good!

f(17, 13)=1
Pretty close, but wrong!

After enough retries, we can infer several important points:

• The server asks us for a value of f(x, y), with x and y in {0, ... 30}

• The only answers that can (sometimes) give "Good!" answers are "0" and "1"

• Our goal is certainly to determine f over [[0, 31]]^2.

At this point I was thinking about what we would get once we fully recovered f. It could not be a binary text because of the length, so I thought of a QR Code because of the square shape.

It happened I had the correct intuition; here's an animation of the script recovering the square:

Retrieving the QR code

What was only left to do was to make an image out of it:

The actual QR code

which decodes as the flag : X-MAS{Th@t's_4_w31rD_fUnCt10n!!!_8082838205}.

Enjoy!

Script

import socket, itertools

def display(S):
    for j in range(31):
        print(''.join(str(u) if u >= 0 else ' ' for u in S[j]))
    print('\n')

s = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
s.connect(('challs.xmas.htsp.ro', 13005))

square = [[-1] * 31 for i in range(31)]

d = s.recv(4096)

while -1 in list(itertools.chain(*square)):
    coords = d.split(b'\n')[-1].replace(b'f(', b'').replace(b')=', b'')
    x, y = map(int, coords.decode('utf-8').split(', '))
    s.send(b'0\n')
    d = s.recv(4096)
    square[y][x] = 1 if b'wrong' in d else 0
    display(square)

s.close()

from PIL import Image

BLOCK = 10
img = Image.new('RGB', (31 * BLOCK, 31 * BLOCK))

for y in range(31):
    for x in range(31):
        color = (0,) * 3 if square[y][x] else (255,) * 3
        for i in range(BLOCK):
            for j in range(BLOCK):
                img.putpixel((x * BLOCK + i, y * BLOCK + j), color)

img.save('out.png')