# 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.
╭─[email protected] /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{[email protected]'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')