FUNction Plotter

Misc, 50 points


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 13005 Author: yakuhito


Let's connect to the server and see what's going on.
╭─[email protected] /den/ctf/xmas
╰─$ nc 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
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{[email protected]'s_4_w31rD_fUnCt10n!!!_8082838205}.


import socket, itertools
def display(S):
for j in range(31):
print(''.join(str(u) if u >= 0 else ' ' for u in S[j]))
s = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
s.connect(('', 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(', '))
d = s.recv(4096)
square[y][x] = 1 if b'wrong' in d else 0
from PIL import Image
BLOCK = 10
img ='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)'out.png')